# Understanding Neural Style Transfer with Tensorflow and Keras

Neural Style Transfer (NST)  is a fascinating area of Deep Learning and Convolutional Neural Networks. NST is an interesting technique, in which the style from an image, known as the ‘style image’ is transferred to another image ‘content image’ and we get a third a image which is a generated image which has the content of the original image and the style of another image.

NST can be used to reimagine how famous painters like Van Gogh, Claude Monet or a Picasso would have visualised a scenery or architecture. NST uses Convolutional Neural Networks (CNNs) to achieve this artistic style transfer from one image to another. NST was originally implemented by Gati et al., in their paper Neural Algorithm of Artistic Style. Convolutional Neural Networks have been very successful in image classification image recognition et cetera. CNN networks have also been have also generated very interesting pictures using Neural Style Transfer which will be shown in this post. An interesting aspect of CNN’s is that the first couple of layers in the CNN capture basic features of the image like edges and  pixel values. But as we go deeper into the CNN, the network captures higher level features of the input image.

To get started with Neural Style transfer  we will be using the VGG19 pre-trained network. The VGG19 CNN is a compact pre-trained your network which can be used for performing the NST. However, we could have also used Resnet or InceptionV3 networks for this purpose but these are very large networks. The idea of using a network trained on a different task and applying it to a new task is called transfer learning.

What needs to be done to transfer the style from one of the image to another image. This brings us to the question – What is ‘style’? What is it that distinguishes Van Gogh’s painting or Picasso’s cubist art. Convolutional Neural Networks capture basic features in the lower layers and much more complex features in the deeper layers.  Style can be computed by taking the correlation of the feature maps in a layer L. This is my interpretation of how style is captured.  Since style  is intrinsic to  the image, it  implies that the style feature would exist across all the filters in a layer. Hence, to pick up this style we would need to get the correlation of the filters across channels of a lawyer. This is computed mathematically, using the Gram matrix which calculates the correlation of the activation of a the filter by the style image and generated image

To transfer the style from one image to the content image we need to do two parallel operations while doing forward propagation
– Compute the content loss between the source image and the generated image
– Compute the style loss between the style image and the generated image
– Finally we need to compute the total loss

In order to get transfer the style from the ‘style’ image to the ‘content ‘image resulting in a  ‘generated’  image  the total loss has to be minimised. Therefore backward propagation with gradient descent  is done to minimise the total loss comprising of the content and style loss.

Initially we make the Generated Image ‘G’ the same as the source image ‘S’

The content loss at layer ‘l’

$L_{content} = 1/2 \sum_{i}^{j} ( F^{l}_{i,j} - P^{l}_{i,j})^{2}$

where $F^{l}_{i,j}$ and $P^{l}_{i,j}$ represent the activations at layer ‘l’ in a filter i, at position ‘j’. The intuition is that the activations will be same for similar source and generated image. We need to minimise the content loss so that the generated stylized image is as close to the original image as possible. An intermediate layer of VGG19 block5_conv2 is used

The Style layers that are are used are

style_layers = [‘block1_conv1’,
‘block2_conv1’,
‘block3_conv1’,
‘block4_conv1’,
‘block5_conv1’]
To compute the Style Loss the Gram matrix needs to be computed. The Gram Matrix is computed by unrolling the filters as shown below (source: Convolutional Neural Networks by Prof Andrew Ng, Coursera). The result is a matrix of size $n_{c}$ x $n_{c}$ where $n_{c}$ is the number of channels
The above diagram shows the filters of height $n_{H}$ and width $n_{W}$ with $n_{C}$ channels
The contribution of layer ‘l’ to style loss is given by
$L^{'}_{style} = \frac{\sum_{i}^{j} (G^{2}_{i,j} - A^l{i,j})^2}{4N^{2}_{l}M^{2}_{l}}$
where $G_{i,j}$  and $A_{i,j}$ are the Gram matrices of the style and generated images respectively. By minimising the distance in the gram matrices of the style and generated image we can ensure that generated image is a stylized version of the original image similar to the style image
The total loss is given by
$L_{total} = \alpha L_{content} + \beta L_{style}$
Back propagation with gradient descent works to minimise the content loss between the source and generated image, while the style loss tries to minimise the discrepancies in the style of the style image and generated image. Running through forward and backpropagation through several epochs successfully transfers the style from the style image to the source image.
You can check the Notebook at Neural Style Transfer

Note: The code in this notebook is largely based on the Neural Style Transfer tutorial from Tensorflow, though I may have taken some changes from other blogs. I also made a few changes to the code in this tutorial, like removing the scaling factor, or the class definition (Personally, I belong to the old school (C language) and am not much in love with the ‘self.”..All references are included below

Note: Here is a interesting thought. Could we do a Neural Style Transfer in music? Imagine Carlos Santana playing ‘Hotel California’ or Brian May style in ‘Another brick in the wall’. While our first reaction would be that it may not sound good as we are used to style of these songs, we may be surprised by a possible style transfer. This is definitely music to the ears!

Here are few runs from this

## A) Run 1

1. Neural Style Transfer – a) Content Image – My portrait.  b) Style Image – Wassily Kadinsky Oil on canvas, 1913, Vassily Kadinsky’s composition

2. Result of Neural Style Transfer

2) Run 2

a) Content Image – Portrait of my parents b) Style Image –  Vincent Van Gogh’s ,Starry Night Oil on canvas 1889

2. Result of Neural Style Transfer

## Run 3

1.  Content Image – Caesar 2 (Masai Mara- 20 Jun 2018).  Style Image – The Great Wave at Kanagawa – Katsushika Hokosai, 1826-1833

2. Result of Neural Style Transfer

## Run 4

1.   Content Image – Junagarh Fort , Rajasthan   Sep 2016              b) Style Image – Le Pont Japonais by Claude Monet, Oil on canvas, 1920

2. Result of Neural Style Transfer

Neural Style Transfer is a very ingenious idea which shows that we can segregate the style of a painting and transfer to another image.

### References

1. A Neural Algorithm of Artistic Style, Leon A. Gatys, Alexander S. Ecker, Matthias Bethge
2. Neural style transfer
3. Neural Style Transfer: Creating Art with Deep Learning using tf.keras and eager execution
4. Convolutional Neural Network, DeepLearning.AI Specialization, Prof Andrew Ng
5. Intuitive Guide to Neural Style Transfer