13.12. Neural Style Transfer¶
If you are a photography enthusiast, you may be familiar with the filter. It can change the color style of photos so that landscape photos become sharper or portrait photos have whitened skins. However, one filter usually only changes one aspect of the photo. To apply an ideal style to a photo, you probably need to try many different filter combinations. This process is as complex as tuning the hyperparameters of a model.
In this section, we will leverage layerwise representations of a CNN to automatically apply the style of one image to another image, i.e., style transfer [Gatys et al., 2016]. This task needs two input images: one is the content image and the other is the style image. We will use neural networks to modify the content image to make it close to the style image in style. For example, the content image in Fig. 13.12.1 is a landscape photo taken by us in Mount Rainier National Park in the suburbs of Seattle, while the style image is an oil painting with the theme of autumn oak trees. In the output synthesized image, the oil brush strokes of the style image are applied, leading to more vivid colors, while preserving the main shape of the objects in the content image.
Fig. 13.12.1 Given content and style images, style transfer outputs a synthesized image.¶
13.12.1. Method¶
Fig. 13.12.2 illustrates the CNN-based style transfer method with a simplified example. First, we initialize the synthesized image, for example, into the content image. This synthesized image is the only variable that needs to be updated during the style transfer process, i.e., the model parameters to be updated during training. Then we choose a pretrained CNN to extract image features and freeze its model parameters during training. This deep CNN uses multiple layers to extract hierarchical features for images. We can choose the output of some of these layers as content features or style features. Take Fig. 13.12.2 as an example. The pretrained neural network here has 3 convolutional layers, where the second layer outputs the content features, and the first and third layers output the style features.
Fig. 13.12.2 CNN-based style transfer process. Solid lines show the direction of forward propagation and dotted lines show backward propagation.¶
Next, we calculate the loss function of style transfer through forward propagation (direction of solid arrows), and update the model parameters (the synthesized image for output) through backpropagation (direction of dashed arrows). The loss function commonly used in style transfer consists of three parts: (i) content loss makes the synthesized image and the content image close in content features; (ii) style loss makes the synthesized image and style image close in style features; and (iii) total variation loss helps to reduce the noise in the synthesized image. Finally, when the model training is over, we output the model parameters of the style transfer to generate the final synthesized image.
In the following, we will explain the technical details of style transfer via a concrete experiment.
13.12.2. Reading the Content and Style Images¶
First, we read the content and style images. From their printed coordinate axes, we can tell that these images have different sizes.
%matplotlib inline
from mxnet import autograd, gluon, image, init, np, npx
from mxnet.gluon import nn
from d2l import mxnet as d2l
npx.set_np()
d2l.set_figsize()
content_img = image.imread('../img/rainier.jpg')
d2l.plt.imshow(content_img.asnumpy());
style_img = image.imread('../img/autumn-oak.jpg')
d2l.plt.imshow(style_img.asnumpy());
%matplotlib inline
import torch
import torchvision
from torch import nn
from d2l import torch as d2l
d2l.set_figsize()
content_img = d2l.Image.open('../img/rainier.jpg')
d2l.plt.imshow(content_img);
style_img = d2l.Image.open('../img/autumn-oak.jpg')
d2l.plt.imshow(style_img);
13.12.3. Preprocessing and Postprocessing¶
Below, we define two functions for preprocessing and postprocessing
images. The preprocess function standardizes each of the three RGB
channels of the input image and transforms the results into the CNN
input format. The postprocess function restores the pixel values in
the output image to their original values before standardization. Since
the image printing function requires that each pixel has a floating
point value from 0 to 1, we replace any value smaller than 0 or greater
than 1 with 0 or 1, respectively.
rgb_mean = np.array([0.485, 0.456, 0.406])
rgb_std = np.array([0.229, 0.224, 0.225])
def preprocess(img, image_shape):
img = image.imresize(img, *image_shape)
img = (img.astype('float32') / 255 - rgb_mean) / rgb_std
return np.expand_dims(img.transpose(2, 0, 1), axis=0)
def postprocess(img):
img = img[0].as_in_ctx(rgb_std.ctx)
return (img.transpose(1, 2, 0) * rgb_std + rgb_mean).clip(0, 1)
rgb_mean = torch.tensor([0.485, 0.456, 0.406])
rgb_std = torch.tensor([0.229, 0.224, 0.225])
def preprocess(img, image_shape):
transforms = torchvision.transforms.Compose([
torchvision.transforms.Resize(image_shape),
torchvision.transforms.ToTensor(),
torchvision.transforms.Normalize(mean=rgb_mean, std=rgb_std)])
return transforms(img).unsqueeze(0)
def postprocess(img):
img = img[0].to(rgb_std.device)
img = torch.clamp(img.permute(1, 2, 0) * rgb_std + rgb_mean, 0, 1)
return torchvision.transforms.ToPILImage()(img.permute(2, 0, 1))
13.12.4. Extracting Features¶
We use the VGG-19 model pretrained on the ImageNet dataset to extract image features [Gatys et al., 2016].
pretrained_net = gluon.model_zoo.vision.vgg19(pretrained=True)
pretrained_net = torchvision.models.vgg19(pretrained=True)
In order to extract the content features and style features of the
image, we can select the output of certain layers in the VGG network.
Generally speaking, the closer to the input layer, the easier to extract
details of the image, and vice versa, the easier to extract the global
information of the image. In order to avoid excessively retaining the
details of the content image in the synthesized image, we choose a VGG
layer that is closer to the output as the content layer to output the
content features of the image. We also select the output of different
VGG layers for extracting local and global style features. These layers
are also called style layers. As mentioned in Section 7.2, the
VGG network uses 5 convolutional blocks. In the experiment, we choose
the last convolutional layer of the fourth convolutional block as the
content layer, and the first convolutional layer of each convolutional
block as the style layer. The indices of these layers can be obtained by
printing the pretrained_net instance.
style_layers, content_layers = [0, 5, 10, 19, 28], [25]
style_layers, content_layers = [0, 5, 10, 19, 28], [25]
When extracting features using VGG layers, we only need to use all those
from the input layer to the content layer or style layer that is closest
to the output layer. Let us construct a new network instance net,
which only retains all the VGG layers to be used for feature extraction.
net = nn.Sequential()
for i in range(max(content_layers + style_layers) + 1):
net.add(pretrained_net.features[i])
net = nn.Sequential(*[
pretrained_net.features[i]
for i in range(max(content_layers + style_layers) + 1)])
Given the input X, if we simply invoke the forward propagation
net(X), we can only get the output of the last layer. Since we also
need the outputs of intermediate layers, we need to perform
layer-by-layer computation and keep the content and style layer outputs.
def extract_features(X, content_layers, style_layers):
contents = []
styles = []
for i in range(len(net)):
X = net[i](X)
if i in style_layers:
styles.append(X)
if i in content_layers:
contents.append(X)
return contents, styles
def extract_features(X, content_layers, style_layers):
contents = []
styles = []
for i in range(len(net)):
X = net[i](X)
if i in style_layers:
styles.append(X)
if i in content_layers:
contents.append(X)
return contents, styles
Two functions are defined below: the get_contents function extracts
content features from the content image, and the get_styles function
extracts style features from the style image. Since there is no need to
update the model parameters of the pretrained VGG during training, we
can extract the content and the style features even before the training
starts. Since the synthesized image is a set of model parameters to be
updated for style transfer, we can only extract the content and style
features of the synthesized image by calling the extract_features
function during training.
def get_contents(image_shape, device):
content_X = preprocess(content_img, image_shape).copyto(device)
contents_Y, _ = extract_features(content_X, content_layers, style_layers)
return content_X, contents_Y
def get_styles(image_shape, device):
style_X = preprocess(style_img, image_shape).copyto(device)
_, styles_Y = extract_features(style_X, content_layers, style_layers)
return style_X, styles_Y
def get_contents(image_shape, device):
content_X = preprocess(content_img, image_shape).to(device)
contents_Y, _ = extract_features(content_X, content_layers, style_layers)
return content_X, contents_Y
def get_styles(image_shape, device):
style_X = preprocess(style_img, image_shape).to(device)
_, styles_Y = extract_features(style_X, content_layers, style_layers)
return style_X, styles_Y
13.12.5. Defining the Loss Function¶
Now we will describe the loss function for style transfer. The loss function consists of the content loss, style loss, and total variation loss.
13.12.5.1. Content Loss¶
Similar to the loss function in linear regression, the content loss
measures the difference in content features between the synthesized
image and the content image via the squared loss function. The two
inputs of the squared loss function are both outputs of the content
layer computed by the extract_features function.
def content_loss(Y_hat, Y):
return np.square(Y_hat - Y).mean()
def content_loss(Y_hat, Y):
# We detach the target content from the tree used to dynamically compute
# the gradient: this is a stated value, not a variable. Otherwise the loss
# will throw an error.
return torch.square(Y_hat - Y.detach()).mean()
13.12.5.2. Style Loss¶
Style loss, similar to content loss, also uses the squared loss function
to measure the difference in style between the synthesized image and the
style image. To express the style output of any style layer, we first
use the extract_features function to compute the style layer output.
Suppose that the output has 1 example, \(c\) channels, height
\(h\), and width \(w\), we can transform this output into matrix
\(\mathbf{X}\) with \(c\) rows and \(hw\) columns. This
matrix can be thought of as the concatenation of \(c\) vectors
\(\mathbf{x}_1, \ldots, \mathbf{x}_c\), each of which has a length
of \(hw\). Here, vector \(\mathbf{x}_i\) represents the style
feature of channel \(i\).
In the Gram matrix of these vectors
\(\mathbf{X}\mathbf{X}^\top \in \mathbb{R}^{c \times c}\), element
\(x_{ij}\) in row \(i\) and column \(j\) is the dot product
of vectors \(\mathbf{x}_i\) and \(\mathbf{x}_j\). It represents
the correlation of the style features of channels \(i\) and
\(j\). We use this Gram matrix to represent the style output of any
style layer. Note that when the value of \(hw\) is larger, it likely
leads to larger values in the Gram matrix. Note also that the height and
width of the Gram matrix are both the number of channels \(c\). To
allow style loss not to be affected by these values, the gram
function below divides the Gram matrix by the number of its elements,
i.e., \(chw\).
def gram(X):
num_channels, n = X.shape[1], X.size // X.shape[1]
X = X.reshape((num_channels, n))
return np.dot(X, X.T) / (num_channels * n)
def gram(X):
num_channels, n = X.shape[1], X.numel() // X.shape[1]
X = X.reshape((num_channels, n))
return torch.matmul(X, X.T) / (num_channels * n)
Obviously, the two Gram matrix inputs of the squared loss function for
style loss are based on the style layer outputs for the synthesized
image and the style image. It is assumed here that the Gram matrix
gram_Y based on the style image has been precomputed.
def style_loss(Y_hat, gram_Y):
return np.square(gram(Y_hat) - gram_Y).mean()
def style_loss(Y_hat, gram_Y):
return torch.square(gram(Y_hat) - gram_Y.detach()).mean()
13.12.5.3. Total Variation Loss¶
Sometimes, the learned synthesized image has a lot of high-frequency noise, i.e., particularly bright or dark pixels. One common noise reduction method is total variation denoising. Denote by \(x_{i, j}\) the pixel value at coordinate \((i, j)\). Reducing total variation loss
makes values of neighboring pixels on the synthesized image closer.
def tv_loss(Y_hat):
return 0.5 * (np.abs(Y_hat[:, :, 1:, :] - Y_hat[:, :, :-1, :]).mean() +
np.abs(Y_hat[:, :, :, 1:] - Y_hat[:, :, :, :-1]).mean())
def tv_loss(Y_hat):
return 0.5 * (torch.abs(Y_hat[:, :, 1:, :] - Y_hat[:, :, :-1, :]).mean() +
torch.abs(Y_hat[:, :, :, 1:] - Y_hat[:, :, :, :-1]).mean())
13.12.5.4. Loss Function¶
The loss function of style transfer is the weighted sum of content loss, style loss, and total variation loss. By adjusting these weight hyperparameters, we can balance among content retention, style transfer, and noise reduction on the synthesized image.
content_weight, style_weight, tv_weight = 1, 1e3, 10
def compute_loss(X, contents_Y_hat, styles_Y_hat, contents_Y, styles_Y_gram):
# Calculate the content, style, and total variance losses respectively
contents_l = [
content_loss(Y_hat, Y) * content_weight
for Y_hat, Y in zip(contents_Y_hat, contents_Y)]
styles_l = [
style_loss(Y_hat, Y) * style_weight
for Y_hat, Y in zip(styles_Y_hat, styles_Y_gram)]
tv_l = tv_loss(X) * tv_weight
# Add up all the losses
l = sum(10 * styles_l + contents_l + [tv_l])
return contents_l, styles_l, tv_l, l
content_weight, style_weight, tv_weight = 1, 1e3, 10
def compute_loss(X, contents_Y_hat, styles_Y_hat, contents_Y, styles_Y_gram):
# Calculate the content, style, and total variance losses respectively
contents_l = [
content_loss(Y_hat, Y) * content_weight
for Y_hat, Y in zip(contents_Y_hat, contents_Y)]
styles_l = [
style_loss(Y_hat, Y) * style_weight
for Y_hat, Y in zip(styles_Y_hat, styles_Y_gram)]
tv_l = tv_loss(X) * tv_weight
# Add up all the losses
l = sum(10 * styles_l + contents_l + [tv_l])
return contents_l, styles_l, tv_l, l
13.12.6. Initializing the Synthesized Image¶
In style transfer, the synthesized image is the only variable that needs
to be updated during training. Thus, we can define a simple model,
SynthesizedImage, and treat the synthesized image as the model
parameters. In this model, forward propagation just returns the model
parameters.
class SynthesizedImage(nn.Block):
def __init__(self, img_shape, **kwargs):
super(SynthesizedImage, self).__init__(**kwargs)
self.weight = self.params.get('weight', shape=img_shape)
def forward(self):
return self.weight.data()
class SynthesizedImage(nn.Module):
def __init__(self, img_shape, **kwargs):
super(SynthesizedImage, self).__init__(**kwargs)
self.weight = nn.Parameter(torch.rand(*img_shape))
def forward(self):
return self.weight
Next, we define the get_inits function. This function creates a
synthesized image model instance and initializes it to the image X.
Gram matrices for the style image at various style layers,
styles_Y_gram, are computed prior to training.
def get_inits(X, device, lr, styles_Y):
gen_img = SynthesizedImage(X.shape)
gen_img.initialize(init.Constant(X), ctx=device, force_reinit=True)
trainer = gluon.Trainer(gen_img.collect_params(), 'adam',
{'learning_rate': lr})
styles_Y_gram = [gram(Y) for Y in styles_Y]
return gen_img(), styles_Y_gram, trainer
def get_inits(X, device, lr, styles_Y):
gen_img = SynthesizedImage(X.shape).to(device)
gen_img.weight.data.copy_(X.data)
trainer = torch.optim.Adam(gen_img.parameters(), lr=lr)
styles_Y_gram = [gram(Y) for Y in styles_Y]
return gen_img(), styles_Y_gram, trainer
13.12.7. Training¶
When training the model for style transfer, we continuously extract content features and style features of the synthesized image, and calculate the loss function. Below defines the training loop.
def train(X, contents_Y, styles_Y, device, lr, num_epochs, lr_decay_epoch):
X, styles_Y_gram, trainer = get_inits(X, device, lr, styles_Y)
animator = d2l.Animator(xlabel='epoch', ylabel='loss',
xlim=[10, num_epochs], ylim=[0, 20],
legend=['content', 'style',
'TV'], ncols=2, figsize=(7, 2.5))
for epoch in range(num_epochs):
with autograd.record():
contents_Y_hat, styles_Y_hat = extract_features(
X, content_layers, style_layers)
contents_l, styles_l, tv_l, l = compute_loss(
X, contents_Y_hat, styles_Y_hat, contents_Y, styles_Y_gram)
l.backward()
trainer.step(1)
if (epoch + 1) % lr_decay_epoch == 0:
trainer.set_learning_rate(trainer.learning_rate * 0.8)
if (epoch + 1) % 10 == 0:
animator.axes[1].imshow(postprocess(X).asnumpy())
animator.add(
epoch + 1,
[float(sum(contents_l)),
float(sum(styles_l)),
float(tv_l)])
return X
def train(X, contents_Y, styles_Y, device, lr, num_epochs, lr_decay_epoch):
X, styles_Y_gram, trainer = get_inits(X, device, lr, styles_Y)
scheduler = torch.optim.lr_scheduler.StepLR(trainer, lr_decay_epoch, 0.8)
animator = d2l.Animator(xlabel='epoch', ylabel='loss',
xlim=[10, num_epochs],
legend=['content', 'style',
'TV'], ncols=2, figsize=(7, 2.5))
for epoch in range(num_epochs):
trainer.zero_grad()
contents_Y_hat, styles_Y_hat = extract_features(
X, content_layers, style_layers)
contents_l, styles_l, tv_l, l = compute_loss(X, contents_Y_hat,
styles_Y_hat, contents_Y,
styles_Y_gram)
l.backward()
trainer.step()
scheduler.step()
if (epoch + 1) % 10 == 0:
animator.axes[1].imshow(postprocess(X))
animator.add(
epoch + 1,
[float(sum(contents_l)),
float(sum(styles_l)),
float(tv_l)])
return X
Now we start to train the model. We rescale the height and width of the content and style images to 300 by 450 pixels. We use the content image to initialize the synthesized image.
device, image_shape = d2l.try_gpu(), (450, 300)
net.collect_params().reset_ctx(device)
content_X, contents_Y = get_contents(image_shape, device)
_, styles_Y = get_styles(image_shape, device)
output = train(content_X, contents_Y, styles_Y, device, 0.9, 500, 50)
device, image_shape = d2l.try_gpu(), (300, 450) # PIL Image (h, w)
net = net.to(device)
content_X, contents_Y = get_contents(image_shape, device)
_, styles_Y = get_styles(image_shape, device)
output = train(content_X, contents_Y, styles_Y, device, 0.3, 500, 50)
We can see that the synthesized image retains the scenery and objects of the content image, and transfers the color of the style image at the same time. For example, the synthesized image has blocks of color like those in the style image. Some of these blocks even have the subtle texture of brush strokes.
13.12.8. Summary¶
The loss function commonly used in style transfer consists of three parts: (i) content loss makes the synthesized image and the content image close in content features; (ii) style loss makes the synthesized image and style image close in style features; and (iii) total variation loss helps to reduce the noise in the synthesized image.
We can use a pretrained CNN to extract image features and minimize the loss function to continuously update the synthesized image as model parameters during training.
We use Gram matrices to represent the style outputs from the style layers.
13.12.9. Exercises¶
How does the output change when you select different content and style layers?
Adjust the weight hyperparameters in the loss function. Does the output retain more content or have less noise?
Use different content and style images. Can you create more interesting synthesized images?
Can we apply style transfer for text? Hint: you may refer to the survey paper by Hu et al. [Hu et al., 2020].