题图来自：Experiments with style transfer
终于写到这一篇了。这两年各种艺术风格图像处理的app层出不穷，比如当初火热的Prisma。
本文简单地介绍并实现了风格迁移算法，更多描述可参考之前翻译的文章（图像风格化、AI作曲，机器学习与艺术）。
不过在具体应用时可能还需优化，比如视频中要考虑帧间稳定性等。

01 - 简单线性模型 | 02 - 卷积神经网络 | 03 - PrettyTensor | 04 - 保存& 恢复
05 - 集成学习 | 06 - CIFAR 10 | 07 - Inception 模型 | 08 - 迁移学习
09 - 视频数据 | 11 - 对抗样本 | 12 - MNIST的对抗噪声 | 13 - 可视化分析
14 - DeepDream

by Magnus Erik Hvass Pedersen / GitHub / Videos on YouTube
中文翻译 thrillerist / Github

如有转载，请附上本文链接。

介绍

在之前的教程#14中，我们看到了如何最大化神经网络内部的特征激活，以便放大输入图像中的模式。这个称为DeepDream。

本文采用了类似的想法，不过有两张输入图：一张内容图像和一张风格图像。然后，我们希望创建一张混合图像，它包含了内容图的轮廓以及风格图的纹理。

本文基于之前的教程。你需要大概地熟悉神经网络（详见教程 #01和 #02），熟悉教程 #14中的DeepDream也很有帮助。

流程图

这张流程图显示了风格迁移算法的大体想法，尽管比起图中所展示出来的，我们所使用的VGG-16模型有更多的层次。

输入两张图像到神经网络中：一张内容图像和一张风格图像。我们希望创建一张混合图像，它包含了内容图的轮廓以及风格图的纹理。
我们通过创建几个可以被优化的损失函数来完成这一点。

内容图像的损失函数会试着在网络的某一层或多层上，最小化内容图像以及混合图像激活特征的差距。这使得混合图像和内容图像的的轮廓相似。

风格图像的损失函数稍微复杂一些，因为它试图让风格图像和混合图像的格拉姆矩阵（Gram-matrices）的差异最小化。这在网络的一个或多个层中完成。 Gram-matrices度量了哪个特征在给定层中同时被激活。改变混合图像，使其模仿风格图像的激活模式(activation patterns)，这将导致颜色和纹理的迁移。

我们用TensorFlow来自动导出这些损失函数的梯度。然后用梯度来更新混合图像。重复多次这个过程，直到我们对结果图像满意为止。

风格迁移算法的一些细节没有在这张流程图中显示出来，比如，对于Gram-matrices的计算，计算并保存中间值来提升效率，还有一个用来给混合图像去噪的损失函数，对损失函数做归一化（normalization），这样它们更容易相对彼此缩放。

from IPython.display import Image, display
Image('images/15_style_transfer_flowchart.png')复制代码

Imports

%matplotlib inline
import matplotlib.pyplot as plt
import tensorflow as tf
import numpy as np
import PIL.Image复制代码

使用Python3.5.2（Anaconda）开发，TensorFlow版本是：

tf.__version__复制代码

'0.11.0rc0'

VGG-16 模型

我花了两天时间，想用之前教程#14中在DeepDream上使用的Inception 5h模型来实现风格迁移算法，但无法得到看起来足够好的图像。这有点奇怪，因为教程#14中生成的图像看起来挺好的。但回想起来，我们（在教程#14里）也用了一些技巧来得到这种质量，比如平滑梯度以及递归的降采样并处理图像。

原始论文 使用了VGG-19卷积神经网络。出于由于某些原因，对于TendorFlow来说，预训练的VGG-19模型在本教程中不够稳定。因此我们使用VGG-16模型，这是其他人制作的，可以很容易地获取并在TensorFlow中载入。方便起见，我们封装了一个类。

import vgg16复制代码

VGG-16模型是从网上下载的。这是你保存数据文件的默认文件夹。如果文件夹不存在，它就会被创建。

# vgg16.data_dir = 'vgg16/'复制代码

Download the data for the VGG-16 model if it doesn't already exist in the directory.

WARNING: It is 550 MB!

如果文件夹中没有VGG-16模型，就自动下载。

注意：它有500MB！

vgg16.maybe_download()复制代码

Downloading VGG16 Model ...
Data has apparently already been downloaded and unpacked.

操作图像的帮助函数

这个函数载入一张图像，并返回一个浮点型numpy数组。图像可以被自动地改变大小，因此最大的宽高等于max_size。

def load_image(filename, max_size=None):image = PIL.Image.open(filename)if max_size is not None:# Calculate the appropriate rescale-factor for# ensuring a max height and width, while keeping# the proportion between them.factor = max_size / np.max(image.size)# Scale the image's height and width.size = np.array(image.size) * factor# The size is now floating-point because it was scaled.# But PIL requires the size to be integers.size = size.astype(int)# Resize the image.image = image.resize(size, PIL.Image.LANCZOS)# Convert to numpy floating-point array.return np.float32(image)复制代码

将图像保存成一个jpeg文件。给到的图像是一个包含0到255像素值的numpy数组。

def save_image(image, filename):# Ensure the pixel-values are between 0 and 255.image = np.clip(image, 0.0, 255.0)# Convert to bytes.image = image.astype(np.uint8)# Write the image-file in jpeg-format.with open(filename, 'wb') as file:PIL.Image.fromarray(image).save(file, 'jpeg')复制代码

这个函数绘制出一张大的图像。给到的图像是一个包含0到255像素值的numpy数组。

def plot_image_big(image):# Ensure the pixel-values are between 0 and 255.image = np.clip(image, 0.0, 255.0)# Convert pixels to bytes.image = image.astype(np.uint8)# Convert to a PIL-image and display it.display(PIL.Image.fromarray(image))复制代码

这个函数画出内容图像，混合图像以及风格图像。

def plot_images(content_image, style_image, mixed_image):# Create figure with sub-plots.fig, axes = plt.subplots(1, 3, figsize=(10, 10))# Adjust vertical spacing.fig.subplots_adjust(hspace=0.1, wspace=0.1)# Use interpolation to smooth pixels?smooth = True# Interpolation type.if smooth:interpolation = 'sinc'else:interpolation = 'nearest'# Plot the content-image.# Note that the pixel-values are normalized to# the [0.0, 1.0] range by dividing with 255.ax = axes.flat[0]ax.imshow(content_image / 255.0, interpolation=interpolation)ax.set_xlabel("Content")# Plot the mixed-image.ax = axes.flat[1]ax.imshow(mixed_image / 255.0, interpolation=interpolation)ax.set_xlabel("Mixed")# Plot the style-imageax = axes.flat[2]ax.imshow(style_image / 255.0, interpolation=interpolation)ax.set_xlabel("Style")# Remove ticks from all the plots.for ax in axes.flat:ax.set_xticks([])ax.set_yticks([])# Ensure the plot is shown correctly with multiple plots# in a single Notebook cell.plt.show()复制代码

损失函数

这些帮助函数创建了在TensorFlow优化中用的损失函数。

这个函数创建了一个TensorFlow运算，用来计算两个输入张量的最小平均误差（Mean Squared Error）。

def mean_squared_error(a, b):return tf.reduce_mean(tf.square(a - b))复制代码

这个函数创建了内容图像的损失函数。它是在给定层中，内容图像和混合图像激活特征的最小平均误差。当内容损失最小时，意味着在给定层中，混合图像与内容图像的激活特征很相似。根据你所选择的层次，这会将内容图像的轮廓迁移到混合图像中。

def create_content_loss(session, model, content_image, layer_ids):"""Create the loss-function for the content-image.Parameters:session: An open TensorFlow session for running the model's graph.model: The model, e.g. an instance of the VGG16-class.content_image: Numpy float array with the content-image.layer_ids: List of integer id's for the layers to use in the model."""# Create a feed-dict with the content-image.feed_dict = model.create_feed_dict(image=content_image)# Get references to the tensors for the given layers.layers = model.get_layer_tensors(layer_ids)# Calculate the output values of those layers when# feeding the content-image to the model.values = session.run(layers, feed_dict=feed_dict)# Set the model's graph as the default so we can add# computational nodes to it. It is not always clear# when this is necessary in TensorFlow, but if you# want to re-use this code then it may be necessary.with model.graph.as_default():# Initialize an empty list of loss-functions.layer_losses = []# For each layer and its corresponding values# for the content-image.for value, layer in zip(values, layers):# These are the values that are calculated# for this layer in the model when inputting# the content-image. Wrap it to ensure it# is a const - although this may be done# automatically by TensorFlow.value_const = tf.constant(value)# The loss-function for this layer is the# Mean Squared Error between the layer-values# when inputting the content- and mixed-images.# Note that the mixed-image is not calculated# yet, we are merely creating the operations# for calculating the MSE between those two.loss = mean_squared_error(layer, value_const)# Add the loss-function for this layer to the# list of loss-functions.layer_losses.append(loss)# The combined loss for all layers is just the average.# The loss-functions could be weighted differently for# each layer. You can try it and see what happens.total_loss = tf.reduce_mean(layer_losses)return total_loss复制代码

我们将对风格层做相同的处理，但现在需要度量出哪些特征在风格层和风格图像中同时被激活，接着将这些激活模式复制到混合图像中。

一种办法是为风格层的输出张量计算一个所谓的格拉姆矩阵（Gram-matrix）。Gram-matrix本质上就是风格层中激活特征向量的点乘矩阵。

如果Gram-matrix中的一个元素的值接近于0，这意味着给定层的两个特征在风格图像中没有同时激活。反之亦然，如果Gram-matrix中有很大的值，代表着两个特征同时被激活。接着，我们会试图生成复制了风格图像激活模式的混合图像。

这个帮助函数用来计算神经网络中卷积层输出张量的Gram-matrix。真正的损失函数会在后面创建。

def gram_matrix(tensor):shape = tensor.get_shape()# Get the number of feature channels for the input tensor,# which is assumed to be from a convolutional layer with 4-dim.num_channels = int(shape[3])# Reshape the tensor so it is a 2-dim matrix. This essentially# flattens the contents of each feature-channel.matrix = tf.reshape(tensor, shape=[-1, num_channels])# Calculate the Gram-matrix as the matrix-product of# the 2-dim matrix with itself. This calculates the# dot-products of all combinations of the feature-channels.gram = tf.matmul(tf.transpose(matrix), matrix)return gram复制代码

下面的函数创建了风格图像的损失函数。它和上面的create_content_loss()很像，除了我们是计算Gram-matrix而非layer输出张量的最小平方误差。

def create_style_loss(session, model, style_image, layer_ids):"""Create the loss-function for the style-image.Parameters:session: An open TensorFlow session for running the model's graph.model: The model, e.g. an instance of the VGG16-class.style_image: Numpy float array with the style-image.layer_ids: List of integer id's for the layers to use in the model."""# Create a feed-dict with the style-image.feed_dict = model.create_feed_dict(image=style_image)# Get references to the tensors for the given layers.layers = model.get_layer_tensors(layer_ids)# Set the model's graph as the default so we can add# computational nodes to it. It is not always clear# when this is necessary in TensorFlow, but if you# want to re-use this code then it may be necessary.with model.graph.as_default():# Construct the TensorFlow-operations for calculating# the Gram-matrices for each of the layers.gram_layers = [gram_matrix(layer) for layer in layers]# Calculate the values of those Gram-matrices when# feeding the style-image to the model.values = session.run(gram_layers, feed_dict=feed_dict)# Initialize an empty list of loss-functions.layer_losses = []# For each Gram-matrix layer and its corresponding values.for value, gram_layer in zip(values, gram_layers):# These are the Gram-matrix values that are calculated# for this layer in the model when inputting the# style-image. Wrap it to ensure it is a const,# although this may be done automatically by TensorFlow.value_const = tf.constant(value)# The loss-function for this layer is the# Mean Squared Error between the Gram-matrix values# for the content- and mixed-images.# Note that the mixed-image is not calculated# yet, we are merely creating the operations# for calculating the MSE between those two.loss = mean_squared_error(gram_layer, value_const)# Add the loss-function for this layer to the# list of loss-functions.layer_losses.append(loss)# The combined loss for all layers is just the average.# The loss-functions could be weighted differently for# each layer. You can try it and see what happens.total_loss = tf.reduce_mean(layer_losses)return total_loss复制代码

下面创建了用来给混合图像去噪的损失函数。这个算法称为Total Variation Denoising，本质上就是在x和y轴上将图像偏移一个像素，计算它与原始图像的差异，取绝对值保证差异是正值，然后对整个图像所有像素求和。这个步骤创建了一个可以最小化的损失函数，用来抑制图像中的噪声。

def create_denoise_loss(model):loss = tf.reduce_sum(tf.abs(model.input[:,1:,:,:] - model.input[:,:-1,:,:])) + \tf.reduce_sum(tf.abs(model.input[:,:,1:,:] - model.input[:,:,:-1,:]))return loss复制代码

风格迁移算法

这是风格迁移主要的优化算法。它基本上就是在上面定义的那些损失函数上做梯度下降。

算法也使用了损失函数的归一化。这似乎是一个之前未发表过的新颖想法。在每次优化迭代中，调整损失值，使它们等于一。这让用户可以独立地设置所选风格层以及内容层的损失权重。同时，在优化过程中也修改权重，来确保保留风格、内容、去噪之间所需的比重。

def style_transfer(content_image, style_image,content_layer_ids, style_layer_ids,weight_content=1.5, weight_style=10.0,weight_denoise=0.3,num_iterations=120, step_size=10.0):"""Use gradient descent to find an image that minimizes theloss-functions of the content-layers and style-layers. Thisshould result in a mixed-image that resembles the contoursof the content-image, and resembles the colours and texturesof the style-image.Parameters:content_image: Numpy 3-dim float-array with the content-image.style_image: Numpy 3-dim float-array with the style-image.content_layer_ids: List of integers identifying the content-layers.style_layer_ids: List of integers identifying the style-layers.weight_content: Weight for the content-loss-function.weight_style: Weight for the style-loss-function.weight_denoise: Weight for the denoising-loss-function.num_iterations: Number of optimization iterations to perform.step_size: Step-size for the gradient in each iteration."""# Create an instance of the VGG16-model. This is done# in each call of this function, because we will add# operations to the graph so it can grow very large# and run out of RAM if we keep using the same instance.model = vgg16.VGG16()# Create a TensorFlow-session.session = tf.InteractiveSession(graph=model.graph)# Print the names of the content-layers.print("Content layers:")print(model.get_layer_names(content_layer_ids))print()# Print the names of the style-layers.print("Style layers:")print(model.get_layer_names(style_layer_ids))print()# Create the loss-function for the content-layers and -image.loss_content = create_content_loss(session=session,model=model,content_image=content_image,layer_ids=content_layer_ids)# Create the loss-function for the style-layers and -image.loss_style = create_style_loss(session=session,model=model,style_image=style_image,layer_ids=style_layer_ids)    # Create the loss-function for the denoising of the mixed-image.loss_denoise = create_denoise_loss(model)# Create TensorFlow variables for adjusting the values of# the loss-functions. This is explained below.adj_content = tf.Variable(1e-10, name='adj_content')adj_style = tf.Variable(1e-10, name='adj_style')adj_denoise = tf.Variable(1e-10, name='adj_denoise')# Initialize the adjustment values for the loss-functions.session.run([adj_content.initializer,adj_style.initializer,adj_denoise.initializer])# Create TensorFlow operations for updating the adjustment values.# These are basically just the reciprocal values of the# loss-functions, with a small value 1e-10 added to avoid the# possibility of division by zero.update_adj_content = adj_content.assign(1.0 / (loss_content + 1e-10))update_adj_style = adj_style.assign(1.0 / (loss_style + 1e-10))update_adj_denoise = adj_denoise.assign(1.0 / (loss_denoise + 1e-10))# This is the weighted loss-function that we will minimize# below in order to generate the mixed-image.# Because we multiply the loss-values with their reciprocal# adjustment values, we can use relative weights for the# loss-functions that are easier to select, as they are# independent of the exact choice of style- and content-layers.loss_combined = weight_content * adj_content * loss_content + \weight_style * adj_style * loss_style + \weight_denoise * adj_denoise * loss_denoise# Use TensorFlow to get the mathematical function for the# gradient of the combined loss-function with regard to# the input image.gradient = tf.gradients(loss_combined, model.input)# List of tensors that we will run in each optimization iteration.run_list = [gradient, update_adj_content, update_adj_style, \update_adj_denoise]# The mixed-image is initialized with random noise.# It is the same size as the content-image.mixed_image = np.random.rand(*content_image.shape) + 128for i in range(num_iterations):# Create a feed-dict with the mixed-image.feed_dict = model.create_feed_dict(image=mixed_image)# Use TensorFlow to calculate the value of the# gradient, as well as updating the adjustment values.grad, adj_content_val, adj_style_val, adj_denoise_val \= session.run(run_list, feed_dict=feed_dict)# Reduce the dimensionality of the gradient.grad = np.squeeze(grad)# Scale the step-size according to the gradient-values.step_size_scaled = step_size / (np.std(grad) + 1e-8)# Update the image by following the gradient.mixed_image -= grad * step_size_scaled# Ensure the image has valid pixel-values between 0 and 255.mixed_image = np.clip(mixed_image, 0.0, 255.0)# Print a little progress-indicator.print(". ", end="")# Display status once every 10 iterations, and the last.if (i % 10 == 0) or (i == num_iterations - 1):print()print("Iteration:", i)# Print adjustment weights for loss-functions.msg = "Weight Adj. for Content: {0:.2e}, Style: {1:.2e}, Denoise: {2:.2e}"print(msg.format(adj_content_val, adj_style_val, adj_denoise_val))# Plot the content-, style- and mixed-images.plot_images(content_image=content_image,style_image=style_image,mixed_image=mixed_image)print()print("Final image:")plot_image_big(mixed_image)# Close the TensorFlow session to release its resources.session.close()# Return the mixed-image.return mixed_image复制代码

例子

这个例子展示了如何将多张图像的风格迁移到一张肖像上。

首先，我们载入内容图像，它有混合图像想要的大体轮廓。

content_filename = 'images/willy_wonka_old.jpg'
content_image = load_image(content_filename, max_size=None)复制代码

然后我们载入风格图像，它拥有混合图像想要的颜色和纹理。

style_filename = 'images/style7.jpg'
style_image = load_image(style_filename, max_size=300)复制代码

接着我们定义一个整数列表，它代表神经网络中我们用来匹配内容图像的层次。这些是神经网络层次的索引。对于VGG16模型，第5层（索引4）似乎是唯一有效的内容层。

content_layer_ids = [4]复制代码

然后，我们为风格层定义另外一个整型数组。

# The VGG16-model has 13 convolutional layers.
# This selects all those layers as the style-layers.
# This is somewhat slow to optimize.
style_layer_ids = list(range(13))# You can also select a sub-set of the layers, e.g. like this:
# style_layer_ids = [1, 2, 3, 4]复制代码

现在执行风格迁移。它自动地为风格图像、内容图像创建合适的损失函数，然后进行多次优化迭代。这将逐步地生成一张混合图像，其拥有内容图像的大体轮廓，并且它的纹理、颜色和风格图像类似。

在CPU上这个运算会很慢！

%%time
img = style_transfer(content_image=content_image,style_image=style_image,content_layer_ids=content_layer_ids,style_layer_ids=style_layer_ids,weight_content=1.5,weight_style=10.0,weight_denoise=0.3,num_iterations=60,step_size=10.0)复制代码

Content layers:
['conv3_1/conv3_1']

Style layers:
['conv1_1/conv1_1', 'conv1_2/conv1_2', 'conv2_1/conv2_1', 'conv2_2/conv2_2', 'conv3_1/conv3_1', 'conv3_2/conv3_2', 'conv3_3/conv3_3', 'conv4_1/conv4_1', 'conv4_2/conv4_2', 'conv4_3/conv4_3', 'conv5_1/conv5_1', 'conv5_2/conv5_2', 'conv5_3/conv5_3']

.
Iteration: 0
Weight Adj. for Content: 5.18e-11, Style: 2.14e-29, Denoise: 5.61e-06

. . . . . . . . . .
Iteration: 10
Weight Adj. for Content: 2.79e-11, Style: 4.13e-28, Denoise: 1.25e-07

. . . . . . . . . .
Iteration: 20
Weight Adj. for Content: 2.63e-11, Style: 1.09e-27, Denoise: 1.30e-07

. . . . . . . . . .
Iteration: 30
Weight Adj. for Content: 2.66e-11, Style: 1.27e-27, Denoise: 1.27e-07

. . . . . . . . . .
Iteration: 40
Weight Adj. for Content: 2.73e-11, Style: 1.16e-27, Denoise: 1.26e-07

. . . . . . . . . .
Iteration: 50
Weight Adj. for Content: 2.75e-11, Style: 1.12e-27, Denoise: 1.24e-07

. . . . . . . . .
Iteration: 59
Weight Adj. for Content: 1.85e-11, Style: 3.86e-28, Denoise: 1.01e-07

Final image:

CPU times: user 20min 1s, sys: 45.5 s, total: 20min 46s
Wall time: 3min 4s

总结

这篇教程说明了用神经网络来结合两张图像内容和风格的基本想法。不幸的是，结果并不像一些商业系统那么好，比如 DeepArt，它是由这种技术的一些先驱者开发的。（结果不好的）原因暂不明确。也许我们只是需要更强的计算力，可以在高分辨率图像上以更小的步长，运行更多的优化迭代。或许我们需要更复杂的优化方法。下面的练习给出了一些可能会提升质量的建议，鼓励你尝试一下。

练习

下面使一些可能会让你提升TensorFlow技能的一些建议练习。为了学习如何更合适地使用TensorFlow，实践经验是很重要的。

在你对这个Notebook进行修改之前，可能需要先备份一下。

• 试着使用其他图像。本文中包含了一些风格图像。你可以使用自己的图像。
• 试着更多的迭代次数（比如1000-5000），以及更小的步长（比如1.0-3.0）。它会提升质量吗？
  *　改变风格层、内容层以及去噪时的权重。
• 试着从内容或风格图像开始优化，或许二者的平均。你可以加入一些噪声。
• 试着改变风格图和内容图的分辨率。在load_image()函数中，你可以用max_size参数来改变图像大小。它对结果有什么影响？
• 试着使用VGG-16模型的其他层。
• 改变代码，使其每10次优化迭代就保存图像。
• 在优化过程中使用常数权重。它对结果有何影响？
• 在风格层中使用不同的权重。同样，试着像其他损失函数一样自动调整权重。
• 用TensorFlow的ADAM优化器来代替基本的梯度下降。
• 使用L-BFGS优化器。目前在TensorFlow中没有实现这个。你能在风格迁移算法中使用SciPy中实现的优化器么？它有提升结果吗？
• 用另外的预训练网络，比如我们在教程 #14中使用的Inception 5h模型，或者用你从网上找到的VGG-19模型。
• 向朋友解释程序如何工作。