论文链接：

https://www.cv-foundation.org/openaccess/content_cvpr_2016/papers/Gatys_Image_Style_Transfer_CVPR_2016_paper.pdf
作者运用了一个披着深度学习外表的传统方法做这个问题，技术不提倡，思路、想法很天才。

主要思路：

1、想办法分离style features和content features;
2、怎么得到content features，作者偷懒直接取vgg19里面conv4_2的features，当作content features；
3、怎么得到style features，作者发挥天才的偷懒，认为style就是features之间的相关度，作者直接取vgg19里面conv1_1，conv2_1，conv3_1，conv4_1，conv5_1这5层的feature map来算风格相关度，作者又发现不同的layer对风格有影响，前面的风格细腻，后面的风格粗犷，又给这5个层的loss误差加了权重。
4、那么目标是什么了？就是new_image和content_image的内容接近，new_image和stytle_image的风格接近，LtotalL_{total}Ltotal = LcontentL_{content}Lcontent+LstyleL_{style}Lstyle，首先要像，其次才是风格，所以LcontentL_{content}Lcontent的比重要大。

pytorch实现：

计算content的Loss:

前面提到了作者偷懒直接取vgg19里面conv4_2的features，当作content features，那么只需要比较两个feature map的差别就行了。

# the content losscontent_loss = torch.mean((target_features['conv4_2'] - content_features['conv4_2'])**2)

计算style 的Loss:

def gram_matrix(tensor):""" Calculate the Gram Matrix of a given tensor Gram Matrix: https://en.wikipedia.org/wiki/Gramian_matrix"""# get the batch_size, depth, height, and width of the Tensor_, d, h, w = tensor.size()# reshape so we're multiplying the features for each channeltensor = tensor.view(d, h * w)# calculate the gram matrixgram = torch.mm(tensor, tensor.t())return gram

# weights for each style layer
# weighting earlier layers more will result in *larger* style artifacts
# notice we are excluding `conv4_2` our content representation
style_weights = {'conv1_1': 1.,'conv2_1': 0.75,'conv3_1': 0.2,'conv4_1': 0.2,'conv5_1': 0.2}# get style features only once before training
style_features = get_features(style, vgg)# calculate the gram matrices for each layer of our style representation
style_grams = {layer: gram_matrix(style_features[layer]) for layer in style_features}for layer in style_weights:# get the "target" style representation for the layertarget_feature = target_features[layer]target_gram = gram_matrix(target_feature)_, d, h, w = target_feature.shape# get the "style" style representationstyle_gram = style_grams[layer]# the style loss for one layer, weighted appropriatelylayer_style_loss = style_weights[layer] * torch.mean((target_gram - style_gram)**2)# add to the style lossstyle_loss += layer_style_loss / (d * h * w)

计算total的Loss:


content_weight = 1  # alpha
style_weight = 1e6  # beta# calculate the *total* loss
total_loss = content_weight * content_loss + style_weight * style_loss

训练过程：

有人可能问VGG参数固定住了，需要的参数是什么了，参数就是新图啊？通过上述loss调整图像的像素值，这个和我们一般了解到的有点不一样。
新图就是在原图的基础上慢慢变化,f复制原图并设置新图为trainable的：

# create a third "target" image and prep it for change
# it is a good idea to start of with the target as a copy of our *content* image
# then iteratively change its style
target = content.clone().requires_grad_(True).to(device)

训练大概代码如下：

# for displaying the target image, intermittently
show_every = 400# iteration hyperparameters
optimizer = optim.Adam([target], lr=0.003)
steps = 2000  # decide how many iterations to update your image (5000)for ii in range(1, steps+1):# get the features from your target imagetarget_features = get_features(target, vgg)# the content losscontent_loss = torch.mean((target_features['conv4_2'] - content_features['conv4_2'])**2)# the style loss# initialize the style loss to 0style_loss = 0# then add to it for each layer's gram matrix lossfor layer in style_weights:# get the "target" style representation for the layertarget_feature = target_features[layer]target_gram = gram_matrix(target_feature)_, d, h, w = target_feature.shape# get the "style" style representationstyle_gram = style_grams[layer]# the style loss for one layer, weighted appropriatelylayer_style_loss = style_weights[layer] * torch.mean((target_gram - style_gram)**2)# add to the style lossstyle_loss += layer_style_loss / (d * h * w)# calculate the *total* losstotal_loss = content_weight * content_loss + style_weight * style_loss# update your target imageoptimizer.zero_grad()total_loss.backward()optimizer.step()

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