Autoencoders and latent space fragmentation – I – Encoder, Decoder, latent space

Posted on 20. March 2023 by eremo

This series of posts is about a special kind of Artificial Neural Networks [ANNs] – namely so called Autoencoders [AEs] and their questionable creative abilities.

The series replaces two previous posts in this blog on a similar topic. My earlier posts were not wrong regarding the results of calculations presented there, but they contained premature conclusions. In this series I hope to perform a somewhat better analysis.

Abilities of Autoencoders and the question of a creative application of AEs

On the one hand side AEs can be trained to encode and compress object information. On the other hand side AEs can decode previously encoded information and reconstruct related original objects from the retrieved information.

A simple application of an AE, therefore, is the compression of image data and the reconstruction of images from compressed data. But, after a suitable adaption of the training process and its input data, we can also use AEs for other purposes. Examples are the denoising of disturbed images or the recoloring of grey images. In the latter cases the reconstructive properties of AEs play an important role.

An interesting question is: Can one utilize the reconstructive abilities of an AE for generative or creative purposes?

This post series will give an answer for the special case of images showing human faces. To say it clearly: I am talking about conventional AEs, not about Variational Autoencoders and neither about state of the art AEs based on transformer technology.

Most text books on Machine Learning [ML] would claim that at least Variational Autoencoders (instead of AEs) are required to create reasonable images of human faces … Well, to trigger a bit of your attention: Below you find some images of human faces created by standard Autoencoder – and NOT by a Variational Autoencoder.

I admit: These pictures are far from perfect, but at least they show clear features of human faces. Not exactly what we expect of a pure conventional Autoencoder fed with statistical input. I apologize for the bias towards female faces, but that is a “prejudice” of the AE caused by my chosen set of training data. And the lack of hairdo-details will later be commented on.

I promise: Analyzing the behavior of conventional AEs is still an interesting topic. Despite many and sophisticated modern alternatives for creative purposes. The reason is that we learn something about the way how an AE organizes the information which it gains during training.

Continue reading →

Variational Autoencoder with Tensorflow – XI – image creation by a VAE trained on CelebA

Posted on 22. October 2022 by eremo

I continue with my series on Variational Autoencoders [VAEs] and related methods to control the KL-loss.

VAEs fall into a section of ML which is called “Generative Deep Learning“. The reason is that we can VAEs to create images with contain objects with features of objects learned from training images. One interesting category of such objects are human faces – of different color, with individual expressions and features and hairstyles, seen from different perspectives. One dataset which contains such images is the CelebA dataset.

During the last posts we came so far that we could train a CNN-based Variational Autoencoder [VAE] with images of the CelebA dataset. Even on graphics cards with low VRAM. Our VAE was equipped with a GradientTape()-based method for KL-loss control. We still have to prove that this method works in the expected way:

The distribution of data points (z-points) created by the VAE’s Encoder for training input should be confined to a region around the origin in the latent space (z-space). And neighboring z-points up to a limited distance should result in similar output of the Decoder.

Therefore, we have to look a bit deeper into the results of some VAE-experiments with the CelebA dataset. I have already pointed out why creating rather complex images from arbitrarily chosen points in the latent space is a suitable and good test for a VAE. Please remember that our efforts regarding the KL-loss have to do with the following fact:

not create reasonable images/objects from arbitrarily chosen z-points in the latent space.

This eliminates the use of an AE for creative purposes. A VAE, however, should be able to solve this type of task – at least for z-points in a limited surroundings of the latent space’s origin. Thus, by creating images from randomly selected z-points with the Decoder of a VAE, which has been trained on the CelebA data set, we cover two points:

Test 1: We test the functionality of the VAE-class, which we have developed and which includes the code for KL-loss handling via TF2’s GradientTape() and Keras’ train_step().
Test 2: We test the ability of the VAE’s Decoder to create images with convincing human-like face and hairstyle features from random z-points within an area close to the origin of the latent space.

Most of the experiments discussed below follow the same prescription: We take our trained VAE, select some random points in the latent space, feed the z-point-data into the VAE’s Decoder for a prediction and plot the images created on the Decoder’s output side. The Encoder only plays a role when we want to test reconstruction abilities.

For a low dimension z_dim=256 of the latent space we will find that the generated images display human faces reasonably well. But the images appear a bit blurry or unsharp – as if not fully focused. So, we need to discuss what we can do about this point. I will also name some plausible causes for the loss of accuracy in the representation of details.

Afterwards I want to show you that a VAE Decoder reconstructs original images relatively badly from the z-points calculated by the Encoder. At least when one looks at details. A simple AE with a sufficiently high dimension of the latent space performs much better. One may feel disappointed about the reconstruction ability of a VAE. But actually it is the ability of a VAE to forget about details and instead to focus on general features which enables it (the VAE) to create something meaningful from randomly chosen z-points in the latent space.

In a last step in this post we are going to look at images created from z-points with a growing distance from the origin of the multidimensional latent space [z-space]. (Distance can be defined by a L2-Euclidean norm). We will see that most z-points which have some z-coordinates above a value of 3 produce fancy images where the face structures get dominated or distorted by background structures learned from CelebA images. This effect was to be expected as the KL-loss enforced a distribution of the z-points which is confined to a region relatively close to the origin. Ideally, this distribution would be characterized by a normal distribution in all coordinates with a sigma of only 1. So, the fact that z-points in the vicinity of the origin of the latent space lead to a construction of images which show recognizable human faces is an indirect proof of the confining impact of the KL-loss on the z-point distribution. In another post I shall deliver data which prove this more directly.

Below I will call the latent space of a (V)AE also z-space.

Characteristics of the VAE tested

Our trained VAE with four Conv2D-layers in the Encoder and 4 corresponding Conv2DTranspose-Layers in the Decoder has the following basic characteristics:

(Encoder-CNN-) filters=(32,64,128,256), kernels=(3,3), stride=2,
reconstruction loss = BCE (binary crossentropy), fact=5.0, z_dim=256

The order of the filter- (= map-) numbers is, of course reversed for the Decoder. The factor fact to scale the KL-loss in comparison to the reconstruction loss was chosen to be fact=5, which led to a 3% contribution of the KL-loss to the total loss during training. The VAE was trained on 170,000 CelebA images with 24 epochs and a small epsilon=0.0005 plus Adam optimizer.

When you perform similar experiments on your own you may notice that the total loss values after around 24 epochs ( > 5015) are significantly higher than those of comparable experiments with a standard AE (4850). This already is an indication that our VAE will not reproduce a similar good match between an image reconstructed by the Decoder in comparison to the original input image fed into the Encoder.

Results for z-points with coordinates taken from a normal distribution around the origin of the latent space

The picture below shows some examples of generated face-images coming from randomly chosen z-points in the vicinity of the z-space’s origin. To calculate the coordinates of such z-points I applied a normal distribution:

z_points = np.random.normal(size = (n_to_show, z_dim)) # n_to_show = 28

So, what do the results for z_dim=256 look like?

Ok, we get reasonable images of human-like faces. The variations in perspective, face forms and hairstyles are also clearly visible and reflect part of the related variety in the training set. You will find more variations in more images below. So, we take this result as a success! In contrast to a pure AE we DO get something from random z-points which we clearly can interpret as human faces. The whole effort of confining z-points around the origin and at the same time of smearing out z-points with similar content over a region instead of a fixed point-mapping (as in an AE) has paid off. See for comparison:
Autoencoders, latent space and the curse of high dimensionality – I

Unfortunately, the images and their details details appear a bit blurry and not very sharp. Personally, this reminded me of the times when the first CCD-chips with relative low resolution were introduced in cameras and the raw image data looked disappointing as long as we did not apply some sharpening filters. The basic information to enhance details were there, but they had to be used explicitly to improve the plain raw data of the CCD.

The quality in details is about the same as what we see in example images in the book of D.Foster on “Generative Deep Learning”, 2019, O’Reilly. Despite the fact that Foster used a slightly higher resolution of the input images (128x128x3 pixels). The higher input resolution there also led to a higher resolution of the maps of the innermost convolutional layer. Regarding quality see also the images presented in:
https://datagen.tech/guides/image-datasets/celeba/

Enhancement processing of the images ?

Just for fun, I took a screenshot of my result, saved it and applied two different sharpening filters from the ShowFoto program:

Much better! And we do not have the impression that we added some fake information to the images by our post-processing ….

Now I hear already argument saying that such an enhancement should not be done. Frankly, I do not see any reason against post-processing of images created by a VAE-algorithm.

Remember: This is NOT about reproduction quality with respect to originals or a close-to-reality show. This is about generating new mages of human-like faces based on basic features which a VAE-algorithm hopefully has learned from training images. All of what we do with a VAE is creative. And it also comes close to a proof that ML-algorithms based on convolutional layers really can “learn” something about the basic features of objects presented to them. (The learned features are e.g. in the Encoder’s case saved in the sensitivity of the convolutional maps to typical patterns in the input images.)

And as in the case of raw-images of CCD or CMOS camera chips: Sometimes some post-processing is required to utilize the information optimally for sharpness.

Sharpening by PIL’s enhancement functionality

Of course we do not want to produce images in a ML run, take screenshots and sharpen each image individually. We need some tool that fits into the ML process pipeline. The good old PIL library for Python offers sharpening as one of multiple enhancement options for images. The next examples are results from the application of a PIL enhancement procedure:

These images look quite OK, too. The basic code fragment I used for each individual image in the above grid:

    # reconst_new is the output from my VAE's Decoder 
    ay_img      = reconst_new[i, :,:,:] * 255
    ay_img      = np.asarray(ay_img, dtype="uint8" )
    img_orig    = Image.fromarray(ay_img)
    img_shr_obj = ImageEnhance.Sharpness(img)
    sh_factor   = 7   # Specified Factor for Enhancing Sharpness
    img_sh      = img_shr_obj.enhance(sh_factor)

The sharpening factor I chose was quite high, namely sh_factor = 7.

The effect of PIL’s sharpening factor

Just to further demonstrate the effect of different factors for sharpening by PIL you find some examples below for sh_factor = 0, 3, 6.

sh_factor = 0

sh_factor = 3

sh_factor = 6

Obviously, the enhancement is important to get clearer and sharper images.
However, when you enlarge the images sufficiently enough you see some artifacts in the form of crossing lines. These artifacts are partially already existing in the Decoder’s output, but they are enhanced by the Sharpening mechanism used by PIL (unsharp masking). The artifacts become more pronounced with a growing sh_factor.
Hint: According to ML-literature the use of Upsampling layers instead of Conv2DTranspose layers in the Decoder may reduce such artefacts a bit. I have not yet tried it myself.

Assessment

How do we assess the point of relatively unclear, unsharp images produced by our VAE? What are plausible reasons for the loss of details?

Firstly, already AEs with a latent space dimension z_dim=256 in general do not reconstruct brilliant images from z-points in the latent space. To get a good reconstruction quality even from an AE which does nothing else than to compress and reconstruct images of a size (96x96x3) z_dim-values > 1000 are required in my experience. More about this in another post in the future.
A second important aspect is the following: Enforcing a compact distribution of similar images in the latent space via the KL-loss automatically introduces a loss of detail information. The KL-loss is designed to lead to a smear-out effect in z-space. Only basic concepts and features will be kept by the VAE to ensure a similarity of neighboring images. Details will be omitted and “smoothed” out. This has consequences also with respect to sharpness of detail structures. A detail as an eyebrow in a face is to be considered as an average of similar details found for images in the same region of the z-space. This alone brings some loss of clarity with it.
Thirdly, a simple (V)AE based on some directly connected Conv2D-layers has limited capabilities in general. The reason is that we systematically reduce resolution whilst information is propagated from one Conv2D layer to the next neighboring one. Remember that we use a stride > 2 or pooling layers to cover filters on larger image scales. Due to this information processing a convolutional network automatically suppresses details in its inner layers – their resolution shrinks with growing distance from the input layer. In later posts of this blog we shall see that using ResNets instead of CNNs in the Encoder and Decoder already helps a bit regarding the reconstruction of clearer images. The correlation between details and large scale information is better kept up there than in CNNs.

Regarding the first point one may think of increasing z_dim. This may not be the best idea. It contradicts the whole idea of a VAE which at its core is a reduction of the degrees of freedom for z-points. For a higher dimensional space we may have to raise the ratio of KL-loss to reconstruction loss even further.

Regarding the third point: Of course it would also help to increase kernel sizes for the first two Conv2D layers and the number of maps there. A higher resolution of the input images would also be of advantage. Both methods may, however, conflict with your VRAM or GPU time limits.

If the second point were true then reduction of fact in our models, which controls the ration of KL-loss to reconstruction loss, would lead to a better image quality. In this case we are doomed to find an optimal value for fact – satisfying both the need for generalization and clarity of details in our images. You cannot have both … here we see a basic problem related to VAEs and the creation of realistic images. Actually, I tried this out – the effect is there, but the gain actually is not worth the effort. And for too small values of fact we eventually loose the ability to create reasonable images from arbitrary z-points at all.

All in all post-processing appears to be a simple and effective method to get images with somewhat sharper details.
Hint: If you want to create images of artificially generated faces with a really high quality, you have to turn to GANs.

Further examples – with PIL sharpening

In this example you see that not all points give you good images of faces. The z-point of the middle image in the second to last of the first illustration below has a relatively high distance from the origin. The higher the distance from the origin in z-space the weirder the images get. We shall see this below in a more systematic way.

Reconstruction quality of a VAE vs. an AE – or the “female” side of myself

If I were not afraid of copy and personal rights aspects of using CelebA images directly I could show you now a comparison of the the reconstruction ability of an AE in comparison to a VAE. You find such a comparison, though a limited one, by looking at some images in the book of D. Foster.

To avoid any problems I just tried to work with an image of myself. Which really gave me a funny result.

A plain Autoencoder with

an extended latent space dimension of z_dim = 1600,
a reasonable convolutional filter sequence of (64, 64, 128, 128)
a stride value of stride=2
and kernels ((5,5),(5,5),(3,3),(3,3))

is well able to reproduce many detailed features one’s face after a training on 80,000 CelebA images. Below see the result for an image of myself after 24 training epochs of such an AE:

The left image is the original, the right one the reconstruction. The latter is not perfect, but many details have been reproduced. Please note that the trained AE never had seen an image of myself before. For biometric analysis the reproduction would probably be sufficient.

Ok, so much about an AE and a latent space with a relatively high dimension. But what does a VAE think of me?
With fact = 5.0, filters like (32,64,128,256), (3,3)-kernels, z_dim=256 and after 18 epochs with 170,000 training images of CelebA my image really got a good cure:

My wife just laughed and said: Well, now in the age of 64 at least an AI has found something soft and female in you … Well, had the CelebA included many faces of heavy metal figures the results would have looked differently. I bet …

So with generative VAEs we obviously pay a price: Details are neglected in favor of very general face features and hairstyle aspects. And we loose sharpness. Which is good if you have wrinkles. Good for me and the celebrities, too. 🙂

However, I recommend anybody who wants to study VAEs to check the reproduction quality for CelebA test images (not from the training set). You will see the generalization effect for a broader range of images. And, of course, a better reproduction with smaller values for the ratio of the KL-loss to the reconstruction loss. However, for too small values of fact you will not be able to create realistic face images at all from arbitrary z-points – even if you choose them to be relatively close to the origin of the latent space.

Dependency of the creation of reasonable images on the distance from the origin

In another post in this blog I have discussed why we need VAEs at all if we want to reconstruct reasonable face images from randomly picked points in the latent space. See:
Autoencoders, latent space and the curse of high dimensionality – I

I think the reader is meanwhile convinced that VAEs do a reasonably good job to create images from randomly chosen z-points. But all of the above images were taken from z-points calculated with the help of a function assuming a normal distribution in the z-space coordinates. The width of the resulting distribution around the origin is of course rather limited. Most points lie within a 3 sigma distance around the origin. This is OK as we have put a lot of effort into the KL-loss to force the z-points to approach such a normal distribution around the origin of the latent space.

But what happens if and when we increase the distance of our random z-points from the origin? An easy way to investigate this is to create the z-points with a function that creates the coordinates randomly, but equally distributed in an interval ]0,limit]. The chance that at least one of the coordinates gets a high value is rather big then. This in turn ensures relatively high radius values (in terms of an L2-distance norm).

Below you find the results for z-points created by the function random.uniform:

r_limit = 1.5
l_limit = -r_limit
znew = np.random.uniform(l_limit, r_limit, size = (n_to_show, z_dim))

r_limit is varied as indicated:

r_limit = 0.5

r_limit = 1.0

r_limit = 1.5

r_limit = 2.0

r_limit = 2.5

r_limit = 3.0

r_limit = 3.5

r_limit = 5.0

r_limit = 8.0

Well, this proves that we get reasonable images only up to a certain distance from the origin – and only in certain areas or pockets of the z-space at higher radii.

Another notable aspect is the fact that the background variations are completely smoothed out a low distances from the origin. But they get dominant in the outer regions of the z-space. This is consistent with the fact that we need more information to distinguish various background shapes, forms and colors than basic face patterns. Note also that the faces appear relatively homogeneous for r_limit = 0.5. The farther we are away from the origin the larger the volumes to cover and distinguish certain features of the training images become.

Conclusion

Our VAE with the GradientTape()-mechanism for the control of the KL-loss seems to do its job. In contrast to a pure AE the smear-out effect of the KL-loss allows now for the creation of images with interpretable contents from arbitrary z-points via the VAE’s Decoder – as long as the selected z-points are not too far away from the z-space’s origin. Thus, by indirect evidence we can conclude that the z-points for training images of the CelebA dataset were distributed and at the same time confined around the origin. The strongest indication came from the last series of images. But we pay a price: The reconstruction abilities of a VAE are far below those of AEs. A relatively low number of dimensions of the latent space helps with an effective confinement of the z-points. But it leads to a significant loss in detail sharpness of the generated images, too. However, part of this effect can be compensated by the application of standard procedures for image enhancemnet.

In the next post
Variational Autoencoder with Tensorflow – XII – save some VRAM by an extra Dense layer in the Encoder
I will discuss a simple trick to reduce the VRAM consumption of the Encoder. In a further post we shall then analyze the confinement of the z-point distribution with the help of more explicit data.

And let us all who praise freedom not forget:
The worst fascist, war criminal and killer living today is the Putler. He must be isolated at all levels, be denazified and sooner than later be imprisoned. An aggressor who orders the bombardment of civilian infrastructure, civilian buildings, schools and hospitals with drones bought from other anti-democrats and women oppressors puts himself in the darkest and most rotten corner of human history.

Deep Dreams of a CNN trained on MNIST data – II – some code for pattern carving

Posted on 21. December 2020 by eremo

In the last article of this series

Deep Dreams of a CNN trained on MNIST data – I – a first approach based on one selected map of a convolutional layer

I presented some “Deep Dream” images of a CNN trained on MNIST data. Although one cannot produce spectacular images with a simple CNN based on gray scale, low resolution image data, we still got a glimpse of what the big guys do with more advanced CNNs and image data. But we have only started, yet ….

In the forthcoming articles we shall extend our abilities step by step beyond the present level. Our next goal is to work on different length scales within the image, i.e. we go down into sub-tiles of the original image, analyze the sub-structures there and include the results in the CNN’s dreams. But first we need to understand more precisely how we apply the image manipulation techniques that “carve” some additional dream-like optical elements, which correspond to map triggering features, into an arbitrary input image presented to the CNN.

Carving: A combination of low-resolution OIP-pattern creation and a reproduction of high-resolution details

I used the term “carved” intentionally. Artists or craftsmen who create little figures or faces out of wooden blocks by a steady process of carving often say that they only bring to the surface what already was there – namely in the basic fiber structures of the wood. Well, the original algorithm for the creation of pure OIP- or feature patterns systematically amplifies some minimal correlated pixel “structures” detected in an input image with random pixel values. The values of all other pixels outside the OIP pattern are reduced; sooner or later they form a darker and rather homogeneous background. The “detection” is based on (trained) filters which react to certain pixel constellations. We already encoded an adaption of a related method for CNN filter visualization, which Francois Chollet discusses in his book on “Deep learning with Python”, into a Python class in another article series of this blog (see the link section at the end of this article).

There is, however, a major difference regarding our present context: During the image manipulations for the visualization of Deep Dreams we do not want to remove all details of the original image presented to the DeepDream algorithm. Instead, we just modify it at places where the CNN detects traces of patterns which trigger a strong response of one or multiple maps of our CNN – and keep detail information alive elsewhere. I.e., we must counterbalance the tendency of our OIP algorithm to level out information outside the OIP structures.

How do we do this, when both our present OIP algorithm and the MNIST-trained CNN are limited to a resolution of (28×28) pixels, only?

Carving – amplification of certain OIP structures and intermittent replenishment of details of the original image

In this article we follow the simple strategy explained in the last article:

Preparation:
- We choose a map.
- We turn the colored original input image (about which the CNN shall dream) into a gray one.
- We downscale the original image to a size of (28×28) by interpolation, upscale the result again by interpolating again (with loss) and calculate the difference to the original full resolution image (all interpolations done in a bicubic way). (The difference contains information on detail structures.)
Loop (4 times or so):
- We apply the OIP-algorithm on the downscaled input image for a fixed amount of epochs with a small epsilon.
  The result is a slight emphasis of
  pixel structures resembling OIP patterns.
- We upscale the result by bicubic interpolation to the original size.
- We re-add the difference to the original image, i.e. we supply details again.
- We downscale the result again.
Eventual image optimization: We apply some contrast treatment to the resulting image, whose pixel value range and distribution has gradually been changed in comparison to the original image.

This corresponds to a careful accentuation of an OIP-pattern detected by a certain map in the given structured pixel data of the input image (on coarse scales) – without loosing all details of the initial image. As said – it resembles a process of carving coarse patterns into the original image ..

Note: The above algorithm works on the whole image – a modified version working on a variety of smaller length scales is discussed in further articles.

What does this strategy look like in Python statements for Jupyter cells?

Start with loading required modules and involving your graphics card

We have to load python modules to support our CNN, the OIP algorithm and some plotting. In a second step we need to invoke the graphics card. This is done in two Jupyter cells (1 and 2). Their content was already described in the article

A simple CNN for the MNIST dataset – XI – Python code for filter visualization and OIP detection

of a parallel series in this blog. These initial steps are followed by an instantiation of a class “My_OIP” containing all required methods. The __init__() function of this class restores a Keras model of our basic CNN from a h5-file:

Jupyter cell 3

%matplotlib inline

# Load the CNN-model 
#  ~~~~~~~~~~~~~~~~~
imp.reload(myOIP)
try:
    with tf.device("/GPU:0"):
        MyOIP = myOIP.My_OIP(cnn_model_file = 'cnn_best.h5', layer_name = 'Conv2D_3')

except SystemExit:
    print("stopped")

Turn the original image into a gray one, downscale it and calculate difference-tensors for coarsely re-enlarged versions

In the next Jupyter cell we deal with the following initial image:

We choose a method (out of 3) to turn it into a gray scaled image. Afterwards we calculate the difference between an image tensor of the original (gray) image and a coarse, but softly rescaled image derived from a (28×28)-pixel version.

Jupyter cell 4

# Down-, gray- and Re-scale images, determine correction differences  
# *******************************************************************
import PIL
from PIL import Image, ImageOps

fig_size = plt.rcParams["figure.figsize"]
fig_size[0] = 15
fig_size[1] = 30
fig_1 = plt.figure(1)
ax1_1 = fig_1.add_subplot(531)
ax1_2 = fig_1.add_subplot(532)
ax1_3 = fig_1.add_subplot(533)
ax2_1 = fig_1.add_subplot(534)
ax2_2 = fig_1.add_subplot(535)
ax2_3 = fig_1.add_subplot(536)
ax3_1 = fig_1.add_subplot(537)
ax3_2 = fig_1.add_subplot(538)
ax3_3 = fig_1.add_subplot(539)
ax4_1 = fig_1.add_subplot(5,3,10)
ax4_2 = fig_1.add_subplot(5,3,11)
ax4_3 = fig_1.add_subplot(5,3,12)

# Parameters 
# ************
# size of the image to work with 
img_wk_size = 560 
# method to turn the original picture into a gray scaled one 
gray_scaling_
method = 2

# bring the orig img down to (560, 560) 
# ***************************************
imgvc    = Image.open("rosen_orig_farbe.jpg")
imgvc_g  = imgvc.convert("L")

# downsize with PIL 
# ******************
imgvc_wk_size    = imgvc.resize((img_wk_size,img_wk_size), resample=PIL.Image.BICUBIC)
imgvc_wk_size_g  = imgvc_wk_size.convert("L")
imgvc_28      = imgvc.resize(  (28,28), resample=PIL.Image.BICUBIC)
imgvc_g_28    = imgvc_g.resize((28,28), resample=PIL.Image.BICUBIC)

# Change to np array
ay_picc = np.array(imgvc_wk_size)

# Display orig and wk_size images  
# *********************************
ax1_1.imshow(imgvc)
ax1_2.imshow(imgvc_wk_size)
ax1_3.imshow(imgvc_g, cmap=plt.cm.gray)

# Apply 3 different methods to turn the image into a gray one 
# **************************************************************
#Red * 0.3 + Green * 0.59 + Blue * 0.11
#Red * 0.2126 + Green * 0.7152 + Blue * 0.0722
#Red * 0.299 + Green * 0.587 + Blue * 0.114

ay_picc_g1 = ( 0.3    * ay_picc[:,:,0] + 0.59   * ay_picc[:,:,1] + 0.11   * ay_picc[:,:,2] )  
ay_picc_g2 = ( 0.299  * ay_picc[:,:,0] + 0.587  * ay_picc[:,:,1] + 0.114  * ay_picc[:,:,2] )  
ay_picc_g3 = ( 0.2126 * ay_picc[:,:,0] + 0.7152 * ay_picc[:,:,1] + 0.0722 * ay_picc[:,:,2] )  

ay_picc_g1 = ay_picc_g1.astype('float32') 
ay_picc_g2 = ay_picc_g2.astype('float32') 
ay_picc_g3 = ay_picc_g3.astype('float32') 

# Prepare tensors
# *****************
t_picc_g1 = ay_picc_g1.reshape((1, img_wk_size, img_wk_size, 1))
t_picc_g2 = ay_picc_g2.reshape((1, img_wk_size, img_wk_size, 1))
t_picc_g3 = ay_picc_g3.reshape((1, img_wk_size, img_wk_size, 1))

t_picc_g1 = tf.image.per_image_standardization(t_picc_g1)
t_picc_g2 = tf.image.per_image_standardization(t_picc_g2)
t_picc_g3 = tf.image.per_image_standardization(t_picc_g3)

# Display gray-tensor variants    
# ****************************
ax2_1.imshow(t_picc_g1[0,:,:,0], cmap=plt.cm.gray)
ax2_2.imshow(t_picc_g2[0,:,:,0], cmap=plt.cm.gray)
ax2_3.imshow(t_picc_g3[0,:,:,0], cmap=plt.cm.gray)

# choose one gray img
# ******************
if   gray_scaling_method == 1:
    t_picc_g = t_picc_g1
elif gray_scaling_method == 2:
    t_picc_g = t_picc_g2
else:
    t_picc_g = t_picc_g3

# downsize to (28,28) and standardize
# *****************************************
t_picc_g_28_scd  = tf.image.resize(t_picc_g, [28,28], method="bicubic", antialias=True)
t_picc_g_28_std  = tf.image.per_image_standardization(t_picc_g_28_scd)
t_picc_g_28      = t_picc_g_28_std

# display 
ax3_1.imshow(imgvc_g_28, cmap=plt.cm.gray)
ax3_2.imshow(t_picc_g_28_scd[0,:,:,0], cmap=plt.cm.gray)
ax3_3.imshow(t_picc_g_28_std[0,:,:,0], cmap=plt.cm.gray)

# Upscale and get correction values  
# **********************************
t_picc_g_wk_size_scd     = tf.image.resize(t_picc_g_28, [img_wk_size,img_wk_size], method="bicubic", antialias=True)
t_picc_g_wk_size_scd_std = tf.image.per_image_standardization(t_picc_g_wk_size_scd)
t_picc_g_wk_size_corr    =  t_picc_g - t_picc_g_wk_size_scd_std   

# Correct and display 
# **********************
t_picc_g_wk_size_re   = t_picc_g_wk_size_scd_std + t_picc_g_wk_size_corr 
# Display
ax4_1.imshow(t_picc_g_wk_size_scd_std[0,:,:,0], cmap=plt.cm.gray)
ax4_2.imshow(t_picc_g[0,:,:,0],                 cmap=plt.cm.gray)
ax4_3.imshow(t_picc_g_wk_size_re[0,:,:,0],      cmap=plt.cm.gray)

The code is straightforward – a lot of visualization steps will later on just show tiny differences. For production you may shorten the code significantly.

In a first step we downscale the image to a work-size of (560×560) px with the help of PIL modules. (Note that 560 can be divided by 2, 4, 8, 16, 28). We then test out three methods to turn the image into a gray one. This step is required, because our MNIST-oriented CNN is trained for gray images, only. We
reshape the image data arrays to prepare for tensor-operations and standardize with the help of Tensorflow – and produce image tensors on the fly. Afterwards, we downscale to a size of (28×28) pixels; this is the size of the MNIST images for which the CNN has been trained. We upscale to the work-size again, compare it to the original detailed image and calculate respective differences of the tensor-components. These differences will later be used to re-add details to our manipulated images.

The following picture displays the resulting output:

Note: The last two images should not show any difference. The middle row and the displays how coarse the (28×28) resolution really is and how much information we have lost after upscaling to (560×560)px.

OIP-Carving and detail replenishment

We now follow the algorithm described above. This leads to a main loop with steps for downscaling, OIP-carving on the (28×28)-scale, upscaling and a supplementation of original details:

Jupyter cell 5

# **************************************************+
# OIP analysis (to be used after the previous cell)
# **************************************************+

# Prepare plotting 
# -------------------
#interactive plotting 
#%matplotlib notebook 
#plt.ion()

fig_size = plt.rcParams["figure.figsize"]
fig_size[0] = 15
fig_size[1] = 25
fig_2 = plt.figure(2)
ax2_1_1 = fig_2.add_subplot(531)
ax2_1_2 = fig_2.add_subplot(532)
ax2_1_3 = fig_2.add_subplot(533)
ax2_2_1 = fig_2.add_subplot(534)
ax2_2_2 = fig_2.add_subplot(535)
ax2_2_3 = fig_2.add_subplot(536)
ax2_3_1 = fig_2.add_subplot(537)
ax2_3_2 = fig_2.add_subplot(538)
ax2_3_3 = fig_2.add_subplot(539)
ax2_4_1 = fig_2.add_subplot(5,3,10)
ax2_4_2 = fig_2.add_subplot(5,3,11)
ax2_4_3 = fig_2.add_subplot(5,3,12)

fig_size = plt.rcParams["figure.figsize"]
fig_size[0] = 16
fig_size[1] = 8
fig_3 = plt.figure(3)
axa_1 = fig_3.add_subplot(241)
axa_2 = fig_3.add_subplot(242)
axa_3 = fig_3.add_subplot(243)
axa_4 = fig_3.add_subplot(244)
axa_5 = fig_3.add_subplot(245)
axa_6 = fig_3.add_subplot(246)
axa_7 = fig_3.add_subplot(247)
axa_8 = fig_3.add_subplot(248)
li_axa = [axa_1, axa_2, axa_3, axa_4, axa_5, axa_6, axa_7, axa_8]

fig_size = plt.rcParams["figure.figsize"]
fig_size[0] = 16
fig_size[1] = 4
fig_h = plt.figure(50)
ax_h_1 = fig_h.add_subplot(141)
ax_h_2 = fig_h.add_subplot(142)
ax_h_3 = fig_h.add_subplot(143)
ax_h_4 = fig_h.add_subplot(144)
li_axa = [axa_1, axa_2, axa_3, axa_4, axa_5, axa_6, axa_7, axa_8]

# list for img tensors 
li_t_imgs = []

# Parameters for the OIP run
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
map_index = 56         # map-index we are interested in 
# map_index = -1         # for this value the whole layer is taken; the loss function is averaged over the maps
n_epochs  = 20          # should be divisible by 5  
n_steps   = 6           # number of intermediate reports 
epsilon   = 0.01        # step size for gradient correction  
conv_criterion = 2.e-4  # criterion for a potential stop of optimization 

n_iter    = 5           # number of iterations for down-, upscaling and supplementation of details

# Initial image
# -----------------
MyOIP._initial_inp_img_data = t_picc_g_28

# Main iteration loop 
# ***********************
for i in range(n_iter): 

    # Perform the OIP analysis 
    MyOIP._derive_OIP(map_index = map_index, 
                      n_epochs = n_epochs, n_steps = n_steps, 
       
               epsilon = epsilon , conv_criterion = conv_criterion, 
                      b_stop_with_convergence=False,
                      b_print = False,
                      li_axa = li_axa,
                      ax1_1 = ax2_1_1, ax1_2 = ax2_1_2,
                      centre_move = 0.33, fact = 1.0)

    t_oip_c_g_28  = MyOIP._inp_img_data
    ay_oip_c_g_28 = t_oip_c_g_28[0,:,:,0].numpy()

    ay_oip_c_g_28_cont = MyOIP._transform_tensor_to_img(T_img=t_oip_c_g_28[0,:,:,0], centre_move=0.33, fact=1.0)
    ax2_1_3.imshow(ay_oip_c_g_28_cont, cmap=plt.cm.gray)

    # Rescale to 500
    t_oip_c_g_wk_size  = tf.image.resize(t_oip_c_g_28, [img_wk_size,img_wk_size], method="bicubic", antialias=True)
    #t_oip_c_g_500 = tf.image.per_image_standardization(t_oip_c_g_500)

    t_oip_c_g_wk_size_re     = t_oip_c_g_wk_size + t_picc_g_wk_size_corr 
    t_oip_c_g_wk_size_re_std = tf.image.per_image_standardization(t_oip_c_g_wk_size_re)

    # remember the img tensors of the iterations    
    li_t_imgs.append(t_oip_c_g_wk_size_re_std)
    
    # do not change the gray spectrum for iterations 
    MyOIP._initial_inp_img_data = tf.image.resize(t_oip_c_g_wk_size_re_std, [28,28], method="bicubic", antialias=True)
    
    # Intermediate plotting - if required and if plt.ion() is set 
    # ------------------------
    if b_plot_intermediate and j < n_iter-1: 
        ay_oip_c_g_wk_size = t_oip_c_g_wk_size[0,:,:,0].numpy()
        #display OIPs
        ax2_2_1.imshow(t_picc_g_28[0,:,:,0], cmap=plt.cm.gray)
        ax2_2_2.imshow(ay_oip_c_g_28,  cmap=plt.cm.gray)
        ax2_2_3.imshow(ay_oip_c_g_wk_size, cmap=plt.cm.gray)

        ax2_3_1.imshow(t_oip_c_g_wk_size[0,:,:,0], cmap=plt.cm.gray)
        ax2_3_2.imshow(t_oip_c_g_wk_size_re[0,:,:,0], cmap=plt.cm.gray)
        ax2_3_3.imshow(t_picc_g[0,:,:,0], cmap=plt.cm.gray)
    
        # modify the gray spectrum for plotting - cut off by clipping to limit the extend of the gray color map  
        min1 = tf.reduce_min(t_picc_g)
        min2 = tf.reduce_min(t_oip_c_g_wk_size_re)
        max1 = tf.reduce_max(t_picc_g)
        max2 = tf.reduce_max(t_oip_c_g_wk_size_re)
        # tf.print("min1 = ", min1, " :: min2 = ", min2, " :: max1 = ", max1, " :: max2 = ", max2 )

        #fac1 = min2/min1 * 0.95
        #fac2 = 1.0*fac1
        fac2 = 1.18
        fac3 = 0.92
        cut_lft = fac3*min1
        cut_rht = fac3*max1
        cut_rht = fac3*abs(min1)
        tf.print("cut_lft = ", cut_lft, "  cut_rht = ", cut_rht)

        t_oip_c_g_wk_size_re_std_plt = fac2 * t_oip_c_g_wk_size_re_std 
        t_oip_c_g_wk_size_re_std_plt = tf.clip_by_value(t_oip_c_g_wk_size_re_std_plt, cut_lft, cut_rht)
    
        ax2_4_1.imshow(t_oip_c_g_wk_size[0,:,:,0], cmap=plt.cm.gray)
        ax2_4_2.imshow(t_oip_c_g_wk_size_re_std[0,:,:,0], cmap=plt.cm.gray)
        ax2_4_3.imshow(t_oip_c_g_wk_size_re_std_plt[0,:,:,0], cmap=plt.cm.gray)


# Eventual plotting 
# ********************
ay_oip_c_g_wk_size = t_oip_c_g_wk_size[0,:,:,0].numpy()

#display OIPs
ax2_2_1.imshow(t_picc_g_28[0,:,:,0], cmap=plt.cm.gray)
ax2_2_2.imshow(ay_oip_c_g_28,  cmap=plt.cm.gray)
ax2_2_3.imshow(ay_oip_c_g_wk_size, cmap=plt.cm.gray)

ax2_3_1.imshow(t_oip_c_g_wk_size[0,:,:,0], cmap=plt.cm.gray)
ax2_3_2.imshow(t_oip_c_g_wk_size_re[0,:,:,0], cmap=plt.cm.gray)
ax2_3_3.imshow(t_picc_g[0,:,:,0], cmap=plt.cm.gray)

# modify the gray spectrum for plotting - cut off by clipping to limit the extend of the gray color map  
min1 = tf.reduce_min(t_picc_g)
min2 = tf.reduce_min(t_oip_c_g_wk_size_re)
max1 = tf.reduce_max(t_picc_g)
max2 = tf.reduce_max(t_oip_c_g_wk_size_re)
# tf.print("min1 = ", min1, " :: min2 = ", min2, " :: max1 = ", max1, " :: max2 = ", max2 )

#fac1 = min2/min1 * 0.95
#fac2 = 1.0*fac1
fac2 = 1.10
fac3 = 0.92
cut_lft = fac3*min1
cut_rht = fac3*
max1
#cut_rht = fac3*abs(min1)
tf.print("cut_lft = ", cut_lft, "  cut_rht = ", cut_rht)

t_oip_c_g_wk_size_re_std_plt = fac2 * t_oip_c_g_wk_size_re_std 
t_oip_c_g_wk_size_re_std_plt = tf.clip_by_value(t_oip_c_g_wk_size_re_std_plt, cut_lft, cut_rht)

ax2_4_1.imshow(t_oip_c_g_wk_size[0,:,:,0], cmap=plt.cm.gray)
ax2_4_2.imshow(t_oip_c_g_wk_size_re_std[0,:,:,0], cmap=plt.cm.gray)
ax2_4_3.imshow(t_oip_c_g_wk_size_re_std_plt[0,:,:,0], cmap=plt.cm.gray)
    
# Histogram analysis and plotting 
# *********************************    
# prepare the histograms of greay values for the saved imagetensors     
ay0 = np.sort( t_picc_g[0, :, :, 0].numpy().ravel() )
ay1 = np.sort( li_t_imgs[0][0,:,:,0].numpy().ravel() )
ay2 = np.sort( li_t_imgs[1][0,:,:,0].numpy().ravel() )
ay3 = np.sort( li_t_imgs[2][0,:,:,0].numpy().ravel() )
ay4 = np.sort( li_t_imgs[3][0,:,:,0].numpy().ravel() )
#print(ay1)

nx, binsx, patchesx = ax_h_1.hist(ay0, bins='auto')
nx, binsx, patchesx = ax_h_2.hist(ay2, bins='auto')
nx, binsx, patchesx = ax_h_3.hist(ay3, bins='auto')
nx, binsx, patchesx = ax_h_4.hist(ay4, bins='auto')

We first prepare some Matplotlib axes frames. Note that the references should be clearly distinguishable and unique across the cells of the Jupyter notebook.

Parameters
Then we define parameters for a DeepDream run. [The attentive reader has noticed that I now allow for a value of nmap_index = -1. This corresponds to working with a loss function calculated and averaged over all maps (nmap=-1) of a layer. The changed code of the class My_OIP is given at the end of the article. We come back to this option in a later post of this series. For the time being we just work with a chosen single map and its cost function.]

The most interesting parameters are “n_epochs” and “n_iter“. These parameters help to tune a careful balance between OIP-“carving” and “detail replenishment”. These are parameters you absolutely should experiment with!

Iterations
We first pick the (28×28) gray image prepared in the previous Jupyter cell as the initial image presented to the CNN’s input layer. We then start an iteration by invoking the “My_OIP” class discussed in the article named above. (The parameters “centre_move = 0.33” and “fact = 1.0” refer to an image manipulation, namely a contrast enhancement.)
After OIP-carving over the chosen limited number of epochs we apply a special treatment to the data for the OPI-image derived so far. In a side step we enhance the contrast contrast for displaying the intermediate results. We then rescale by bicubic interpolation from 28×28 to the working size 560×560, add the prepared correction data and standardize. We add the results to a list for a later histogram analysis.

The preparation of plotting (of an intermediate and eventual image) comprises a step to reduce the spectrum of pixel values. This step is required as the iterative image manipulation leads to an extension of the maximum and the minimum values, i.e. the flanks of the value spectrum, up to a factor of 1.7 – although we only find a few pixels in that extended range. If we applied a standard gray-scale color map to the whole wider range of values then we would get a strong reduction in contrast – for the sake of including some extreme pixel values. The remedy is to cut the spectrum off at the original maximum/minimum value.

The histogram analysis performed at the end in addition shows that the central spectrum has become a bit narrower – we can compensate this by some factors fac2 and fac3. Play around with them.

Results of the carving process

Results for map 57 are displayed in the following image:

The effect of the “carving” is clearly visible as an overlayed ghost like pattern apparition. Standardization of the final images makes no big difference – however, the discussed compensation for the widened spectrum of the eventual image is important.

The histogram analysis shows the flank widening and the narrowing of the central core of the pixel value spectrum:

The following image allow a comparison of the original gray image with the carved image for parameters [n_epochs=20, n_iter=5]:

Conclusion

Deep Dreams are based on special image analysis and manipulation techniques. We adapted some of the techniques discussed in literature for high resolution images and advanced CNNs in a special way and for a single deep layer map of a low resolution CNN. We called the required intermittent combination of down- and upscaling, enhancing OIP-patterns and re-adding details “carving“. This helped us to create a “dream” of a CNN – which was trained with a bunch low resolution MNIST images, only; the dream can be based on arbitrary quadratic input images (here: an image of a bunch of roses).

The technique presented in this article can be extended to include a pattern analysis on various sub-parts and length-scales of the original image. In the next blog post we shall have a look at some of the required programming steps.

My_OIP class – V0.65

I have modified the My_OIP code a bit since the last articles on CNNs. You find the new version below.

 
'''
Module to create OIPs as visualizations of filters of a simple CNN for the MNIST data set
@version: 0.65, 12.12.2020
@change: V0.5:  was based on version 0.4 which was originally created in Jupyter cells
@change: V0.6: General revision of class "my_OIP" and its methods
@change: V0.6: Changes to the documentation 
@change: V0.65: Added intermediate plotting of selected input fluctuation patterns 
@attention: General status: For experimental purposes only! 
@requires: A full CNN trained on MNIST data 
@requires: A Keras model of the CNN and weight data saved in a h5-file, e.g."cnn_MIST_best.h5". 
           This file must be placed in the main directory of the Jupyter notebooks.
@requires: A Jupyter environment - from where the class My_OIP is called and where plotting takes place 
@note: The description to the interface to the class via the __init__()-method may be incomplete
@note: The use of prefixes li_ and ay_ is not yet consistent. ay_ should indicate numpy arrays, li_ instead normal Python lists
@warning: This version has not been tested outside a Jupyter environment - plotting in GTK/Qt-environment may require substantial changes 
@status: Under major development with frequent changes 
@author: Dr. Ralph Mönchmeyer
@copyright: Simplified BSD License, 12.12.2020. Copyright (c) 2020, Dr. Ralph Moenchmeyer, Augsburg, Germany

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this
   list of conditions and 
the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
'''

# Modules to be imported - these libs must be imported in a Jupyter cell nevertheless 
# ~~~~~~~~~~~~~~~~~~~~~~~~
import time 
import sys 
import math
import os 
from os import path as path

import numpy as np
from numpy import save  # used to export intermediate data
from numpy import load

import scipy
from sklearn.preprocessing import StandardScaler
from itertools import product 

import tensorflow as tf
from tensorflow import keras as K
from tensorflow.python.keras import backend as B  # this is the only version compatible with TF 1 compat statements
#from tensorflow.keras import backend as B 
from tensorflow.keras import models
from tensorflow.keras import layers
from tensorflow.keras import regularizers
from tensorflow.keras import optimizers
from tensorflow.keras.optimizers import schedules
from tensorflow.keras.utils import to_categorical
from tensorflow.keras.datasets import mnist

from tensorflow.python.client import device_lib

import matplotlib as mpl
from matplotlib import pyplot as plt
from matplotlib.colors import ListedColormap
import matplotlib.patches as mpat 

from IPython.core.tests.simpleerr import sysexit

class My_OIP:
    '''
    @summary: This class allows for the creation and the display of OIP-patterns, 
              to which a selected map of a CNN-model and related filters react maximally
    
    @version: Version 0.6, 10.10.2020
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    @change: Revised methods 
    @requires: In the present version the class My_OIP requires: 
                * a CNN-model which works with standardized (!) input images, size 28x28,
                * a CNN-Modell which was trained on MNIST digit data,
                * exactly 4 length scales for random data fluctations are used to compose initial statistial image data 
                  (the length scales should roughly have a factor of 2 between them) 
                * Assumption : exactly 1 input image and not a batch of images is assumed in various methods 
    
    @note: Main Functions:     
    0) _init__()
    1) _load_cnn_model()             => load cnn-model
    2) _build_oip_model()            => build an oip-model to create OIP-images
    3) _setup_gradient_tape_and_iterate_function()        
                                    => Implements TF2 GradientTape to watch input data for eager gradient calculation
                                    => Creates a convenience function by the help of Keras to iterate and optimize the OIP-adjustments
    4) _oip_strat_0_optimization_loop():
                                     => Method implementing a simple strategy to create OIP-images, 
                                        based on superposition of random data on long range data (compared to 28 px) 
                                        The optimization uses "gradient ascent"
 to get an optimum output of the selected Conv map 
    6) _derive_OIP():                => Method used to start the creation of an OIP-image for a chosen map 
                                        - based on an input image with statistical random date 
    6) _derive_OIP_for_Prec_Img():   => Method used to start the creation of an OIP-image for a chosen map 
                                       - based on an input image with was derived from a PRECURSOR run, 
                                       which tests the reaction of the map to large scale fluctuations 
                                        
    7) _build_initial_img_data():    => Builds an input image based on random data for fluctuations on 4 length scales 
    8) _build_initial_img_from_prec():    
                                     => Reconstruct an input image based on saved random data for long range fluctuations 
    9) _prepare_precursor():         => Prepare a _precursor run by setting up TF2 GradientTape and the _iterate()-function 
    10) _precursor():                => Precursor run which systematically tests the reaction of a selected convolutional map 
                                        to long range fluctuations based on a (3x3)-grid upscaled to the real image size  
    11) _display_precursor_imgs():   => A method which plots up to 8 selected precursor images with fluctuations,
                                        which triggered a maximum map reaction 
    12) _transfrom_tensor_to_img():  => A method which allows to transform tensor data of a standardized (!) image to standard image data 
                                        with (gray)pixel valus in [0, 255]. Parameters allow for a contrast enhancement. 
    
    Usage hints 
    ~~~~~~~~~~~
    @note: If maps of a new convolutional layer are to be investigated then method _build_oip_model(layer_name) has to be rerun 
           with the layer's name as input parameter
    '''
    
    # Method to initialize an instantiation object 
    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    def __init__(self, cnn_model_file = 'cnn_MNIST_best.h5', 
                 layer_name = 'Conv2D_3', 
                 map_index = 0, 
                 img_dim = 28, 
                 b_build_oip_model = True  
                ): 
        '''
        @summary: Initialization of an object instance - read in a CNN model, build an OIP-Model 
        @note: Input: 
        ~~~~~~~~~~~~
        @param cnn_model_file:  Name of a file containing a fully trained CNN-model; 
                                the model can later be overwritten by self._load_cnn_model()
        @param layer_name:      We can define a layer name, which we are interested in,  already when starting;
                                the layer can later be overwritten by self._build_oip_model()
        @param map_index:       We can define a map, which we are interested in, already when starting;
                                A map-index is NOT required for building the OIP-model, but for the GradientTape-object 
        @param img_dim:         The dimension of the assumed quadratic images (2 for MNIST)

        @note: Major internal variables:
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @ivar _cnn_model:        A reference to the CNN model object
        @ivar _layer_name:       The name of convolutional layer 
                                 (can be overwritten by method _build_oip_model() ) 
        @ivar _map_index:        Index of the map in the chosen layer's output array 
                                 (can later be overwritten by other methods) 
        @ivar _r_cnn_inputs:     A reference to the input tensor of the CNN model 
                                 Could be a batch of images; but in this class only 1 image is assumed
        @ivar _layer_output:     Tensor with all maps of a certain layer    
        @
ivar _oip_submodel:     A new model connecting the input of the CNN-model with a certain map's (!) output
        @ivar _tape:             An instance of TF2's GradientTape-object 
                                    Watches input, output, loss of a model 
                                    and calculates gradients in TF2 eager mode 
        @ivar _r_oip_outputs:    Reference to the output of the new OIP-model = map-activation
        @ivar _r_oip_grads:      Reference to gradient tensors for the new OIP-model (output dependency on input image pixels)
        @ivar _r_oip_loss:       Reference to a loss defined on the OIP-output - i.e. on the activation values of the map's nodes;
                                 Normally chosen to be an average of the nodes' activations 
                                 The loss defines a hyperplane on the (28x28)-dim representation space of the input image pixel values  
        @ivar _val_oip_loss:     Loss value for a certain input image 
        @ivar _iterate           Reference toa Keras backend function which invokes the new OIP-model for a given image
                                 and calculates both loss and gradient values (in TF2 eager mode) 
                                 This is the function to be used in the optimization loop for OIPs
        
        @note: Internal Parameters controlling the optimization loop:
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @ivar _oip_strategy:        0, 1 - There are two strategies to evolve OIP patterns out of statistical data 
                                    - only the first strategy is supported in this version 
                                    Both strategies can be combined with a precursor calculation 
                                    0: Simple superposition of fluctuations at different length scales
                                    1: NOT YET SUPPORTED 
                                    Evolution over partially evolved images based on longer scale variations 
                                    enriched with fluctuations on shorter length scales 

        @ivar _ay_epochs:           A list of 4 optimization epochs to be used whilst 
                                    evolving the img data via strategy 1 and intermediate images 
        @ivar _n_epochs:            Number of optimization epochs to be used with strategy 0 
        @ivar _n_steps:             Defines at how many intermediate points we show images and report 
                                    during the optimization process 
        @ivar _epsilon:             Factor to control the amount of correction imposed by the gradient values of the oip-model 

        @note: Input image data of the OIP-model and references to it 
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @ivar _initial_precursor_img:  The initial image to start a precursor optimization with.
                                       Would normally be an image of only long range fluctuations. 
        @ivar _precursor_image:        The evolved image created and selected by the precursor loop 

        @ivar _initial_inp_img_data:  A tensor representing the data of the input image 
        @ivar _inp_img_data:          A tensor representig the 
        @ivar _img_dim:               We assume quadratic images to work with 
                                      with dimension _img_dim along each axis
                                      For the time being we only support MNIST images 
        
        @note: Internal parameters controlling the composition of random initial image data 
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @ivar _li_dim_steps:        A list of the intermediate dimensions for random data;
                                    these data are smoothly scaled to the image dimensions 
        @ivar _ay_facts:            A Numpy array of 4 factors to control the amount of 
                         
           contribution of the statistical variations 
                                    on the 4 length scales to the initial image
        
        @note: Internal variables to save data of a precursor run
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
        @ivar _list_of_covs: list of long range fluctuation data for a (3x3)-grid covering the image area 
        @ivar _li_fluct_enrichments: [li_facts, li_dim_steps] data for enrichment with small fluctuations 
        
        
        @note: Internal variables for plotting
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @ivar _li_axa: A Python list of references to external (Jupyter-) axes-frames for plotting 
        
        '''    
        
        # Input data and variable initializations
        # ****************************************
        
        # the model 
        # ~~~~~~~~~~
        self._cnn_model_file = cnn_model_file
        self._cnn_model      = None 
        
        # the chosen layer of the CNN-model
        self._layer_name = layer_name
        # the index of the map in the layer array
        self._map_index  = map_index
        
        # References to objects and the OIP-submodel
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self._r_cnn_inputs  = None # reference to input of the CNN_model, also used in the oip-model  
        self._layer_output  = None
        self._oip_submodel  = None
        
        # References to watched GradientTape objects 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self._tape          = None # TF2 GradientTape variable
        # some "references"
        self._r_oip_outputs = None # output of the oip-submodel to be watched 
        self._r_oip_grads   = None # gradients determined by GradientTape   
        self._r_oip_loss    = None # loss function
        # loss and gradient values (to be produced ba a backend function _iterate() )
        self._val_oip_grads = None
        self._val_oip_loss  = None
        
        # The Keras function to produce concrete outputs of the new OIP-model  
        self._iterate       = None
        
        # The strategy to produce an OIP pattern out of statistical input images 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~--------~~~~~~
        # 0: Simple superposition of fluctuations at different length scales 
        # 1: Move over 4 interediate images - partially optimized 
        self._oip_strategy = 0
        
        # Parameters controlling the OIP-optimization process 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~--------~~~~~~
        # number of epochs for optimization strategy 1
        self._ay_epochs    = np.array((20, 40, 80, 400), dtype=np.int32)
        len_epochs         = len(self._ay_epochs)
        
        # number of epochs for optimization strategy 0
        self._n_epochs     = self._ay_epochs[len_epochs-1]   
        self._n_steps      = 6   # divides the number of n_epochs into n_steps to produce intermediate outputs
        
        # size of corrections by gradients
        self._epsilon       = 0.01 # step-size for gradient correction
        
        # Input image-typess and references 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # precursor image
        self._initial_precursor_img = None
        self._precursor_img         = None # output of the _precursor-method 
        
        # The input image for the OIP-creation - a superposition of inial random fluctuations
        self._initial_inp_img_data  = None  # The initial data constructed 
        self._inp_img_data          = None  # The data used and varied for optimization 
        # image dimension
        self._img_dim               = img_dim   # = 28 => MNIST images for the time being 
        
        # Parameters controlling the setup of an initial image 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~--------
~~~~~~~~~~~~~~~~~~~
        # The length scales for initial input fluctuations
        self._li_dim_steps = ( (3, 3), (7,7), (14,14), (28,28) ) # can later be overwritten 
        # Parameters for fluctuations  - used both in strategy 0 and strategy 1  
        self._ay_facts     = np.array( (0.5, 0.5, 0.5, 0.5), dtype=np.float32 )
        
        # Data of a _precursor()-run 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self._list_of_covs = None       # list of long range fluctuation data for a (3x3)-grid covering the image area 
        self._li_fluct_enrichments = None # = [li_facts, li_dim_steps] list with with 2 list of data enrichment for small fluctuations 
        # These data are required to reconstruct the input image to which a map reacted 
        
        # List of references to axis subplots
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # These references may change from Jupyter cell to Jupyter cell and provided by the called methods
        self._li_axa = None # will be set by methods according to axes-frames in Jupyter cells 
        # axis frames for a single image in 2 versions (with contrast enhancement)
        self._ax1_1 = None
        self._ax1_2 = None 
        
        
        # Variables for Deep Dream Analysis 
        # ***********************************
        #     Here we need a stack of tiled sub-images of a large image, as we subdivide on different length scales 
        self._num_tiles = 1
        self._t_image_stack = None 
        
        # ********************************************************
        # Model setup - load the cnn-model and build the OIP-model
        # ************
        if path.isfile(self._cnn_model_file): 
            # We trigger the initial load of a model 
            self._load_cnn_model(file_of_cnn_model = self._cnn_model_file, b_print_cnn_model = True)
            # We trigger the build of a new sub-model based on the CNN model used for OIP search 
            self._build_oip_model(layer_name = self._layer_name, b_print_oip_model = True ) 
        else:
            print("<\nWarning: The standard file " + self._cnn_model_file + 
                  " for the cnn-model could not be found!\n " + 
                  " Please use method _load_cnn_model() to load a valid model")
            sys.exit()
        return
    
    
    #
    # Method to load a specific CNN model
    # **********************************
    def _load_cnn_model(self, file_of_cnn_model=None, b_print_cnn_model=True ):
        '''
        @summary: Method to load a CNN-model from a h5-file and create a reference to its input (image)
        @version: 0.2 of 28.09.2020
        @requires: filename must already have been saved in _cnn_model_file or been given as a parameter 
        @requires: file must be a h5-file 
        @change: minor changes - documentation 
        @note: A reference to the CNN's input is saved internally
        @warning: An input in form of an image - a MNIST-image - is implicitly assumed
        
        @note: Parameters
        -----------------
        @param file_of_cnn_model: Name of h5-file with the trained (!) CNN-model
        @param b_print_cnn_model: boolean - Print some information on the CNN-model 
        '''
        if file_of_cnn_model != None:
            self._cnn_model_file = file_of_cnn_model
        
        # Check existence of the file
        if not path.isfile(self._cnn_model_file): 
            print("\nWarning: The file " + file_of_cnn_model + 
                  " for the cnn-model could not be found!\n" + 
                  "Please change the parameter \"file_of_cnn_model\"" + 
                  " to load a valid model")
        
        # load the CNN model 
        self._cnn_model = models.load_model(self._cnn_model_file)
        
        # Inform about the model and its 
file
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~
        print("Used file to load a ´ model = ", self._cnn_model_file)
        # we print out the models structure
        if b_print_cnn_model:
            print("Structure of the loaded CNN-model:\n")
            self._cnn_model.summary()
        
        # handle/references to the models input => more precise the input image 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        #    Note: As we only have one image instead of a batch 
        #    we pick only the first tensor element!
        #    The inputs will be needed for buildng the oip-model 
        self._r_cnn_inputs = self._cnn_model.inputs[0]  # !!! We have a btach with just ONE image 
        
        # print out the shape - it should be known from the original cnn-model
        if b_print_cnn_model:
            print("shape of cnn-model inputs = ", self._r_cnn_inputs.shape)
        
        return
    
    
    #
    # Method to construct a model to optimize input for OIP creation 
    # ***************************************
    def _build_oip_model(self, layer_name = 'Conv2D_3', b_print_oip_model=True ): 
        '''
        @summary: Method to build a new (sub-) model - the "OIP-model" - of the CNN-model by 
                  connectng the input of the CNN-model with one of its Conv-layers
        @version: 0.4 of 28.09.2020
        @change: Minor changes - documentation 
        @note: We need a Conv layer to build a working model for input image optimization
        We get the Conv layer by the layer's name 
        The new model connects the first input element of the CNN to the output maps of the named Conv layer CNN 
        We use Keras' models.Model() functionality 
        @note: The layer's name is crucial for all later investigations - if you want to change it this method has to be rerun 
        @requires: The original, trained CNN-model must be loaded and referenced by self._cnn_model 
        @warning: Only 1 input image and not a batch is implicitly assumed 
        
        @note: Parameters
        -----------------
        @param layer_name: Name of the convolutional layer of the CNN for whose maps we want to find OIP patterns
        @param b_print_oip_model: boolean - Print some information on the OIP-model 
        
        '''
        # free some RAM - hopefully 
        del self._oip_submodel
        
        # check for loaded CNN-model
        if self._cnn_model == None: 
            print("Error: CNN-model not yet defined.")
            sys.exit()
        
        # get layer name 
        self._layer_name = layer_name
        
        # We build a new model based on the model inputs and the output 
        self._layer_output = self._cnn_model.get_layer(self._layer_name).output
        # Note: We do not care at the moment about a complex composition of the input 
        # We trust in that we handle only one image - and not a batch
        
        # Create the sub-model via Keras' models.Model()
        model_name = "mod_oip__" + layer_name 
        self._oip_submodel = models.Model( [self._r_cnn_inputs], [self._layer_output], name = model_name)                                    

        # We print out the oip model structure
        if b_print_oip_model:
            print("Structure of the constructed OIP-sub-model:\n")
            self._oip_submodel.summary()
        return
    
    
    #
    # Method to set up GradientTape and an iteration function providing loss and gradient values  
    # *********************************************************************************************
    def _setup_gradient_tape_and_iterate_function(self, b_print = True, b_full_layer = False):
        '''
        @summary: Central method to watch input variables and resulting gradient changes 
        @version: 0.6 of 12.12.2020
n        @change: V0.6: We add the definition of a loss function for a whole layer 
        @note: For TF2 eager execution we need to watch input changes and trigger automatic gradient evaluation
        @note: The normalization of the gradient is strongly recommended; as we fix epsilon for correction steps 
               we thereby will get changes to the input data of an approximately constant order.
               This - together with standardization of the images (!) - will lead to convergence at the size of epsilon !
        @param b_full_layer: Boolean; define a loss function for a single map (map_index > -1) or the full layer (map_index = -1)
        '''   
        # Working with TF2 GradientTape
        self._tape = None

        # Watch out for input, output variables with respect to gradient changes
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        with tf.GradientTape() as self._tape: 
            # Input
            # ~~~~~
            self._tape.watch(self._r_cnn_inputs)
            # Output
            # ~~~~~~
            self._r_oip_outputs = self._oip_submodel(self._r_cnn_inputs)
            
            # only for testing
            # *******************
            #t_shape = self._r_oip_outputs[0, :, :, :].shape  # the 0 is important, else "Noen" => problems 
            #scaling_factor = tf.cast(tf.reduce_prod(t_shape), tf.float32) 
            #tf.print("scaling_factor: ", scaling_factor)
            #t_loss = tf.reduce_sum(tf.math.square(self._r_oip_outputs[0, :, :, :])) / scaling_factor
            
            # Define Loss 
            # ***********
            if (b_full_layer):
                # number of neurons over all layer maps 
                t_shape = self._r_oip_outputs[0, :, :, :].shape  # the 0 is important, else "Noen" => problems 
                scaling_factor = tf.cast(tf.reduce_prod(t_shape), tf.float32) # shape! eg. 3x3x128 for layer 3 
                tf.print("scaling_factor: ", scaling_factor)
                
                # The scaled total loss of the layer 
                self._r_oip_loss = tf.reduce_sum(tf.math.square(self._r_oip_outputs[0, :, :, :])) / scaling_factor
                
                # self._r_oip_loss = tf.reduce_mean(self._r_oip_outputs[0, :, :, self._map_index])
            else:
                self._r_oip_loss = tf.reduce_mean(self._r_oip_outputs[0, :, :, self._map_index])
            
            #self._loss = B.mean(oip_output[:, :, :, map_index])
            #self._loss = B.mean(oip_outputs[-1][:, :, map_index])
            #self._loss = tf.reduce_mean(oip_outputs[-1][ :, :, map_index])
            if b_print:
                print(self._r_oip_loss)
                print("shape of oip_loss = ", self._r_oip_loss.shape)
        
        # Gradient definition and normalization
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self._r_oip_grads  = self._tape.gradient(self._r_oip_loss, self._r_cnn_inputs)
        print("shape of grads = ", self._r_oip_grads.shape)

        # normalization of the gradient - required for convergence 
        t_tiny = tf.constant(1.e-7, tf.float32)
        self._r_oip_grads /= (tf.sqrt(tf.reduce_mean(tf.square(self._r_oip_grads))) + t_tiny)
        #self._r_oip_grads /= (B.sqrt(B.mean(B.square(self._r_oip_grads))) + 1.e-7)
        #self._r_oip_grads = tf.image.per_image_standardization(self._r_oip_grads)

        # Define an abstract recallable Keras function as a convenience function for iterations 
        #     The _iterate()-function produces loss and gradient values for corrected img data 
        #     The first list of addresses points to the input data, the last to the output data 
        self._iterate = B.function( [self._r_cnn_inputs], [self._r_oip_loss, self._r_oip_grads] )
        
    
    #        
    # Method to optimize an emerging OIP out of statistical input 
image data 
    # (simple strategy - just optimize, no precursor, no intermediate pattern evolution, ..) 
    # ********************************
    def _oip_strat_0_optimization_loop(self, conv_criterion = 5.e-4, 
                                            b_stop_with_convergence = False,
                                            b_show_intermediate_images = True,
                                            b_print = True):
        '''
        @summary: Method to control the optimization loop for OIP reconstruction of an initial input image
                  with a statistical distribution of pixel values. 
        @version: 0.4 of 28.09.2020
        @changes: Minor changes - eliminated some unused variables
        @note:    The function also provides intermediate output in the form of printed data and images !.
        @requires: An input image tensor must already be available at _inp_img_data - created by _build_initial_img_data()
        @requires: Axis-objects for plotting, typically provided externally by the calling functions 
                  _derive_OIP() or _precursor()
        
        @note: Parameters:
        ----------------- 
        @param conv_criterion:  A small threshold number for (difference of loss-values / present loss value )
        @param b_stop_with_convergence: Booelan which decides whether we stop a loop if the conv-criterion is fulfilled
        @param b_show_intermediate_image: Boolean which decides whether we show up to 8 intermediate images 
        @param b_print: Boolean which decides whether we print intermediate loss values 
        
        @note: Intermediate information is provided at _n_steps intervals, 
               which are logarithmically distanced with respect to _n_epochs
               Reason: Most changes happen at the beginning 
        @note: This method produces some intermediate output during the optimization loop in form of images.
        It uses an external grid of plot frames and their axes-objects. The addresses of the 
        axis-objects must provided by an external list "li_axa[]" to self._li_axa[].  
        We need a seqence of _n_steps+2 axis-frames (or more) => length(_li_axa) >= _n_steps + 2). 
        
        @todo: Loop not optimized for TF 2 - but not so important here - a run takes less than a second 
        
        '''
        
        # Check that we already an input image tensor
        if ( (self._inp_img_data == None) or 
             (self._inp_img_data.shape[1] != self._img_dim) or 
             (self._inp_img_data.shape[2] != self._img_dim) ) :
            print("There is no initial input image or it does not fit dimension requirements (28,28)")
            sys.exit()

        # Print some information
        if b_print:
            print("*************\nStart of optimization loop\n*************")
            print("Strategy: Simple initial mixture of long and short range variations")
            print("Number of epochs = ", self._n_epochs)
            print("Epsilon =  ", self._epsilon)
            print("*************")

        # some initial value
        loss_old = 0.0
        
        # Preparation of intermediate reporting / img printing
        # --------------------------------------
        # Logarithmic spacing of steps (most things happen initially)
        n_el = math.floor(self._n_epochs / 2**(self._n_steps) ) 
        li_int = []
        if n_el != 0:
            for j in range(self._n_steps):
                li_int.append(n_el*2**j)
        else:  # linear spacing
            n_el = math.floor(self._n_epochs / (self._n_steps+1) ) 
            for j in range(self._n_steps+1):
                li_int.append(n_el*j)
        
        if b_print:
            print("li_int = ", li_int)
        
        # A counter for intermediate reporting  
        n_rep = 0
        
        # 
Convergence? - A list for steps meeting the convergence criterion
        # ~~~~~~~~~~~~
        li_conv = []
        
        
        # optimization loop 
        # *******************
        # counter for steps with zero loss and gradient values 
        n_zeros = 0
        
        for j in range(self._n_epochs):
            
            # Get output values of our Keras iteration function 
            # ~~~~~~~~~~~~~~~~~~~
            self._val_oip_loss, self._val_oip_grads = self._iterate([self._inp_img_data])
            
            # loss difference to last step - shuold steadily become smaller 
            loss_diff = self._val_oip_loss - loss_old 
            #if b_print:
            #    print("j: ", j, " :: loss_val = ", self._val_oip_loss, " :: loss_diff = ",  loss_diff)
            #    # print("loss_diff = ", loss_diff)
            loss_old = self._val_oip_loss
            
            if j > 10 and (loss_diff/(self._val_oip_loss + 1.-7)) < conv_criterion:
                li_conv.append(j)
                lenc = len(li_conv)
                # print("conv - step = ", j)
                # stop only after the criterion has been met in 4 successive steps
                if b_stop_with_convergence and lenc > 5 and li_conv[-4] == j-4:
                    return
            
            grads_val     = self._val_oip_grads
            #grads_val =   normalize_tensor(grads_val)
            
            # The gradients average value 
            avg_grads_val = (tf.reduce_mean(grads_val)).numpy()
            
            # Check if our map reacts at all
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            if self._val_oip_loss == 0.0 and avg_grads_val == 0.0 and b_print :
                print( "0-values, j= ", j, 
                       " loss = ", self._val_oip_loss, " avg_loss = ", avg_grads_val )
                n_zeros += 1
            
            if n_zeros > 10 and b_print: 
                print("More than 10 times zero values - Try a different initial random distribution of pixel values")
                return
            
            # gradient ascent => Correction of the input image data 
            # ~~~~~~~~~~~~~~~
            self._inp_img_data += self._val_oip_grads * self._epsilon
            
            # Standardize the corrected image - we won't get a convergence otherwise 
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            self._inp_img_data = tf.image.per_image_standardization(self._inp_img_data)
            
            # Some output at intermediate points 
            #     Note: We us logarithmic intervals because most changes 
            #           appear in the intial third of the loop's range  
            if (j == 0) or (j in li_int) or (j == self._n_epochs-1) :
                if b_print or (j == self._n_epochs-1):
                    # print some info 
                    print("\nstep " + str(j) + " finalized")
                    #print("Shape of grads = ", grads_val.shape)
                    print("present loss_val = ", self._val_oip_loss)
                    print("loss_diff = ", loss_diff)
                # show the intermediate image data 
                if b_show_intermediate_images: 
                    imgn = self._inp_img_data[0,:,:,0].numpy()
                    # print("Shape of intermediate img = ", imgn.shape)
                    self._li_axa[n_rep].imshow(imgn, cmap=plt.cm.get_cmap('viridis'))
                    # counter
                    n_rep += 1
        
        return
    
    
    #        
    # Standard UI-method to derive OIP from a given initial input image
    # ********************
    def _derive_OIP(self, map_index = 1, 
                          n_epochs = None, 
                          n_steps = 6, 
                          epsilon = 
0.01, 
                          conv_criterion = 5.e-4, 
                          li_axa = [], 
                          ax1_1 = None, ax1_2 = None, 
                          b_stop_with_convergence = False,
                          b_show_intermediate_images = True,
                          b_print = True,
                          centre_move = 0.33, fact = 1.0):
        '''
        @summary: Method to create an OIP-image for a given initial input image
                  This is the standard user interface for finding an OIP 
        @warning: This method should NOT be used for finding an initial precursor image 
                  Use _prepare_precursor() to define the map first and then _precursor() to evaluate initial images 
        @version: V0.5, 12.12.2020
        @change:  V0.4: Minor changes - added internal _li_axa for plotting, added documentation 
                  This method starts the process of producing an OIP of statistical input image data
        @change:  V0.5 : map_index can now have the value "-". Then a loss function for the whole layer (instead of a single map) is prepared
        @requires: A map index (or -1) should be provided to this method 
        @requires: An initial input image with statistical fluctuations of pixel values must have been created. 

        @warning:    This version only supports the most simple strategy - "strategy 0" 
        -------------    Optimize in one loop - starting from a superposition of fluctuations
                         No precursor, no intermediate evolutions

        @note: Parameters:
        -----------------
        @param map_index: We can and should chose a map here  (overwrites previous settings)
                          If map_index == -1 => We take a loss for the whole layer  
        @param n_epochs: Number of optimization steps  (overwrites previous settings) 
        @param n_steps:  Defines number of intervals (with length n_epochs/ n_steps) for reporting
                         standard value: 6 => 8 images - start image, end image + 6 intermediate 
                         This number also sets a requirement for providing (n_step + 2) external axis-frames 
                         to display intermediate images of the emerging OIP  
                         => see _oip_strat_0_optimization_loop()
        @param epsilon:  Size for corrections by gradient values
        @param conv_criterion: A small threshold number for convegenc (checks:  difference of loss-values / present loss value )
        @param b_stop_with_convergence: 
                         Booelan which decides whether we stop a loop if the conv-criterion is fulfilled
        @param _li_axa: A Python list of references to external (Jupyter-) axes-frames for plotting 
                 
        
        @note: Preparations for plotting: 
        We need n_step + 2 axis-frames which must be provided externally
        
        With Jupyter this can externally be done by statements like 

        # figure
        # -----------
        #sizing
        fig_size = plt.rcParams["figure.figsize"]
        fig_size[0] = 16
        fig_size[1] = 8
        fig_a = plt.figure()
        axa_1 = fig_a.add_subplot(241)
        axa_2 = fig_a.add_subplot(242)
        axa_3 = fig_a.add_subplot(243)
        axa_4 = fig_a.add_subplot(244)
        axa_5 = fig_a.add_subplot(245)
        axa_6 = fig_a.add_subplot(246)
        axa_7 = fig_a.add_subplot(247)
        axa_8 = fig_a.add_subplot(248)
        li_axa = [axa_1, axa_2, axa_3, axa_4, axa_5, axa_6, axa_7, axa_8]
        
        '''
        # Get input parameters
        self._map_index = map_index
        self._n_epochs  = n_epochs   
        self._n_steps   = n_steps
        self._epsilon   = epsilon
        
        # references to plot frames 
        self._li_axa = li_axa
        num_frames = len(li_
axa)
        if num_frames < n_steps+2:
            print("The number of available image frames (", num_frames, ") is smaller than required for intermediate output (", n_steps+2, ")")
            sys.exit()
        
        # 2 axes frames to display the final OIP image (with contrast enhancement) 
        self._ax1_1 = ax1_1
        self._ax1_2 = ax1_2
        
        # number of epochs for optimization strategy 0 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if n_epochs == None:
            len_epochs = len(self._ay_epochs)
            self._n_epochs   = self._ay_epochs[len_epochs-1]
        else: 
            self._n_epochs = n_epochs

        # Reset some variables  
        self._val_oip_grads = None
        self._val_oip_loss  = None 
        self._iterate       = None 

        # Setup the TF2 GradientTape watch and a Keras function for iterations 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # V0.5 => map_index == "-1"
        if self._map_index == -1: 
            self._setup_gradient_tape_and_iterate_function(b_print = b_print, b_full_layer=True)
            if b_print:
                print("GradientTape watch activated (map-based: map = ", self._map_index, ")")
        else: 
            self._setup_gradient_tape_and_iterate_function(b_print = b_print, b_full_layer=False)
            if b_print:
                print("GradientTape watch activated (layer-based: layer = ", self._layer_name, ")")
        
        '''
        # Gradient handling - so far we only deal with addresses 
        # ~~~~~~~~~~~~~~~~~~
        self._r_oip_grads  = self._tape.gradient(self._r_oip_loss, self._r_cnn_inputs)
        print("shape of grads = ", self._r_oip_grads.shape)
        
        # normalization of the gradient 
        self._r_oip_grads /= (B.sqrt(B.mean(B.square(self._r_oip_grads))) + 1.e-7)
        #self._r_oip_grads = tf.image.per_image_standardization(self._r_oip_grads)
        
        # define an abstract recallable Keras function 
        # producing loss and gradients for corrected img data 
        # the first list of addresses points to the input data, the last to the output data 
        self._iterate = B.function( [self._r_cnn_inputs], [self._r_oip_loss, self._r_oip_grads] )
        '''
            
        # get the initial image into a variable for optimization 
        self._inp_img_data = self._initial_inp_img_data

        # Start optimization loop for strategy 0 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if self._oip_strategy == 0: 
            self._oip_strat_0_optimization_loop( conv_criterion = conv_criterion, 
                                                b_stop_with_convergence = b_stop_with_convergence,  
                                                b_show_intermediate_images = b_show_intermediate_images,
                                                b_print = b_print
                                               )
        
        # Display the last OIP-image created at the end of the optimization loop
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # standardized image 
        oip_img = self._inp_img_data[0,:,:,0].numpy()
        # transformed image 
        oip_img_t = self._transform_tensor_to_img(T_img=self._inp_img_data[0,:,:,0], 
                                                  centre_move = centre_move,
                                                  fact = fact)
        
        # display 
        ax1_1.imshow(oip_img, cmap=plt.cm.get_cmap('viridis'))
        ax1_2.imshow(oip_img_t, cmap=plt.cm.get_cmap('viridis'))
        
        return
    
    
    # 
    # Method to derive OIP from a given initial input image if map_index is already defined 
    # ********************
    def _derive_OIP_for_Prec_
Img(self, 
                          n_epochs = None, 
                          n_steps = 6, 
                          epsilon = 0.01, 
                          conv_criterion = 5.e-4, 
                          li_axa = [], 
                          ax1_1 = None, ax1_2 = None, 
                          b_stop_with_convergence = False,
                          b_show_intermediate_images = True,
                          b_print = True):
        '''
        @summary: Method to create an OIP-image for an already given map-index and a given initial input image
                  This is the core of OIP-detection, which starts the optimization loop  
        @warning: This method should NOT be used directly for finding an initial precursor image 
                  Use _prepare_precursor() to define the map first and then _precursor() to evaluate initial images 
        @version: V0.4, 28.09.2020
        @changes: Minor changes - added internal _li_axa for plotting, added documentation 
                  This method starts the process of producing an OIP of statistical input image data
        
        @note:    This method should only be called after _prepare_precursor(), _precursor(), _build_initial_img_prec() 
                  For a trial of different possible precursor images rerun _build_initial_img_prec() with a different index
        
        @requires: A map index should be provided to this method 
        @requires: An initial input image with statistical fluctuations of pixel values must have been created. 

        @warning:    This version only supports the most simple strategy - "strategy 0" 
        -------------    Optimize in one loop - starting from a superposition of fluctuations
                         no intermediate evolutions

        @note: Parameters:
        -----------------
        @param n_epochs: Number of optimization steps  (overwrites previous settings) 
        @param n_steps:  Defines number of intervals (with length n_epochs/ n_steps) for reporting
                         standard value: 6 => 8 images - start image, end image + 6 intermediate 
                         This number also sets a requirement for providing (n_step + 2) external axis-frames 
                         to display intermediate images of the emerging OIP  
                         => see _oip_strat_0_optimization_loop()
        @param epsilon:  Size for corrections by gradient values
        @param conv_criterion: A small threshold number for convegenc (checks:  difference of loss-values / present loss value )
        @param b_stop_with_convergence: 
                         Booelan which decides whether we stop a loop if the conv-criterion is fulfilled
        @param _li_axa: A Python list of references to external (Jupyter-) axes-frames for plotting 
                 
        
        @note: Preparations for plotting: 
        We need n_step + 2 axis-frames which must be provided externally
        
        With Jupyter this can externally be done by statements like 

        # figure
        # -----------
        #sizing
        fig_size = plt.rcParams["figure.figsize"]
        fig_size[0] = 16
        fig_size[1] = 8
        fig_a = plt.figure()
        axa_1 = fig_a.add_subplot(241)
        axa_2 = fig_a.add_subplot(242)
        axa_3 = fig_a.add_subplot(243)
        axa_4 = fig_a.add_subplot(244)
        axa_5 = fig_a.add_subplot(245)
        axa_6 = fig_a.add_subplot(246)
        axa_7 = fig_a.add_subplot(247)
        axa_8 = fig_a.add_subplot(248)
        li_axa = [axa_1, axa_2, axa_3, axa_4, axa_5, axa_6, axa_7, axa_8]
        
        '''
        # Get input parameters
        self._n_epochs  = n_epochs   
        self._n_steps   = n_steps
        self._epsilon   = epsilon
        
        # references to plot frames 
        self._li_axa = li_axa
        num_frames 
= len(li_axa)
        if num_frames < n_steps+2:
            print("The number of available image frames (", num_frames, ") is smaller than required for intermediate output (", n_steps+2, ")")
            sys.exit()
            
        # 2 axes frames to display the final OIP image (with contrast enhancement) 
        self._ax1_1 = ax1_1
        self._ax1_2 = ax1_2
        
        # number of epochs for optimization strategy 0 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if n_epochs == None:
            len_epochs = len(self._ay_epochs)
            self._n_epochs   = self._ay_epochs[len_epochs-1]
        else: 
            self._n_epochs = n_epochs
        
        # Note: No setup of GradientTape and _iterate(required) - this is done by _prepare_precursor 
            
        # get the initial image into a variable for optimization 
        self._inp_img_data = self._initial_inp_img_data

        # Start optimization loop for strategy 0 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if self._oip_strategy == 0: 
            self._oip_strat_0_optimization_loop( conv_criterion = conv_criterion, 
                                                b_stop_with_convergence = b_stop_with_convergence,  
                                                b_show_intermediate_images = b_show_intermediate_images,
                                                b_print = b_print
                                               )
        # Display the last OIP-image created at the end of the optimization loop
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # standardized image 
        oip_img = self._inp_img_data[0,:,:,0].numpy()
        # transfored image 
        oip_img_t = self._transform_tensor_to_img(T_img=self._inp_img_data[0,:,:,0])
        
        # display 
        ax1_1.imshow(oip_img, cmap=plt.cm.get_cmap('viridis'))
        ax1_2.imshow(oip_img_t, cmap=plt.cm.get_cmap('viridis'))
        
        return
    
    
    # 
    # Method to build an initial image from a superposition of random data on different length scales 
    # ***********************************
    def _build_initial_img_data( self, 
                                 strategy = 0, 
                                 li_epochs    = [20, 50, 100, 400], 
                                 li_facts     = [0.5, 0.5, 0.5, 0.5],
                                 li_dim_steps = [ (3,3), (7,7), (14,14), (28,28) ], 
                                 b_smoothing = False,
                                 ax1_1 = None, ax1_2 = None):
        
        '''
        @summary: Standard method to build an initial image with random fluctuations on 4 length scales
        @version: V0.2 of 29.09.2020
        
        @note: This method should NOT be used for initial images based on a precursor images. 
               See _build_initial_img_prec(), instead.  
        
        @note: This method constructs an initial input image with a statistical distribution of pixel-values.
        We use 4 length scales to mix fluctuations with different "wave-length" by a simple approach: 
        We fill four square with a different numer of cells below the number of pixels 
        in each dimension of the real input image; e.g. (4x4), (7x7, (14x14), (28,28) <= (28,28). 
        We fill the cells with random numbers in [-1.0, 1.]. We smootly scale the resulting pattern 
        up to (28,28) (or what ever the input image dimensions are) by bicubic interpolations 
        and eventually add up all values. As a final step we standardize the pixel value distribution.          
        
        @warning: This version works with 4 length scales, only. 
        @warning: In the present version th eparameters "strategy " and li_epochs have no effect 
        
        @note: Parameters:
        -----------------
r
        @param strategy:  The strategy, how to build an image (overwrites previous settings) - presently only 0 is supported 
        @param li_epochs: A list of epoch numbers which will be used in strategy 1 - not yet supported 
        @param li_facts:  A list of factors which the control the relative strength of the 4 fluctuation patterns 
        @param li_dim_steps: A list of square dimensions for setting the length scale of the fluctuations  
        @param b_smoothing: Parameter which builds a control image   
        @param ax1_1: matplotlib axis-frame to display the built image 
        @param ax1_2: matplotlib axis-frame to display a second version of the built image 
        
        '''
        
        # Get input parameters 
        # ~~~~~~~~~~~~~~~~~~
        self._oip_strategy = strategy               # no effect in this version 
        self._ay_epochs    = np.array(li_epochs)    # no effect in this version 
        
        # factors by which to mix the random number fluctuations of the different length scales 
        self._ay_facts     = np.array(li_facts)
        # dimensions of the squares which simulate fluctuations 
        self._li_dim_steps = li_dim_steps
        
        # A Numpy array for the eventual superposition of random data 
        fluct_data = None
        
        
        # Strategy 0: Simple superposition of random patterns at 4 different wave-length
        # ~~~~~~~~~~
        if self._oip_strategy == 0:
            
            dim_1_1 = self._li_dim_steps[0][0] 
            dim_1_2 = self._li_dim_steps[0][1] 
            dim_2_1 = self._li_dim_steps[1][0] 
            dim_2_2 = self._li_dim_steps[1][1] 
            dim_3_1 = self._li_dim_steps[2][0] 
            dim_3_2 = self._li_dim_steps[2][1] 
            dim_4_1 = self._li_dim_steps[3][0] 
            dim_4_2 = self._li_dim_steps[3][1] 
            
            fact1 = self._ay_facts[0]
            fact2 = self._ay_facts[1]
            fact3 = self._ay_facts[2]
            fact4 = self._ay_facts[3]
            
            # print some parameter information
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            print("\nInitial image composition - strategy 0:\n Superposition of 4 different wavelength patterns")
            print("Parameters:\n", 
                 fact1, " => (" + str(dim_1_1) +", " + str(dim_1_2) + ") :: ", 
                 fact2, " => (" + str(dim_2_1) +", " + str(dim_2_2) + ") :: ", 
                 fact3, " => (" + str(dim_3_1) +", " + str(dim_3_2) + ") :: ", 
                 fact4, " => (" + str(dim_4_1) +", " + str(dim_4_2) + ")" 
                 )
            
            # fluctuations
            fluct1 =  2.0 * ( np.random.random((1, dim_1_1, dim_1_2, 1)) - 0.5 ) 
            fluct2 =  2.0 * ( np.random.random((1, dim_2_1, dim_2_2, 1)) - 0.5 ) 
            fluct3 =  2.0 * ( np.random.random((1, dim_3_1, dim_3_2, 1)) - 0.5 ) 
            fluct4 =  2.0 * ( np.random.random((1, dim_4_1, dim_4_2, 1)) - 0.5 ) 
            
            # Scaling with bicubic interpolation to the required image size
            fluct1_scale = tf.image.resize(fluct1, [28,28], method="bicubic", antialias=True)
            fluct2_scale = tf.image.resize(fluct2, [28,28], method="bicubic", antialias=True)
            fluct3_scale = tf.image.resize(fluct3, [28,28], method="bicubic", antialias=True)
            fluct4_scale = fluct4
            
            # superposition
            fluct_data = fact1*fluct1_scale + fact2*fluct2_scale + fact3*fluct3_scale + fact4*fluct4_scale
            
        
        # get the standardized plus smoothed and unsmoothed image 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        #  TF2 provides a function performing standardization of image data function
        fluct_data_unsmoothed = tf.image.per_image_
standardization(fluct_data) 
        fluct_data_smoothed   = tf.image.per_image_standardization(
                                    tf.image.resize( fluct_data, [28,28], method="bicubic", antialias=True) )
        
        if b_smoothing: 
            self._initial_inp_img_data = fluct_data_smoothed
        else:
            self._initial_inp_img_data = fluct_data_unsmoothed
        
        # Display of both variants => there should be no difference 
        # ~~~~~~~~~~~~~~~~~~~~~~~~
        img_init_unsmoothed = fluct_data_unsmoothed[0,:,:,0].numpy()
        img_init_smoothed   = fluct_data_smoothed[0,:,:,0].numpy()
        ax1_1.imshow(img_init_unsmoothed, cmap=plt.cm.get_cmap('viridis'))
        ax1_2.imshow(img_init_smoothed, cmap=plt.cm.get_cmap('viridis'))
        
        print("Initial images plotted")
        
        return self._initial_inp_img_data    


    # 
    # Method to build an initial image from a superposition of a PRECURSOR image with random data on different length scales 
    # ***********************************
    def _build_initial_img_from_prec( self, 
                                 prec_index = -1,
                                 strategy = 0, 
                                 li_epochs    = (20, 50, 100, 400), 
                                 li_facts     = (1.0, 0.0, 0.0, 0.0, 0.0),
                                 li_dim_steps = ( (3,3), (7,7), (14,14), (28,28) ), 
                                 b_smoothing = False,
                                 b_print = True, 
                                 b_display = False, 
                                 ax1_1 = None, ax1_2 = None):
        
        '''
        @summary: Method to build an initial image based on a Precursor image => Input for _derive_OIP_for_Prec_Img()
        @version: V0.3, 03.10.2020
        @changes: V0.2: Minor- only documentation and comparison of index to length of _li_of_flucts[] 
        @changes: V0.3: Added Booleans to control the output and display of images 
        @changes: V0.4: Extended the reconstruction part / extended documentation
        
        @note: This method differs from _build_initial_img_data() as follows:
                * It uses a Precursor image as the fundamental image 
                * The data of the Precursor Image will be reconstructed from a (3x3) fluctuation pattern and enrichments
                * This method adds even further fluctuations if requested 
        @note: This method should be called manually from a Jupyter cell 
        @note: This method saves the reconstructed input image into self._initial_inp_img_data
        @note: This method should be followed by a call of self._derive_OIP_for_Prec_Img()
        
        @requires: Large scale fluctuation data saved in self._li_of_flucts[]
        @requires: Additional enrichment information in self._li_of_fluct_enrichments[]
        
        @param prec_index: This is an index ([0, 7[) of a large scale fluctuation pattern which was saved in self._li_of_flucts[] 
                           during the run of the method "_precursor()". The image tensor is reconstructed from the fluctuation pattern. 
        @warning: We support a maximum of 8 selected fluctuation patterns for which a map reacts 
        @warning: However, less precursor patterns may be found - so you should watch for the output of _precursor() before you run this method
        
        @param li_facts:  A list of factors which the control the relative strength of the precursor image vs. 
                          4 additional fluctuation patterns 
        @warning: Normally, it makes no sense to set li_facts[1] > 0 - because this will destroy the original large scale pattern 
        
        @note: For other input parameters see _build_initial_img_data()
        '''
        
        # Get input parameters 
        self._oip_strategy 
= strategy
        self._ay_facts     = np.array(li_facts)
        self._ay_epochs    = np.array(li_epochs)
        self._li_dim_steps = li_dim_steps
        
        fluct_data = None
        
        # Reconstruct an precursor image from a saved large scale fluctuation pattern (result of _precursor() ) 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        length_li_cov = len(self._li_of_flucts)
        if prec_index > -1: 
            if length_li_cov < prec_index+1:
                print("index too large for number of detected patterns (", length_li_cov, ")")
                sys.exit()
            cov_p = self._li_of_flucts[prec_index][1][1]
            
            fluct0_scale_p = tf.image.resize(cov_p, [28,28], method="bicubic", antialias=True)
            
            # Add fluctuation enrichments - if saved [ len(self._li_fluct_enrichments) > 0 ]
            if len(self._li_fluct_enrichments) > 0:
                # Scaling enrichment flucts with bicubic interpolation to the required image size
                fluct1_p = self._li_fluct_enrichments[2][0] 
                fluct2_p = self._li_fluct_enrichments[2][1] 
                fluct3_p = self._li_fluct_enrichments[2][2] 
                fluct4_p = self._li_fluct_enrichments[2][3] 
                
                fact0_p = self._li_fluct_enrichments[0][0]
                fact1_p = self._li_fluct_enrichments[0][1]
                fact2_p = self._li_fluct_enrichments[0][2]
                fact3_p = self._li_fluct_enrichments[0][3]
                fact4_p = self._li_fluct_enrichments[0][4]
                
                fluct1_scale_p = tf.image.resize(fluct1_p, [28,28], method="bicubic", antialias=True)
                fluct2_scale_p = tf.image.resize(fluct2_p, [28,28], method="bicubic", antialias=True)
                fluct3_scale_p = tf.image.resize(fluct3_p, [28,28], method="bicubic", antialias=True)
                fluct4_scale_p = fluct4_p
                
                fluct_scale_p = fact0_p*fluct0_scale_p \
                 + fact1_p*fluct1_scale_p + fact2_p*fluct2_scale_p \
                 + fact3_p*fluct3_scale_p + fact4_p*fluct4_scale_p
                 
            else: 
                fluct_scale_p = fluct0_scale_p
            
            # get the img-data 
            fluct_data_p  = tf.image.per_image_standardization(fluct_scale_p)     
            fluct_data_p  = tf.where(fluct_data_p > 5.e-6, fluct_data_p, tf.zeros_like(fluct_data_p))
            self._initial_inp_img_data = fluct_data_p
            self._inp_img_data         = fluct_data_p
            
        
        # Strategy 0: Simple superposition of the precursor image AND additional patterns at 4 different wave-length
        # ~~~~~~~~~~
        if self._oip_strategy == 0:
            
            dim_1_1 = self._li_dim_steps[0][0] 
            dim_1_2 = self._li_dim_steps[0][1] 
            dim_2_1 = self._li_dim_steps[1][0] 
            dim_2_2 = self._li_dim_steps[1][1] 
            dim_3_1 = self._li_dim_steps[2][0] 
            dim_3_2 = self._li_dim_steps[2][1] 
            dim_4_1 = self._li_dim_steps[3][0] 
            dim_4_2 = self._li_dim_steps[3][1] 
            
            fact0 = self._ay_facts[0]
            fact1 = self._ay_facts[1]
            fact2 = self._ay_facts[2]
            fact3 = self._ay_facts[3]
            fact4 = self._ay_facts[4]
            
            # print some parameter information
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            if b_print:
                print("\nInitial image composition - strategy 0:\n Superposition of 4 different wavelength patterns")
                print("Parameters:\n", 
                     fact0, " => precursor image \n", 
                     fact1, " => (" + str(dim_1_1) +", " + str(dim_1_2) + ") :: ", 
                  
   fact2, " => (" + str(dim_2_1) +", " + str(dim_2_2) + ") :: ", 
                     fact3, " => (" + str(dim_3_1) +", " + str(dim_3_2) + ") :: ", 
                     fact4, " => (" + str(dim_4_1) +", " + str(dim_4_2) + ")" 
                     )
            
            # fluctuations
            fluct1 =  2.0 * ( np.random.random((1, dim_1_1, dim_1_2, 1)) - 0.5 ) 
            fluct2 =  2.0 * ( np.random.random((1, dim_2_1, dim_2_2, 1)) - 0.5 ) 
            fluct3 =  2.0 * ( np.random.random((1, dim_3_1, dim_3_2, 1)) - 0.5 ) 
            fluct4 =  2.0 * ( np.random.random((1, dim_4_1, dim_4_2, 1)) - 0.5 ) 
            
            # Scaling with bicubic interpolation to the required image size
            fluct1_scale = tf.image.resize(fluct1, [28,28], method="bicubic", antialias=True)
            fluct2_scale = tf.image.resize(fluct2, [28,28], method="bicubic", antialias=True)
            fluct3_scale = tf.image.resize(fluct3, [28,28], method="bicubic", antialias=True)
            fluct4_scale = fluct4
            
            # superposition with the already calculated image 
            fluct_data = fact0 * self._initial_inp_img_data  \
                         + fact1*fluct1_scale + fact2*fluct2_scale \
                         + fact3*fluct3_scale + fact4*fluct4_scale
            
        
        # get the standardized plus smoothed and unsmoothed image 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        #    TF2 provides a function performing standardization of image data function
        fluct_data_unsmoothed = fluct_data 
        fluct_data_smoothed   = tf.image.per_image_standardization(
                                    tf.image.resize( fluct_data, [28,28], 
                                                     method="bicubic", antialias=True) )
        
        if b_smoothing: 
            self._initial_inp_img_data = fluct_data_smoothed
        else:
            self._initial_inp_img_data = fluct_data_unsmoothed
        
        # There should be no difference 
        img_init_unsmoothed = fluct_data_unsmoothed[0,:,:,0].numpy()
        img_init_smoothed   = fluct_data_smoothed[0,:,:,0].numpy()
        
        if b_display:
            ax1_1.imshow(img_init_unsmoothed, cmap=plt.cm.get_cmap('viridis'))
            ax1_2.imshow(img_init_smoothed, cmap=plt.cm.get_cmap('viridis'))
            print("Initial images plotted")
        
        return self._initial_inp_img_data    
    
    #
    # Method to prepare a Precursor run which checks a variety of large scale fluctuations for optimum actvation  
    # ***********************************
    def _prepare_precursor(self, map_index = 120, b_print = False):
        '''
        @summary: A method to prepare a Precursor run by setting up GradientTape and the _ierate() function for an optimization loop
        @version: 0.2, 30.09.2020
        @changes: Minor - adaption to _setup_gradient_tape_and_iterate_function() instead of the obsolete _setup_gradient_tape()
        @requires: A loaded CNN-Model and an already built OIP-model 
        @requires: A valid map-index as input parameter 
        
        @note: This method sets up the GradientTape and _iterate only once 
               - it will not be done again during the investigation of thousands of different input images (with large scale fluctuations) 
               which we investigate during the _precursor()-run. 
        
        @param map_index: Index selecting a map for the CNN layer defined previously by _build_oip_model()
        @param b_print: Boolean - decides about intemediate output 
        
        '''
        
        # Get input parameters 
        # ~~~~~~~~~~~~~~~~~~~~~~
        self._map_index = map_index
        # Rest some variables  
        self._val_oip_grads = None
        self._val_oip_loss  = None 
 
       self._iterate       = None 
        
        # Setup the TF2 GradientTape watch
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self._setup_gradient_tape_and_iterate_function(b_print = b_print)
        if b_print:
            print("GradientTape watch activated and _iterate()-function defined")
    
    
    # Method to prepare a Precursor run which checks a variety of large scale fluctuations for optimum actvation
    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    def _precursor(self, 
                   li_pre_val=[0.2, 0.5, 0.8], 
                   num_epochs=10, 
                   loss_limit = 0.5, 
                   b_print = True, 
                   b_with_enriched_fluct = False, 
                   li_facts     = (1.0, 0.0, 0.0, 0.0, 0.1),
                   li_dim_steps = ( (3,3), (7,7), (14,14), (28,28) ), 
                   b_check = True, 
                   fig_a = None, 
                   li_axa = None,
                   # the next parameters are new in V0.6
                   b_show_test_input_images = False,
                   fig_test_img = None,
                   ax_b = None, 
                   interval_test_img = 1):

        '''
        @summary: Method to investigate thousands of input images with large scale fluctuations for the reaction of a specified map (filters)
                  and a given number of epochs in pattern creation
        @version: 0.6, 12.12.2020
        @changes: V0.5: Minor - documentation, skipped some superfluous statements 
        @changes: V0.6: Added intermediate plot output of constructed input images (a fig_a-reference must have been provided!) 
        @note: We select the 8 most dominant images - or less, if there are fewer input images which trigger the map 
        @requires: Previous run of _prepare_cursor() with a definition of the map-index
        @note: We vary only 3 given pixel values on (3x3) grids (19683 possibilities)
        @note: The optimization loop is completely done within this method - due to performance reasons
        
        @param li_pre_val: A list of three scaled pixel values between ]0, 1[ which shall be combined in (3x3)-fluctuation patterns
        
        @param num_epochs: The number of epochs used in the optimization loop for pattern creation
        @note: It is worthwile to experiment with the number of epochs - the (3x3)-pattern selection may change !!!
        
        @param loss_limit: Threshold of loss for which we register a fluctuation image as relevant 
        
        @param b_print: Boolean - controls printout for intermediate results - useful to see map response 
        @param b_check: Check the response of map for the first saved pattern - check the image reconstruction at the same time
        
        @note: Parameters to enrich the (3x3)-large scale fluctuation with a small scale pattern 
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @param b_with_enriched_fluct: Boolean - controls whether we enrich the long-range pattern with other additional patterns 
        @param li_facts:  A list of factors which the control the relative strength of the precursor image vs. 
                          4 additional fluctuation patterns 
        @param li_dim_steps: A list of square dimensions for setting the length scale of the fluctuations  
        
        @note: Parameters for plotting  
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @param fig_a: reference to the 8 axes-frame 
        @param li_axa: A Python list of references to external (Jupyter-) axes-frames for plotting 
        
        Plots for intermediate test images 
        Note that for inernediate image plotting the cell must have a command line with metacommand 
        %matplotlib notebook
        plt.ion()
        @param b_show_test_input_images = Boolean; show intermediate 
fluctuation patterns 
        @param fig_test_img: reference to external image plot frame. 
        @param ax_b: Rference to axis-frame for the intermediate display of test-images  
        
        @note: Preparations for plotting: 
        ---------------------------------
        fig_b : a simple figure for an image
        fig_a: We need 8 axis-frames which must be provided externally
        With Jupyter this can externally be done by statements like 

        # figure
        # -----------
        fig_b_pre, ax_b_pre = plt.subplots(1, figsize=(3,3))
        fig_b_pre.canvas.draw()
        
        fig_a_pre = plt.figure(2, figsize=(10,5))
        axa_1 = fig_a_pre.add_subplot(241)
        axa_2 = fig_a_pre.add_subplot(242)
        axa_3 = fig_a_pre.add_subplot(243)
        axa_4 = fig_a_pre.add_subplot(244)
        axa_5 = fig_a_pre.add_subplot(245)
        axa_6 = fig_a_pre.add_subplot(246)
        axa_7 = fig_a_pre.add_subplot(247)
        axa_8 = fig_a_pre.add_subplot(248)
        li_axa = [axa_1, axa_2, axa_3, axa_4, aab_5, axa_6, axa_7, axa_8]
        fig_a_pre.canvas.draw()
        
        
        '''
        # Internal parameter for number of selected input patterns 
        num_selected = 8 
        # check if length of li_axa is sufficient
        if li_axa == None or len(li_axa) < num_selected:
            print("Error: The length of the provided list with axes-frames for plotting must be at least ", num_selected )
            sys.exit()
        
        # get required exernal params 
        # ~~~~~~~~~~~~~~~~~~~~~~~~
        self._n_steps   = 2           # only a dummy 
        self._epsilon   = 0.01        # only a dummy  
        
        # number of epochs for optimization strategy 0 
        if num_epochs == None:
            len_epochs = len(self._ay_epochs)
            self._n_epochs   = self._ay_epochs[len_epochs-1]
        else: 
            self._n_epochs = num_epochs  
        
        # Create a fixed random flutution pattern which we later can overlay to the long range fluctuation patterns 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        self._li_dim_steps = li_dim_steps # dimensions for fluctuations 
        self._ay_facts     = np.array(li_facts)
        
        dim_1_1 = self._li_dim_steps[0][0] 
        dim_1_2 = self._li_dim_steps[0][1] 
        dim_2_1 = self._li_dim_steps[1][0] 
        dim_2_2 = self._li_dim_steps[1][1] 
        dim_3_1 = self._li_dim_steps[2][0] 
        dim_3_2 = self._li_dim_steps[2][1] 
        dim_4_1 = self._li_dim_steps[3][0] 
        dim_4_2 = self._li_dim_steps[3][1] 
        
        fact0 = self._ay_facts[0]
        fact1 = self._ay_facts[1]
        fact2 = self._ay_facts[2]
        fact3 = self._ay_facts[3]
        fact4 = self._ay_facts[4]
        
        # Create fluctuation patterns for enrichment 
        fluct1 =  2.0 * ( np.random.random((1, dim_1_1, dim_1_2, 1)) - 0.5 ) 
        fluct2 =  2.0 * ( np.random.random((1, dim_2_1, dim_2_2, 1)) - 0.5 ) 
        fluct3 =  2.0 * ( np.random.random((1, dim_3_1, dim_3_2, 1)) - 0.5 ) 
        fluct4 =  2.0 * ( np.random.random((1, dim_4_1, dim_4_2, 1)) - 0.5 ) 
        
        li_fluct = [fluct1, fluct2, fluct3, fluct4]
        
        # Scaling with bicubic interpolation to the required image size
        fluct1_scale = tf.image.resize(fluct1, [28,28], method="bicubic", antialias=True)
        fluct2_scale = tf.image.resize(fluct2, [28,28], method="bicubic", antialias=True)
        fluct3_scale = tf.image.resize(fluct3, [28,28], method="bicubic", antialias=True)
        fluct4_scale = fluct4

        
        # Create cartesian product of combinatoric possibilities for a (3x3)-grid of long range fluctuations
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        cp = list(product(li_pre_val, repeat=9))
      
  num = len(cp) 
        print ("We test ", num, " possibilities for a (3x3) fluctuations ")
        
        # Prepare lists to save parameter data for the fluctuation pattern 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        # Intermediate list to save relevant long scale fluctuations 
        d_cov = {}
        # list to save parameters for an enrichments of the large scale pattern with small fluctuations
        if b_with_enriched_fluct:
            self._li_fluct_enrichments = [li_facts, li_dim_steps, li_fluct]
        else:
            self._li_fluct_enrichments = []
            
        # Loop to check for relevant fluctuations => Loop over all combinations
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        for i_cp in range(num): 
            
            # create the value distribution 
            cov = np.array(cp[i_cp])
            cov = cov.reshape(1,3,3,1) 

            # create basic image to investigate
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            fluct_scale = tf.image.resize(cov, [28,28], method="bicubic", antialias=True) 
            
            # enrich with additional smallscale fluctuations 
            if b_with_enriched_fluct: 
                # superposition with the already calculated image 
                fluct_scale = fact0 * fluct_scale \
                             + fact1*fluct1_scale + fact2*fluct2_scale \
                             + fact3*fluct3_scale + fact4*fluct4_scale
            
            #standardization of the image data 
            fluct_data  = tf.image.per_image_standardization(fluct_scale)     
            # eliminatng very small values - prove to be helpful in many cases 
            fluct_data = tf.where(fluct_data > 5.e-6, fluct_data, tf.zeros_like(fluct_data))
            
            # save image data 
            self._initial_inp_img_data = fluct_data
            self._inp_img_data         = fluct_data
            
            # Display the present input image 
            if b_show_test_input_images and i_cp%interval_test_img == 0: 
                img_b = fluct_data[0, :,:, 0].numpy()
                ax_b.imshow(img_b, cmap=plt.cm.get_cmap('viridis'))
                fig_test_img.canvas.draw()
            
            # optimization loop 
            # ~~~~~~~~~~~~~~~~~
            for j in range(self._n_epochs):
                # Get output values of our Keras iteration function 
                self._val_oip_loss, self._val_oip_grads = self._iterate([self._inp_img_data])
                # gradient ascent => Correction of the input image data 
                self._inp_img_data += self._val_oip_grads * self._epsilon
                # Standardize the corrected image - we won't get a convergence otherwise 
                self._inp_img_data = tf.image.per_image_standardization(self._inp_img_data)
                
            # Check if we have a loss value > 0.x and save the (3x3)-data
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            if self._val_oip_loss > loss_limit:
                d_cov[i_cp] = [self._val_oip_loss, cov] 
                if b_print:
                    tf.print("i = ", i_cp, " loss = ", self._val_oip_loss)

        # We restrict the number to those 8 with highest loss 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        if len(d_cov) > 0: 
            self._li_of_flucts = sorted(d_cov.items() , reverse = True,  key=lambda x: x[1][0])
            # print("num of relevant covs = ", len(self._li_of_flucts), len(d_cov))   
            print("\nnum of relevant covs = ", len(self._li_of_flucts))   
            self._li_of_flucts = self._li_of_flucts[:num_selected].copy()
            #save( 'li_of_flucts.npy', np.array(self._li_of_flucts, dtype=np.float32) )
   
         save( 'li_of_flucts.npy', self._li_of_flucts)
            # save the enrichment-setting 
            save('li_of_cov_enrichments.npy',self._li_fluct_enrichments)
            
            
            # Check of map really reacted - and check the reconstruction mechanism 
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            if b_check: 
                print("check of map reaction to first selected image")
                cov_t = self._li_of_flucts[0][1][1]
                #print("cov_t-shape = ", cov_t.shape)
                #cov_del = cov_t - cov
                #print("cov_del =\n", cov_del)
                
                fluct0_scale_t = tf.image.resize(cov_t, [28,28], method="bicubic", antialias=True) 
                        
                # Add fluctuation enrichments - if saved
                if b_with_enriched_fluct:
                    
                    # Scaling enrichment flucts with bicubic interpolation to the required image size
                    fluct1_t = self._li_fluct_enrichments[2][0] 
                    fluct2_t = self._li_fluct_enrichments[2][1] 
                    fluct3_t = self._li_fluct_enrichments[2][2] 
                    fluct4_t = self._li_fluct_enrichments[2][3] 
                    
                    fact0_t = self._li_fluct_enrichments[0][0]
                    fact1_t = self._li_fluct_enrichments[0][1]
                    fact2_t = self._li_fluct_enrichments[0][2]
                    fact3_t = self._li_fluct_enrichments[0][3]
                    fact4_t = self._li_fluct_enrichments[0][4]
                    
                    fluct1_scale_t = tf.image.resize(fluct1_t, [28,28], method="bicubic", antialias=True)
                    fluct2_scale_t = tf.image.resize(fluct2_t, [28,28], method="bicubic", antialias=True)
                    fluct3_scale_t = tf.image.resize(fluct3_t, [28,28], method="bicubic", antialias=True)
                    fluct4_scale_t = fluct4_t
                    
                    fluct_scale_t = fact0_t*fluct0_scale_t \
                                 + fact1_t*fluct1_scale_t + fact2_t*fluct2_scale_t \
                                 + fact3_t*fluct3_scale_t + fact4_t*fluct4_scale_t
                    
                else: 
                    fluct_scale_t = fluct0_scale_t
                
                #standardization
                fluct_data_t  = tf.image.per_image_standardization(fluct_scale_t)     
                fluct_data_t  = tf.where(fluct_data_t > 5.e-6, fluct_data_t, tf.zeros_like(fluct_data_t))
                self._initial_inp_img_data = fluct_data_t
                self._inp_img_data         = fluct_data_t
                self._precursor_img        = fluct_data_t
                
                # optimization loop 
                for j in range(self._n_epochs):
                    self._val_oip_loss, self._val_oip_grads = self._iterate([self._inp_img_data])
                    self._inp_img_data += self._val_oip_grads * self._epsilon
                    self._inp_img_data = tf.image.per_image_standardization(self._inp_img_data)
                print("loss for 1st selected img = ", self._val_oip_loss )

            # show the imgs 
            # ~~~~~~~~~~~~~~
            self._display_precursor_imgs(li_axa = li_axa, fig_a = fig_a)
            
        # list contains no patterns 
        else:
            print("No image found !")
    
    
    # Method to display initial fluctuation images identified as objects for OIP creation 
    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    def _display_precursor_imgs(self, li_axa = None, fig_a = None):
        '''
        @summary: Method to display up to 8 selected precursor images 
        @version: 0.2, 02.10.2020
        @change: Only some documentation 
        @note: We first 
reconstruct the image from saved data of the large scale fluctuations 
        @note: We then display the images in externally delivered axes-frames of matplotlib
        @requires: A filled set of valid fluctuation patterns in self._li_of_flucts[][][] - determined by a run of _precursor()
        @requires: Information on fluctuation enrichments in self._li_fluct_enrichments[][] - determined by a _precursor() run
        @requires: A set of axes-frames for plotting - preferably defined in a Jupyter cell calling thi smethod 
        @note: Parameters for plotting  
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        @param _li_axa: A Python list of references to external (Jupyter-) axes-frames for plotting 
         '''
        # length of _li_of_flucts[] vs. length of li_axa
        len_cov = len(self._li_of_flucts)
        if li_axa == None or len(li_axa) < len_cov:
            print("Error: The length of the provided list with axes-frames for plotting must be at least ", len_cov )
            sys.exit()
        
        # Loop to reconstruct and display the found precursor images 
        # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        for j in range(len(self._li_of_flucts)):
            print(j, "loss = ", self._li_of_flucts[j][1][0])
            
            # reconstruct the image from the data of the precursor run 
            # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
            cov = self._li_of_flucts[j][1][1]
            fluct0_scale_t  = tf.image.resize(cov, [28,28], method="bicubic", antialias=True)        
            
            # add enrichments if defined 
            if len(self._li_fluct_enrichments) > 0: 
                # Scaling enrichment flucts with bicubic interpolation to the required image size
                fluct1_t = self._li_fluct_enrichments[2][0] 
                fluct2_t = self._li_fluct_enrichments[2][1] 
                fluct3_t = self._li_fluct_enrichments[2][2] 
                fluct4_t = self._li_fluct_enrichments[2][3] 
                
                fact0_t = self._li_fluct_enrichments[0][0]
                fact1_t = self._li_fluct_enrichments[0][1]
                fact2_t = self._li_fluct_enrichments[0][2]
                fact3_t = self._li_fluct_enrichments[0][3]
                fact4_t = self._li_fluct_enrichments[0][4]
                
                fluct1_scale_t = tf.image.resize(fluct1_t, [28,28], method="bicubic", antialias=True)
                fluct2_scale_t = tf.image.resize(fluct2_t, [28,28], method="bicubic", antialias=True)
                fluct3_scale_t = tf.image.resize(fluct3_t, [28,28], method="bicubic", antialias=True)
                fluct4_scale_t = fluct4_t
                
                fluct_scale_t = fact0_t*fluct0_scale_t \
                             + fact1_t*fluct1_scale_t + fact2_t*fluct2_scale_t \
                             + fact3_t*fluct3_scale_t + fact4_t*fluct4_scale_t
            else:
                fluct_scale_t = fluct0_scale_t                 
            
            fluct_datx  = tf.image.per_image_standardization(fluct_scale_t)     
            fluct_dat  = tf.where(fluct_datx > 5.e-6, fluct_datx, tf.zeros_like(fluct_datx))
            img = fluct_dat[0, :,:, 0].numpy()
            li_axa[j].imshow(img, cmap=plt.cm.get_cmap('viridis'))
        
        fig_a.canvas.draw()
        return
    
    
    # Method to transform an img tensor into a standard image - used for contrast enhancemant  
    # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    def _transform_tensor_to_img(self, T_img = None, centre_move = 0.33, fact = 1.0):
        '''
        @summary: Method to transform (standardized) tensor img data into standard img array data 
                  and to apply contrast enhancement(> V0.2)
        @change: V0.2: Additional 
parameers to control contrast enhancement. 
                 We scale the the value distribution, move its center and apply some clipping  
        @note: Clipping is used to remove pixel values outside [0, 255] 
        @version: 0.2, 12.10.2020
        
        @requires: A defined TF2/Keras backend 
        
        @param T_img: The TF2 or keras tensor for image data 
        @param centre_move: A decimal to move the centre of the pixel value distribution  
        
        
        '''
        ay_x = T_img.numpy()  # floating point array  
        
        maxi_o    = np.max(T_img)
        avg_o     = np.mean(T_img)
        mini_o    = np.min(T_img)
        std_dev_o = np.std(T_img)
        print("\nInfos on pixel value distribution during contrast enhancement: ") 
        print("\max_orig = ", maxi_o, " :: avg_orig = ", avg_o, " :: min_orig: ", mini_o) 
        print("std_dev_orig = ", std_dev_o)

        # the following operation should have no effect on standardized images
        ay_x -= ay_x.mean()
        ay_x /= (ay_x.std() + B.epsilon())
        
        maxi    = np.max(ay_x)
        avg     = np.mean(ay_x)
        mini    = np.min(ay_x)
        std_dev = np.std(ay_x)
        print("max_ay = ", maxi, " :: avg_ay = ", avg, " :: min_ay: ", mini) 
        print("std_dev_ay = ", std_dev)
        
        div = fact * 0.5 * ( abs(maxi_o) + abs(mini_o) )
        print("div = ", div)
        ay_x /= div          # scaling  
        ay_x += centre_move  # moving the data center - 0.5 would move of the distribution into [0,1]
        #                    # smaller values emphasize light/dark contratss 
        maxi = np.max(ay_x)
        avg  = np.mean(ay_x)
        mini = np.min(ay_x)
        std_dev = np.std(ay_x)
        print("max_fin = ", maxi, " :: avg_fin = ", avg, " :: min_fin: ", mini) 
        print("std_dev_fin = ", std_dev)
        
        ay_x = np.clip(ay_x, 0, 1)
        
        ay_x *= 255
        ay_x_img = np.clip(ay_x, 0, 255).astype('uint8')
        
        maxi = np.max(ay_x_img)
        avg  = np.mean(ay_x_img)
        mini = np.min(ay_x_img)
        std_dev = np.std(ay_x_img)
        print("max_img = ", maxi, " :: avg_img = ", avg, " :: min_img: ", mini) 
        print("std_dev_img = ", std_dev, "\n")
        
        
        return ay_x_img

Links

A simple CNN for the MNIST dataset – XI – Python code for filter visualization and OIP detection

Linux-Blog – Dr. Mönchmeyer / anracon

Notes about Linux, ML and some simple math …

Tag Archives: convolutional layers

Autoencoders and latent space fragmentation – I – Encoder, Decoder, latent space

Abilities of Autoencoders and the question of a creative application of AEs

Variational Autoencoder with Tensorflow – XI – image creation by a VAE trained on CelebA

Characteristics of the VAE tested

Results for z-points with coordinates taken from a normal distribution around the origin of the latent space

Enhancement processing of the images ?

Sharpening by PIL’s enhancement functionality

The effect of PIL’s sharpening factor

Assessment

Further examples – with PIL sharpening

Reconstruction quality of a VAE vs. an AE – or the “female” side of myself

Dependency of the creation of reasonable images on the distance from the origin

Conclusion

Deep Dreams of a CNN trained on MNIST data – II – some code for pattern carving

Carving: A combination of low-resolution OIP-pattern creation and a reproduction of high-resolution details

Carving – amplification of certain OIP structures and intermittent replenishment of details of the original image

Start with loading required modules and involving your graphics card

Turn the original image into a gray one, downscale it and calculate difference-tensors for coarsely re-enlarged versions

OIP-Carving and detail replenishment

Results of the carving process

Conclusion

My_OIP class – V0.65

Links