png

Author: Alexis Jacq

Edited by: Winston Herring

基本原则（Underlying Principle）

定义两个距离，一个用于内容（$ D_C $），一个用于样式$ D_S $）。 $ D_C $测量两个图像之间内容的差异，$ D_S $测量两个图像之间的样式的差异。 新建第三个图像对其进行变换，尽量减小其与内容图像的内容距离和与样式图像的样式距离。

先看结果：

png

代码第一段，自行更改style.jpg和content.jpg文件

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55

from __future__ import print_function
# 用于Jupyter
%matplotlib inline 
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim

from PIL import Image
import matplotlib.pyplot as plt

import torchvision.transforms as transforms
import torchvision.models as models

import copy
import time

T0=0
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
imsize = 768 if torch.cuda.is_available() else 128  # 根据机器合理选择

loader = transforms.Compose([
    transforms.Resize(imsize),  
    transforms.ToTensor()]) 

def image_loader(image_name):
    image = Image.open(image_name)
    # 单张图片变tensor的dataloader方法
    image = loader(image).unsqueeze(0)
    return image.to(device, torch.float)

style_img = image_loader("style.jpg")
content_img = image_loader("content.jpg")

assert style_img.size() == content_img.size(), \
    "图片最好是正方形"

unloader = transforms.ToPILImage()  # tensor 转为 PIL image

plt.ion()

def imshow(tensor, title=None):
    image = tensor.cpu().clone()  
    image = image.squeeze(0)      # 降维
    image = unloader(image)
    plt.imshow(image)
    if title is not None:
        plt.title(title)
#     plt.pause(0.001) # Jupyter不需要，其它可能需要
ax = plt.subplot(1, 2, 1)
ax.axis('off')
imshow(style_img, title='Style')
ax = plt.subplot(1, 2, 2)
ax.axis('off')
imshow(content_img, title='Content')

损失函数（Loss Functions）

内容损失就是我们常用的mse损失，关键是风格损失是什么？数学家们告诉我们要使用Gram矩阵，下面引用知乎上的关于Gram矩阵的简介：

Gram Matrix实际上可看做是feature之间的偏心协方差矩阵（即没有减去均值的协方差矩阵），在feature map中，每一个数字都来自于一个特定滤波器在特定位置的卷积，因此每个数字就代表一个特征的强度，而Gram计算的实际上是两两特征之间的相关性，哪两个特征是同时出现的，哪两个是此消彼长的等等，同时，Gram的对角线元素，还体现了每个特征在图像中出现的量，因此，Gram有助于把握整个图像的大体风格。有了表示风格的Gram Matrix，要度量两个图像风格的差异，只需比较他们Gram Matrix的差异即可。

alt text

因此风格损失就是Gram损失。

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38

class ContentLoss(nn.Module):

    def __init__(self, target,):
        super(ContentLoss, self).__init__()
        # we 'detach' the target content from the tree used
        # to dynamically compute the gradient: this is a stated value,
        # not a variable. Otherwise the forward method of the criterion
        # will throw an error.
        self.target = target.detach()

    def forward(self, input):
        self.loss = F.mse_loss(input, self.target)
        return input

def gram_matrix(input):
    a, b, c, d = input.size() 
    # a=batch size(=1)
    # b=特征数
    # (c,d)=特征 map (N=c*d)

    features = input.view(a * b, c * d)  # resise F_XL into \hat F_XL

    G = torch.mm(features, features.t())  # Gram矩阵=特征矩阵乘以其转置
    # torch.mm(mat1, mat2, out=None) → Tensor 矩阵乘法非点乘
    
    # 通过除以特征map的全部数目来归一化
    return G.div(a * b * c * d)

class StyleLoss(nn.Module):

    def __init__(self, target_feature):
        super(StyleLoss, self).__init__()
        self.target = gram_matrix(target_feature).detach()

    def forward(self, input):
        G = gram_matrix(input)
        self.loss = F.mse_loss(G, self.target)
        return input

迁移模型（采用vgg Model）

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87

cnn = models.vgg19(pretrained=True).features.to(device).eval()

cnn_normalization_mean = torch.tensor([0.485, 0.456, 0.406]).to(device)
cnn_normalization_std = torch.tensor([0.229, 0.224, 0.225]).to(device)

# 创建模型并归一化数据，类似dataloader导入
class Normalization(nn.Module):
    def __init__(self, mean, std):
        super(Normalization, self).__init__()
        #  [C x 1 x 1] 转为tensor [B x C x H x W].
        # B - batchsize， C - channels， H - height ， W - width.
        self.mean = torch.tensor(mean).view(-1, 1, 1)
        self.std = torch.tensor(std).view(-1, 1, 1)

    def forward(self, img):
        # 255->1
        return (img - self.mean) / self.std

# 创建模型
content_layers_default = ['conv_4']
style_layers_default = ['conv_1', 'conv_2', 'conv_3', 'conv_4', 'conv_5']

def get_style_model_and_losses(cnn, normalization_mean, normalization_std,
                               style_img, content_img,
                               content_layers=content_layers_default,
                               style_layers=style_layers_default):
    cnn = copy.deepcopy(cnn)

    # 导入数据
    normalization = Normalization(normalization_mean, normalization_std).to(device)

    # 迭代器
    content_losses = []
    style_losses = []

    # 生成新的 nn.Sequential
    model = nn.Sequential(normalization)

    i = 0  
    for layer in cnn.children():
        if isinstance(layer, nn.Conv2d):
            i += 1
            name = 'conv_{}'.format(i)
        elif isinstance(layer, nn.ReLU):
            name = 'relu_{}'.format(i)
            #更改原始模型，以适应新环境，迁移学习
            layer = nn.ReLU(inplace=False)
        elif isinstance(layer, nn.MaxPool2d):
            name = 'pool_{}'.format(i)
        elif isinstance(layer, nn.BatchNorm2d):
            name = 'bn_{}'.format(i)
        else:
            raise RuntimeError('Unrecognized layer: {}'.format(layer.__class__.__name__))

        model.add_module(name, layer)

        if name in content_layers:
            # 增加 content loss:
            target = model(content_img).detach()
            content_loss = ContentLoss(target)
            model.add_module("content_loss_{}".format(i), content_loss)
            content_losses.append(content_loss)

        if name in style_layers:
            # 增加 style loss:
            target_feature = model(style_img).detach()
            style_loss = StyleLoss(target_feature)
            model.add_module("style_loss_{}".format(i), style_loss)
            style_losses.append(style_loss)

    # 改变
    for i in range(len(model) - 1, -1, -1):
        if isinstance(model[i], ContentLoss) or isinstance(model[i], StyleLoss):
            break

    model = model[:(i + 1)]

    return model, style_losses, content_losses

# 生成一幅新图画，既有content的内容，又有style的风格，可以以content为基础，也可以以随机图为基础。
input_img = content_img.clone()
# 随机白噪声图
# input_img = torch.randn(content_img.data.size(), device=device)

plt.figure()
plt.axis('off')
imshow(input_img, title='Input Image')

优化算法（Gradient Descent）

采用这种优化器：L-BFGS optimizer optim.LBFGS alt text

1
2
3
4

def get_input_optimizer(input_img):
    # 要求梯度的输入
    optimizer = optim.LBFGS([input_img.requires_grad_()])
    return optimizer

最后，我们必须定义一个执行神经传递的函数。对于网络的每次迭代，它被馈送更新的输入并计算新的损失。我们将运行backward每个损耗模块的方法来动态计算它们的梯度。优化器需要一个“closure”函数，它重新评估模块并返回损失。

我们还有一个最后的约束要解决。网络可以尝试使用超过图像的0到1张量范围的值来优化输入。我们可以通过在每次运行网络时将输入值更正为0到1来解决此问题。

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48

def run_style_transfer(cnn, normalization_mean, normalization_std,
                       content_img, style_img, input_img, num_steps=300,
                       style_weight=1000000, content_weight=1):
    """Run the style transfer."""
    print('Building the style transfer model..')
    model, style_losses, content_losses = get_style_model_and_losses(cnn,
        normalization_mean, normalization_std, style_img, content_img)
    optimizer = get_input_optimizer(input_img)
    print(model)
    print('Optimizing..')
    run = [0]
    while run[0] <= num_steps:

        def closure():
            # correct the values of updated input image
            input_img.data.clamp_(0, 1)

            optimizer.zero_grad()
            model(input_img)
            style_score = 0
            content_score = 0

            for sl in style_losses:
                style_score += sl.loss
            for cl in content_losses:
                content_score += cl.loss

            style_score *= style_weight
            content_score *= content_weight

            loss = style_score + content_score
            loss.backward()

            run[0] += 1
            if run[0] % 50 == 0:
                print("run {}:".format(run))
                print('Style Loss : {:4f} Content Loss: {:4f}'.format(
                    style_score.item(), content_score.item()))
                print()

            return style_score + content_score

        optimizer.step(closure)

    # a last correction...
    input_img.data.clamp_(0, 1)

    return input_img

运行算法（Run the algorithm）

1
2
3

output = run_style_transfer(cnn, cnn_normalization_mean, cnn_normalization_std,
                            content_img, style_img, input_img)
print('用时:','{:.2f}'.format(time.clock() - T0),'s')

图像显示结果

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19

plt.figure(figsize=(19,19),edgecolor='r',frameon=True) #指定图像显示大小，单位inch

ax = plt.subplot(1, 3, 1)# 1行3列第1副图
ax.axis('off')
imshow(style_img, title='Style')

ax = plt.subplot(1, 3, 2)
ax.axis('off')
imshow(content_img, title='Content')

ax = plt.subplot(1,3, 3)
ax.axis('off')
imshow(output, title='Output')

plt.ioff()
plt.show()
# tensor格式图像存储
import torchvision
torchvision.utils.save_image(output, 'out.jpg', nrow=8, padding=2, normalize=False, range=None, scale_each=False, pad_value=0)

png