引言
本文是由NVIDIA提出的一种基于局部卷积的图像修复算法。
图像修复，即修复图像中缺失的块，可用于图像编辑，替换掉图像中不想要的内容。本文使用自动mask更新的局部卷积网络进行图像修复。
方法
partial convolutional layer
假设是卷积核的权重，
是相应的偏差。
是当前卷积窗口的特征值，
是相应的二进制mask。则卷积计算为
由上式可知，输出是由没有mask的输入决定。
在局部卷积操作之后，需要更新mask：
网络结构
整体网络使用UNet结构，将所有的卷积换成局部卷积层，在decoder阶段使用最近邻上采样。skip连接连接两个特征图和两个mask作为下一层的输入，最后一个卷积层的输入为有洞的原始输入和原始mask的组成。
损失函数
给定有洞的输入，初始化二进制mask
(有洞的地方为0)，网络的输出为
，原始的图像为
1、像素损失：
2、感知损失
其中，是未加工的输出图像
，
使用vgg16的pool1，pool2,pool3
3、风格损失
4、全变差损失
总的损失函数为：
代码分析
1、局部卷积层
from keras.utils import conv_utils
from keras import backend as K
from keras.engine import InputSpec
from keras.layers import Conv2D
class PConv2D(Conv2D):
def __init__(self, *args, n_channels=3, mono=False, **kwargs):
super().__init__(*args, **kwargs)
self.input_spec = [InputSpec(ndim=4), InputSpec(ndim=4)]
def build(self, input_shape):
if self.data_format == 'channels_first':
channel_axis = 1
else:
channel_axis = -1
if input_shape[0][channel_axis] is None:
raise ValueError('The channel dimension of the inputs should be defined. Found `None`.')
self.input_dim = input_shape[0][channel_axis]
kernel_shape = self.kernel_size + (self.input_dim, self.filters)
self.kernel = self.add_weight(shape=kernel_shape,
initializer=self.kernel_initializer,
name='img_kernel',
regularizer=self.kernel_regularizer,
constraint=self.kernel_constraint)
self.kernel_mask = K.ones(shape=self.kernel_size + (self.input_dim, self.filters))
# Calculate padding size to achieve zero-padding
self.pconv_padding = (
(int((self.kernel_size[0]-1)/2), int((self.kernel_size[0]-1)/2)),
(int((self.kernel_size[0]-1)/2), int((self.kernel_size[0]-1)/2)),
)
# Window size - used for normalization
self.window_size = self.kernel_size[0] * self.kernel_size[1]
if self.use_bias:
self.bias = self.add_weight(shape=(self.filters,),
initializer=self.bias_initializer,
name='bias',
regularizer=self.bias_regularizer,
constraint=self.bias_constraint)
else:
self.bias = None
self.built = True
def call(self, inputs, mask=None):
if type(inputs) is not list or len(inputs) != 2:
raise Exception('PartialConvolution2D must be called on a list of two tensors [img, mask]. Instead got: ' + str(inputs))
# Padding done explicitly so that padding becomes part of the masked partial convolution
images = K.spatial_2d_padding(inputs[0], self.pconv_padding, self.data_format)
masks = K.spatial_2d_padding(inputs[1], self.pconv_padding, self.data_format)
# Apply convolutions to mask
mask_output = K.conv2d(
masks, self.kernel_mask,
strides=self.strides,
padding='valid',
data_format=self.data_format,
dilation_rate=self.dilation_rate
)
# Apply convolutions to image
img_output = K.conv2d(
(images*masks), self.kernel,
strides=self.strides,
padding='valid',
data_format=self.data_format,
dilation_rate=self.dilation_rate
)
# Calculate the mask ratio on each pixel in the output mask
mask_ratio = self.window_size / (mask_output + 1e-8)
# Clip output to be between 0 and 1
mask_output = K.clip(mask_output, 0, 1)
# Remove ratio values where there are holes
mask_ratio = mask_ratio * mask_output
# Normalize iamge output
img_output = img_output * mask_ratio
# Apply bias only to the image (if chosen to do so)
if self.use_bias:
img_output = K.bias_add(
img_output,
self.bias,
data_format=self.data_format)
# Apply activations on the image
if self.activation is not None:
img_output = self.activation(img_output)
return [img_output, mask_output]
def compute_output_shape(self, input_shape):
if self.data_format == 'channels_last':
space = input_shape[0][1:-1]
new_space = []
for i in range(len(space)):
new_dim = conv_utils.conv_output_length(
space[i],
self.kernel_size[i],
padding='same',
stride=self.strides[i],
dilation=self.dilation_rate[i])
new_space.append(new_dim)
new_shape = (input_shape[0][0],) + tuple(new_space) + (self.filters,)
return [new_shape, new_shape]
if self.data_format == 'channels_first':
space = input_shape[2:]
new_space = []
for i in range(len(space)):
new_dim = conv_utils.conv_output_length(
space[i],
self.kernel_size[i],
padding='same',
stride=self.strides[i],
dilation=self.dilation_rate[i])
new_space.append(new_dim)
new_shape = (input_shape[0], self.filters) + tuple(new_space)
return [new_shape, new_shape]
2、损失函数
def loss_hole(self, mask, y_true, y_pred):
"""Pixel L1 loss within the hole / mask"""
return self.l1((1-mask) * y_true, (1-mask) * y_pred)
def loss_valid(self, mask, y_true, y_pred):
"""Pixel L1 loss outside the hole / mask"""
return self.l1(mask * y_true, mask * y_pred)
def loss_perceptual(self, vgg_out, vgg_gt, vgg_comp):
"""Perceptual loss based on VGG16, see. eq. 3 in paper"""
loss = 0
for o, c, g in zip(vgg_out, vgg_comp, vgg_gt):
loss += self.l1(o, g) + self.l1(c, g)
return loss
def loss_style(self, output, vgg_gt):
"""Style loss based on output/computation, used for both eq. 4 & 5 in paper"""
loss = 0
for o, g in zip(output, vgg_gt):
loss += self.l1(self.gram_matrix(o), self.gram_matrix(g))
return loss
def loss_tv(self, mask, y_comp):
"""Total variation loss, used for smoothing the hole region, see. eq. 6"""
# Create dilated hole region using a 3x3 kernel of all 1s.
kernel = K.ones(shape=(3, 3, mask.shape[3], mask.shape[3]))
dilated_mask = K.conv2d(1-mask, kernel, data_format='channels_last', padding='same')
# Cast values to be [0., 1.], and compute dilated hole region of y_comp
dilated_mask = K.cast(K.greater(dilated_mask, 0), 'float32')
P = dilated_mask * y_comp
# Calculate total variation loss
a = self.l1(P[:,1:,:,:], P[:,:-1,:,:])
b = self.l1(P[:,:,1:,:], P[:,:,:-1,:])
return a+b
参考文献
[1]Image Inpainting for Irregular Holes Using
Partial Convolutions
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