吴恩达深度学习课程deeplearning.ai课程作业：Class 4 Week 4 Art Generation with Neural Style Transfer
吳恩達deeplearning.ai課程作業(yè)，自己寫的答案。
補充說明：
1. 評論中總有人問為什么直接復制這些notebook運行不了？請不要直接復制粘貼，不可能運行通過的，這個只是notebook中我們要自己寫的那部分，要正確運行還需要其他py文件，請自己到GitHub上下載完整的。這里的部分僅僅是參考用的，建議還是自己按照提示一點一點寫，如果實在卡住了再看答案。個人覺得這樣才是正確的學習方法，況且作業(yè)也不算難。
2. 關于評論中有人說我是抄襲，注釋還沒別人詳細，復制下來還運行不過。答復是：做伸手黨之前，請先搞清這個作業(yè)是干什么的。大家都是從GitHub上下載原始的作業(yè)，然后根據(jù)代碼前面的提示（通常會指定函數(shù)和公式）來編寫代碼，而且后面還有expected output供你比對，如果程序正確，結果一般來說是一樣的。請不要無腦噴，說什么跟別人的答案一樣的。說到底，我們要做的就是，看他的文字部分，根據(jù)提示在代碼中加入部分自己的代碼。我們自己要寫的部分只有那么一小部分代碼。
3. 由于實在很反感無腦噴子，故禁止了下面的評論功能，請見諒。如果有問題，請私信我，在力所能及的范圍內會盡量幫忙。
注：作業(yè)中要使用vgg的預訓練模型imagenet-vgg-verydeep-19.mat，下面給出百度云鏈接：
鏈接：https://pan.baidu.com/s/1slYrvqt 密碼：6cy1
Deep Learning & Art: Neural Style Transfer
Welcome to the second assignment of this week. In this assignment, you will learn about Neural Style Transfer. This algorithm was created by Gatys et al. (2015) (https://arxiv.org/abs/1508.06576).
In this assignment, you will:
- Implement the neural style transfer algorithm
- Generate novel artistic images using your algorithm
Most of the algorithms you’ve studied optimize a cost function to get a set of parameter values. In Neural Style Transfer, you’ll optimize a cost function to get pixel values!
import os import sys import scipy.io import scipy.misc import matplotlib.pyplot as plt from matplotlib.pyplot import imshow from PIL import Image from nst_utils import * import numpy as np import tensorflow as tf%matplotlib inline1 - Problem Statement
Neural Style Transfer (NST) is one of the most fun techniques in deep learning. As seen below, it merges two images, namely, a “content” image (C) and a “style” image (S), to create a “generated” image (G). The generated image G combines the “content” of the image C with the “style” of image S.
In this example, you are going to generate an image of the Louvre museum in Paris (content image C), mixed with a painting by Claude Monet, a leader of the impressionist movement (style image S).
Let’s see how you can do this.
2 - Transfer Learning
Neural Style Transfer (NST) uses a previously trained convolutional network, and builds on top of that. The idea of using a network trained on a different task and applying it to a new task is called transfer learning.
Following the original NST paper (https://arxiv.org/abs/1508.06576), we will use the VGG network. Specifically, we’ll use VGG-19, a 19-layer version of the VGG network. This model has already been trained on the very large ImageNet database, and thus has learned to recognize a variety of low level features (at the earlier layers) and high level features (at the deeper layers).
Run the following code to load parameters from the VGG model. This may take a few seconds.
model = load_vgg_model("pretrained-model/imagenet-vgg-verydeep-19.mat") print(model) {'conv1_2': <tf.Tensor 'Relu_17:0' shape=(1, 300, 400, 64) dtype=float32>, 'conv5_4': <tf.Tensor 'Relu_31:0' shape=(1, 19, 25, 512) dtype=float32>, 'conv3_2': <tf.Tensor 'Relu_21:0' shape=(1, 75, 100, 256) dtype=float32>, 'conv4_4': <tf.Tensor 'Relu_27:0' shape=(1, 38, 50, 512) dtype=float32>, 'conv5_1': <tf.Tensor 'Relu_28:0' shape=(1, 19, 25, 512) dtype=float32>, 'conv1_1': <tf.Tensor 'Relu_16:0' shape=(1, 300, 400, 64) dtype=float32>, 'conv5_2': <tf.Tensor 'Relu_29:0' shape=(1, 19, 25, 512) dtype=float32>, 'conv2_1': <tf.Tensor 'Relu_18:0' shape=(1, 150, 200, 128) dtype=float32>, 'conv5_3': <tf.Tensor 'Relu_30:0' shape=(1, 19, 25, 512) dtype=float32>, 'input': <tf.Variable 'Variable_1:0' shape=(1, 300, 400, 3) dtype=float32_ref>, 'conv4_1': <tf.Tensor 'Relu_24:0' shape=(1, 38, 50, 512) dtype=float32>, 'conv3_4': <tf.Tensor 'Relu_23:0' shape=(1, 75, 100, 256) dtype=float32>, 'avgpool2': <tf.Tensor 'AvgPool_6:0' shape=(1, 75, 100, 128) dtype=float32>, 'conv3_1': <tf.Tensor 'Relu_20:0' shape=(1, 75, 100, 256) dtype=float32>, 'conv4_2': <tf.Tensor 'Relu_25:0' shape=(1, 38, 50, 512) dtype=float32>, 'conv3_3': <tf.Tensor 'Relu_22:0' shape=(1, 75, 100, 256) dtype=float32>, 'avgpool5': <tf.Tensor 'AvgPool_9:0' shape=(1, 10, 13, 512) dtype=float32>, 'avgpool1': <tf.Tensor 'AvgPool_5:0' shape=(1, 150, 200, 64) dtype=float32>, 'conv4_3': <tf.Tensor 'Relu_26:0' shape=(1, 38, 50, 512) dtype=float32>, 'avgpool4': <tf.Tensor 'AvgPool_8:0' shape=(1, 19, 25, 512) dtype=float32>, 'conv2_2': <tf.Tensor 'Relu_19:0' shape=(1, 150, 200, 128) dtype=float32>, 'avgpool3': <tf.Tensor 'AvgPool_7:0' shape=(1, 38, 50, 256) dtype=float32>}The model is stored in a python dictionary where each variable name is the key and the corresponding value is a tensor containing that variable’s value. To run an image through this network, you just have to feed the image to the model. In TensorFlow, you can do so using the tf.assign function. In particular, you will use the assign function like this:
model["input"].assign(image)This assigns the image as an input to the model. After this, if you want to access the activations of a particular layer, say layer 4_2 when the network is run on this image, you would run a TensorFlow session on the correct tensor conv4_2, as follows:
sess.run(model["conv4_2"])3 - Neural Style Transfer
We will build the NST algorithm in three steps:
- Build the content cost function Jcontent(C,G)Jcontent(C,G)
- Build the style cost function Jstyle(S,G)Jstyle(S,G)
- Put it together to get J(G)=αJcontent(C,G)+βJstyle(S,G)J(G)=αJcontent(C,G)+βJstyle(S,G).
3.1 - Computing the content cost
In our running example, the content image C will be the picture of the Louvre Museum in Paris. Run the code below to see a picture of the Louvre.
content_image = scipy.misc.imread("images/louvre.jpg") imshow(content_image) <matplotlib.image.AxesImage at 0x7fc36924e0f0>The content image (C) shows the Louvre museum’s pyramid surrounded by old Paris buildings, against a sunny sky with a few clouds.
* 3.1.1 - How do you ensure the generated image G matches the content of the image C?*
As we saw in lecture, the earlier (shallower) layers of a ConvNet tend to detect lower-level features such as edges and simple textures, and the later (deeper) layers tend to detect higher-level features such as more complex textures as well as object classes.
We would like the “generated” image G to have similar content as the input image C. Suppose you have chosen some layer’s activations to represent the content of an image. In practice, you’ll get the most visually pleasing results if you choose a layer in the middle of the network–neither too shallow nor too deep. (After you have finished this exercise, feel free to come back and experiment with using different layers, to see how the results vary.)
So, suppose you have picked one particular hidden layer to use. Now, set the image C as the input to the pretrained VGG network, and run forward propagation. Let a(C)a(C) be the hidden layer activations in the layer you had chosen. (In lecture, we had written this as a[l](C)a[l](C), but here we’ll drop the superscript [l][l] to simplify the notation.) This will be a nH×nW×nCnH×nW×nC tensor. Repeat this process with the image G: Set G as the input, and run forward progation. Let
a(G)a(G) be the corresponding hidden layer activation. We will define as the content cost function as:Jcontent(C,G)=14×nH×nW×nC∑all entries(a(C)?a(G))2(1)(1)Jcontent(C,G)=14×nH×nW×nC∑all entries(a(C)?a(G))2
Here, nH,nWnH,nW and nCnC are the height, width and number of channels of the hidden layer you have chosen, and appear in a normalization term in the cost. For clarity, note that a(C)a(C) and a(G)a(G) are the volumes corresponding to a hidden layer’s activations. In order to compute the cost Jcontent(C,G)Jcontent(C,G), it might also be convenient to unroll these 3D volumes into a 2D matrix, as shown below. (Technically this unrolling step isn’t needed to compute JcontentJcontent, but it will be good practice for when you do need to carry out a similar operation later for computing the style const JstyleJstyle.)
Exercise: Compute the “content cost” using TensorFlow.
Instructions: The 3 steps to implement this function are:
1. Retrieve dimensions from a_G:
- To retrieve dimensions from a tensor X, use: X.get_shape().as_list()
2. Unroll a_C and a_G as explained in the picture above
- If you are stuck, take a look at Hint1 and Hint2.
3. Compute the content cost:
- If you are stuck, take a look at Hint3, Hint4 and Hint5.
Expected Output:
| J_content | 6.76559 |
What you should remember:
- The content cost takes a hidden layer activation of the neural network, and measures how different a(C)a(C) and a(G)a(G) are.
- When we minimize the content cost later, this will help make sure GG has similar content as CC.
3.2 - Computing the style cost
For our running example, we will use the following style image:
style_image = scipy.misc.imread("images/monet_800600.jpg") imshow(style_image) <matplotlib.image.AxesImage at 0x7fc369506da0>This painting was painted in the style of impressionism.
Lets see how you can now define a “style” const function Jstyle(S,G)Jstyle(S,G).
3.2.1 - Style matrix
The style matrix is also called a “Gram matrix.” In linear algebra, the Gram matrix G of a set of vectors (v1,…,vn)(v1,…,vn) is the matrix of dot products, whose entries are Gij=vTivj=np.dot(vi,vj)Gij=viTvj=np.dot(vi,vj). In other words, GijGij compares how similar vivi is to vjvj: If they are highly similar, you would expect them to have a large dot product, and thus for GijGij to be large.
Note that there is an unfortunate collision in the variable names used here. We are following common terminology used in the literature, but GG is used to denote the Style matrix (or Gram matrix) as well as to denote the generated image GG. We will try to make sure which GG we are referring to is always clear from the context.
In NST, you can compute the Style matrix by multiplying the “unrolled” filter matrix with their transpose:
The result is a matrix of dimension (nC,nC)(nC,nC) where nCnC is the number of filters. The value GijGij measures how similar the activations of filter ii are to the activations of filter jj.
One important part of the gram matrix is that the diagonal elements such as GiiGii also measures how active filter ii is. For example, suppose filter ii is detecting vertical textures in the image. Then GiiGii measures how common vertical textures are in the image as a whole: If GiiGii is large, this means that the image has a lot of vertical texture.
By capturing the prevalence of different types of features (GiiGii), as well as how much different features occur together (GijGij), the Style matrix GG measures the style of an image.
Exercise:
Using TensorFlow, implement a function that computes the Gram matrix of a matrix A. The formula is: The gram matrix of A is GA=AATGA=AAT. If you are stuck, take a look at Hint 1 and Hint 2.
Expected Output:
| GA | [[ 6.42230511 -4.42912197 -2.09668207] [ -4.42912197 19.46583748 19.56387138] [ -2.09668207 19.56387138 20.6864624 ]] |
3.2.2 - Style cost
After generating the Style matrix (Gram matrix), your goal will be to minimize the distance between the Gram matrix of the “style” image S and that of the “generated” image G. For now, we are using only a single hidden layer a[l]a[l], and the corresponding style cost for this layer is defined as:
J[l]style(S,G)=14×nC2×(nH×nW)2∑i=1nC∑j=1nC(G(S)ij?G(G)ij)2(2)(2)Jstyle[l](S,G)=14×nC2×(nH×nW)2∑i=1nC∑j=1nC(Gij(S)?Gij(G))2
where G(S)G(S) and G(G)G(G) are respectively the Gram matrices of the “style” image and the “generated” image, computed using the hidden layer activations for a particular hidden layer in the network.
Exercise: Compute the style cost for a single layer.
Instructions: The 3 steps to implement this function are:
1. Retrieve dimensions from the hidden layer activations a_G:
- To retrieve dimensions from a tensor X, use: X.get_shape().as_list()
2. Unroll the hidden layer activations a_S and a_G into 2D matrices, as explained in the picture above.
- You may find Hint1 and Hint2 useful.
3. Compute the Style matrix of the images S and G. (Use the function you had previously written.)
4. Compute the Style cost:
- You may find Hint3, Hint4 and Hint5 useful.
Expected Output:
| J_style_layer | 9.19028 |
3.2.3 Style Weights
So far you have captured the style from only one layer. We’ll get better results if we “merge” style costs from several different layers. After completing this exercise, feel free to come back and experiment with different weights to see how it changes the generated image GG. But for now, this is a pretty reasonable default:
STYLE_LAYERS = [('conv1_1', 0.2),('conv2_1', 0.2),('conv3_1', 0.2),('conv4_1', 0.2),('conv5_1', 0.2)]You can combine the style costs for different layers as follows:
Jstyle(S,G)=∑lλ[l]J[l]style(S,G)Jstyle(S,G)=∑lλ[l]Jstyle[l](S,G)
where the values for λ[l]λ[l] are given in STYLE_LAYERS.
We’ve implemented a compute_style_cost(…) function. It simply calls your compute_layer_style_cost(...) several times, and weights their results using the values in STYLE_LAYERS. Read over it to make sure you understand what it’s doing.
def compute_style_cost(model, STYLE_LAYERS):"""Computes the overall style cost from several chosen layersArguments:model -- our tensorflow modelSTYLE_LAYERS -- A python list containing:- the names of the layers we would like to extract style from- a coefficient for each of themReturns: J_style -- tensor representing a scalar value, style cost defined above by equation (2)"""# initialize the overall style costJ_style = 0for layer_name, coeff in STYLE_LAYERS:# Select the output tensor of the currently selected layerout = model[layer_name]# Set a_S to be the hidden layer activation from the layer we have selected, by running the session on outa_S = sess.run(out)# Set a_G to be the hidden layer activation from same layer. Here, a_G references model[layer_name] # and isn't evaluated yet. Later in the code, we'll assign the image G as the model input, so that# when we run the session, this will be the activations drawn from the appropriate layer, with G as input.a_G = out# Compute style_cost for the current layerJ_style_layer = compute_layer_style_cost(a_S, a_G)# Add coeff * J_style_layer of this layer to overall style costJ_style += coeff * J_style_layerreturn J_styleNote: In the inner-loop of the for-loop above, a_G is a tensor and hasn’t been evaluated yet. It will be evaluated and updated at each iteration when we run the TensorFlow graph in model_nn() below.
What you should remember:
- The style of an image can be represented using the Gram matrix of a hidden layer’s activations. However, we get even better results combining this representation from multiple different layers. This is in contrast to the content representation, where usually using just a single hidden layer is sufficient.
- Minimizing the style cost will cause the image GG to follow the style of the image SS.
3.3 - Defining the total cost to optimize
Finally, let’s create a cost function that minimizes both the style and the content cost. The formula is:
J(G)=αJcontent(C,G)+βJstyle(S,G)J(G)=αJcontent(C,G)+βJstyle(S,G)
Exercise: Implement the total cost function which includes both the content cost and the style cost.
# GRADED FUNCTION: total_costdef total_cost(J_content, J_style, alpha = 10, beta = 40):"""Computes the total cost functionArguments:J_content -- content cost coded aboveJ_style -- style cost coded abovealpha -- hyperparameter weighting the importance of the content costbeta -- hyperparameter weighting the importance of the style costReturns:J -- total cost as defined by the formula above."""### START CODE HERE ### (≈1 line)J = J_content * alpha + J_style * beta### END CODE HERE ###return J tf.reset_default_graph()with tf.Session() as test:np.random.seed(3)J_content = np.random.randn() J_style = np.random.randn()J = total_cost(J_content, J_style)print("J = " + str(J)) J = 35.34667875478276Expected Output:
| J | 35.34667875478276 |
What you should remember:
- The total cost is a linear combination of the content cost Jcontent(C,G)Jcontent(C,G) and the style cost Jstyle(S,G)Jstyle(S,G)
- αα and ββ are hyperparameters that control the relative weighting between content and style
4 - Solving the optimization problem
Finally, let’s put everything together to implement Neural Style Transfer!
Here’s what the program will have to do:
- Run the content image through the VGG16 model and compute the content cost
- Run the style image through the VGG16 model and compute the style cost
- Compute the total cost
- Define the optimizer and the learning rate
Lets go through the individual steps in detail.
You’ve previously implemented the overall cost J(G)J(G). We’ll now set up TensorFlow to optimize this with respect to GG<script type="math/tex" id="MathJax-Element-60">G</script>. To do so, your program has to reset the graph and use an “Interactive Session“. Unlike a regular session, the “Interactive Session” installs itself as the default session to build a graph. This allows you to run variables without constantly needing to refer to the session object, which simplifies the code.
Lets start the interactive session.
# Reset the graph tf.reset_default_graph()# Start interactive session sess = tf.InteractiveSession()Let’s load, reshape, and normalize our “content” image (the Louvre museum picture):
content_image = scipy.misc.imread("images/louvre_small.jpg") content_image = reshape_and_normalize_image(content_image)Let’s load, reshape and normalize our “style” image (Claude Monet’s painting):
style_image = scipy.misc.imread("images/monet.jpg") style_image = reshape_and_normalize_image(style_image)Now, we initialize the “generated” image as a noisy image created from the content_image. By initializing the pixels of the generated image to be mostly noise but still slightly correlated with the content image, this will help the content of the “generated” image more rapidly match the content of the “content” image. (Feel free to look in nst_utils.py to see the details of generate_noise_image(...); to do so, click “File–>Open…” at the upper-left corner of this Jupyter notebook.)
generated_image = generate_noise_image(content_image) imshow(generated_image[0]) <matplotlib.image.AxesImage at 0x7fc286ba1c50>Next, as explained in part (2), let’s load the VGG16 model.
model = load_vgg_model("pretrained-model/imagenet-vgg-verydeep-19.mat")To get the program to compute the content cost, we will now assign a_C and a_G to be the appropriate hidden layer activations. We will use layer conv4_2 to compute the content cost. The code below does the following:
Note: At this point, a_G is a tensor and hasn’t been evaluated. It will be evaluated and updated at each iteration when we run the Tensorflow graph in model_nn() below.
# Assign the input of the model to be the "style" image sess.run(model['input'].assign(style_image))# Compute the style cost J_style = compute_style_cost(model, STYLE_LAYERS)Exercise: Now that you have J_content and J_style, compute the total cost J by calling total_cost(). Use alpha = 10 and beta = 40.
### START CODE HERE ### (1 line) J = total_cost(J_content, J_style, alpha = 10, beta = 40) ### END CODE HERE ###You’d previously learned how to set up the Adam optimizer in TensorFlow. Lets do that here, using a learning rate of 2.0. See reference
# define optimizer (1 line) optimizer = tf.train.AdamOptimizer(2.0)# define train_step (1 line) train_step = optimizer.minimize(J)Exercise: Implement the model_nn() function which initializes the variables of the tensorflow graph, assigns the input image (initial generated image) as the input of the VGG16 model and runs the train_step for a large number of steps.
def model_nn(sess, input_image, num_iterations = 200):# Initialize global variables (you need to run the session on the initializer)### START CODE HERE ### (1 line)sess.run(tf.global_variables_initializer())### END CODE HERE #### Run the noisy input image (initial generated image) through the model. Use assign().### START CODE HERE ### (1 line)sess.run(model['input'].assign(input_image))### END CODE HERE ###for i in range(num_iterations):# Run the session on the train_step to minimize the total cost### START CODE HERE ### (1 line)sess.run(train_step)### END CODE HERE #### Compute the generated image by running the session on the current model['input']### START CODE HERE ### (1 line)generated_image = sess.run(model['input'])### END CODE HERE #### Print every 20 iteration.if i%20 == 0:Jt, Jc, Js = sess.run([J, J_content, J_style])print("Iteration " + str(i) + " :")print("total cost = " + str(Jt))print("content cost = " + str(Jc))print("style cost = " + str(Js))# save current generated image in the "/output" directorysave_image("output/" + str(i) + ".png", generated_image)# save last generated imagesave_image('output/generated_image.jpg', generated_image)return generated_imageRun the following cell to generate an artistic image. It should take about 3min on CPU for every 20 iterations but you start observing attractive results after ≈140 iterations. Neural Style Transfer is generally trained using GPUs.
model_nn(sess, generated_image) Iteration 0 : total cost = 5.0224e+09 content cost = 7886.73 style cost = 1.25558e+08Expected Output:
| Iteration 0 : | total cost = 5.05035e+09 content cost = 7877.67 style cost = 1.26257e+08 |
You’re done! After running this, in the upper bar of the notebook click on “File” and then “Open”. Go to the “/output” directory to see all the saved images. Open “generated_image” to see the generated image! :)
You should see something the image presented below on the right:
We didn’t want you to wait too long to see an initial result, and so had set the hyperparameters accordingly. To get the best looking results, running the optimization algorithm longer (and perhaps with a smaller learning rate) might work better. After completing and submitting this assignment, we encourage you to come back and play more with this notebook, and see if you can generate even better looking images.
Here are few other examples:
- The beautiful ruins of the ancient city of Persepolis (Iran) with the style of Van Gogh (The Starry Night)
- The tomb of Cyrus the great in Pasargadae with the style of a Ceramic Kashi from Ispahan.
- A scientific study of a turbulent fluid with the style of a abstract blue fluid painting.
5 - Test with your own image (Optional/Ungraded)
Finally, you can also rerun the algorithm on your own images!
To do so, go back to part 4 and change the content image and style image with your own pictures. In detail, here’s what you should do:
to:
content_image = scipy.misc.imread("images/my_content.jpg") style_image = scipy.misc.imread("images/my_style.jpg")You can also tune your hyperparameters:
- Which layers are responsible for representing the style? STYLE_LAYERS
- How many iterations do you want to run the algorithm? num_iterations
- What is the relative weighting between content and style? alpha/beta
6 - Conclusion
Great job on completing this assignment! You are now able to use Neural Style Transfer to generate artistic images. This is also your first time building a model in which the optimization algorithm updates the pixel values rather than the neural network’s parameters. Deep learning has many different types of models and this is only one of them!
What you should remember:
- Neural Style Transfer is an algorithm that given a content image C and a style image S can generate an artistic image
- It uses representations (hidden layer activations) based on a pretrained ConvNet.
- The content cost function is computed using one hidden layer’s activations.
- The style cost function for one layer is computed using the Gram matrix of that layer’s activations. The overall style cost function is obtained using several hidden layers.
- Optimizing the total cost function results in synthesizing new images.
This was the final programming exercise of this course. Congratulations–you’ve finished all the programming exercises of this course on Convolutional Networks! We hope to also see you in Course 5, on Sequence models!
References:
The Neural Style Transfer algorithm was due to Gatys et al. (2015). Harish Narayanan and Github user “l(fā)og0” also have highly readable write-ups from which we drew inspiration. The pre-trained network used in this implementation is a VGG network, which is due to Simonyan and Zisserman (2015). Pre-trained weights were from the work of the MathConvNet team.
- Leon A. Gatys, Alexander S. Ecker, Matthias Bethge, (2015). A Neural Algorithm of Artistic Style (https://arxiv.org/abs/1508.06576)
- Harish Narayanan, Convolutional neural networks for artistic style transfer. https://harishnarayanan.org/writing/artistic-style-transfer/
- Log0, TensorFlow Implementation of “A Neural Algorithm of Artistic Style”. http://www.chioka.in/tensorflow-implementation-neural-algorithm-of-artistic-style
- Karen Simonyan and Andrew Zisserman (2015). Very deep convolutional networks for large-scale image recognition (https://arxiv.org/pdf/1409.1556.pdf)
- MatConvNet. http://www.vlfeat.org/matconvnet/pretrained/
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