参考

https://cv-tricks.com/image-segmentation/transpose-convolution-in-tensorflow/

https://zhuanlan.zhihu.com/p/32414293

目标

现在我们要将3×6的图象转变为6×12的图象，即已知upscale_factor=2。

目标结果：

align_corners=True

align_corners=False

1. 计算卷积核大小

bilinear = get_bilinear_filter([4,4,1,1,],2)
print(bilinear)
array([[ 0.0625,  0.1875,  0.1875,  0.0625],[ 0.1875,  0.5625,  0.5625,  0.1875],[ 0.1875,  0.5625,  0.5625,  0.1875],[ 0.0625,  0.1875,  0.1875,  0.0625]])

filter_shape是卷积核的形状，由
kernel_size=2∗upscale_factor−upscale_factor%2kernel\_size = 2*upscale\_factor - upscale\_factor\%2kernel_size=2∗upscale_factor−upscale_factor%2
计算得到，filter_shape=[4,4,1,1]。

import numpy as np
def get_bilinear_filter(filter_shape, upscale_factor):##filter_shape is [width, height, num_in_channels, num_out_channels]kernel_size = 2*upscale_factor - upscale_factor%2### Centre location of the filter for which value is calculatedif kernel_size % 2 == 1:centre_location = upscale_factor - 1else:centre_location = upscale_factor - 0.5bilinear = np.zeros([filter_shape[0], filter_shape[1]], dtype='float32')for x in range(filter_shape[0]):for y in range(filter_shape[1]):##Interpolation Calculationvalue = (1 - abs((x - centre_location)/ upscale_factor)) * (1 - abs((y - centre_location)/ upscale_factor))bilinear[x, y] = valuereturn bilinear

2. deconvolution计算得到6×12的目标图象

deconvolution操作首先要在3×6的图像上（对应上图中第1张图像）不同像素间进行插0的操作，即得到5×11的图象（第2张图像的中间部分）。

该5×11的图象要与已知是4×4的卷积核（第2个箭头上的卷积核）进行步长为1卷积，得到目标6×12的图象（第3张图像），计算得到padding为2。用 0 padding后，得到第2张图像。

卷积核的取值上面已经由代码得到，下面用示意图给出卷积核中4个位置的数值的具体计算方法，其他12个位置的计算类似：

右图卷积核作用在左图中虚线框出的4×4区域时，真正有效的卷积核参数是填充色为红色的4个位置的参数。采样点为centre_location = upscale_factor - 0.5=3/2，即为下图中的红色点：

以上就是在高分辨率图像上做卷积核不变的卷积运算得到双线性插值后图像的方法。这种方法采样点的取法为：

#3*6图像
bottom = tf.constant([[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17,18]], dtype='float32')
bottom = tf.reshape(bottom, [1, 3, 6, 1])
weights = tf.reshape(bilinear, [4, 4, 1, 1])
stride = upscale_factor
strides = [1, stride, stride, 1]
deconv = tf.nn.conv2d_transpose(bottom, weights, [1,6,12,1],strides, padding='SAME')
with tf.Session() as sess:print("deconv: ", deconv.eval())

可以验证opencv中的imresize方法采样点也是这种取法，但是它不是直接用 0 padding，而是由边界的像素点决定padding数值。所以cv2.resize的计算结果和tf.nn.conv2d_transpose的计算结果不同。

完整代码

import numpy as np
import tensorflow as tf
def get_bilinear_filter(filter_shape, upscale_factor):##filter_shape is [width, height, num_in_channels, num_out_channels]kernel_size = 2*upscale_factor - upscale_factor%2### Centre location of the filter for which value is calculatedif kernel_size % 2 == 1:centre_location = upscale_factor - 1else:centre_location = upscale_factor - 0.5bilinear = np.zeros([filter_shape[0], filter_shape[1]], dtype='float32')for x in range(filter_shape[0]):for y in range(filter_shape[1]):##Interpolation Calculationvalue = (1 - abs((x - centre_location)/ upscale_factor)) * (1 - abs((y - centre_location)/ upscale_factor))bilinear[x, y] = valuereturn bilinearupscale_factor =2
bilinear = get_bilinear_filter([4,4,1,1,],2)
print(bilinear)#3*6图像
bottom = tf.constant([[1,2,3,4,5,6],[7,8,9,10,11,12],[13,14,15,16,17,18]], dtype='float32')
bottom = tf.reshape(bottom, [1, 3, 6, 1])
weights = tf.reshape(bilinear, [4, 4, 1, 1])
stride = upscale_factor
strides = [1, stride, stride, 1]
deconv = tf.nn.conv2d_transpose(bottom, weights, [1,6,12,1],strides, padding='SAME')
print(deconv)
# with tf.Session() as sess:# print("deconv: ", deconv.eval())

附录1：tf 反卷积实现：4×4 到8×8

反卷积的weight是：

[[0.0625 0.1875 0.1875 0.0625][0.1875 0.5625 0.5625 0.1875][0.1875 0.5625 0.5625 0.1875][0.0625 0.1875 0.1875 0.0625]]

import numpy as np
import tensorflow as tf
def get_bilinear_filter(filter_shape, upscale_factor):##filter_shape is [width, height, num_in_channels, num_out_channels]kernel_size = 2*upscale_factor - upscale_factor%2### Centre location of the filter for which value is calculatedif kernel_size % 2 == 1:centre_location = upscale_factor - 1else:centre_location = upscale_factor - 0.5bilinear = np.zeros([filter_shape[0], filter_shape[1]], dtype='float32')for x in range(filter_shape[0]):for y in range(filter_shape[1]):##Interpolation Calculationvalue = (1 - abs((x - centre_location)/ upscale_factor)) * (1 - abs((y - centre_location)/ upscale_factor))bilinear[x, y] = valuereturn bilinearupscale_factor =2
bilinear = get_bilinear_filter([4,4,1,1,],2)
print(bilinear)#3*6图像
bottom = tf.constant([[0.,  1.,  2.,  3.],[4.,  5.,  6.,  7.],[8.,  9., 10., 11.],[12., 13., 14., 15.]], dtype='float32')
bottom = tf.reshape(bottom, [1, 4, 4, 1])
weights = tf.reshape(bilinear, [4, 4, 1, 1])
stride = upscale_factor
strides = [1, stride, stride, 1]
deconv = tf.nn.conv2d_transpose(bottom, weights, [1,8,8,1],strides, padding='SAME')
print(deconv)
with tf.Session() as sess:print("deconv: ", deconv.eval())ouuu =  tf.image.resize_images(bottom, [6,12], method=tf.image.ResizeMethod.BILINEAR, align_corners=True)print(ouuu)
with tf.Session() as sess:print("deconv: ", ouuu.eval())

附录2：pytorch 反卷积实现：4×4 到8×8

from torch import nn
from torch.nn import init
from torch.autograd import Variable
import torchimport numpy as np
def get_bilinear_filter(filter_shape, upscale_factor):##filter_shape is [width, height, num_in_channels, num_out_channels]kernel_size = 2*upscale_factor - upscale_factor%2### Centre location of the filter for which value is calculatedif kernel_size % 2 == 1:centre_location = upscale_factor - 1else:centre_location = upscale_factor - 0.5bilinear = np.zeros([filter_shape[0], filter_shape[1]], dtype='float32')for x in range(filter_shape[0]):for y in range(filter_shape[1]):##Interpolation Calculationvalue = (1 - abs((x - centre_location)/ upscale_factor)) * (1 - abs((y - centre_location)/ upscale_factor))bilinear[x, y] = valuereturn bilinear# kernel_size=2∗upscale_factor−upscale_factor%2
upscale_factor =2
bilinear = get_bilinear_filter([4,4,1,1,],upscale_factor)inputv = torch.arange(4*4).view(1, 1, 4, 4).float()
print(inputv)# inputv = N,Cin,Hin,Win
dconv = nn.ConvTranspose2d(in_channels=1, out_channels= 1,  kernel_size=4, stride=2, padding=1,output_padding=0, bias= False)
# Hout=(Hin−1)×stride[0]−2×padding[0]+dilation[0]×(kernel_size[0]−1)+output_padding[0]+1
# https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.htmlbilinear = torch.reshape(torch.from_numpy (bilinear), [1, 1, 4, 4])#NHWC
print(bilinear.shape) # 先创建一个自定义权值的Tensor，这里为了方便将所有权值设为1
dconv.weight=torch.nn.Parameter(bilinear)
print(dconv.weight.shape)# print(inputv)
print(dconv(inputv)) # torch.Size([1, 1, 8, 8])
print(dconv.weight)

结果均为：

tensor([[[[ 0.0000,  0.1875,  0.5625,  0.9375,  1.3125,  1.6875,  2.0625,1.6875],[ 0.7500,  1.2500,  1.7500,  2.2500,  2.7500,  3.2500,  3.7500,3.0000],[ 2.2500,  3.2500,  3.7500,  4.2500,  4.7500,  5.2500,  5.7500,4.5000],[ 3.7500,  5.2500,  5.7500,  6.2500,  6.7500,  7.2500,  7.7500,6.0000],[ 5.2500,  7.2500,  7.7500,  8.2500,  8.7500,  9.2500,  9.7500,7.5000],[ 6.7500,  9.2500,  9.7500, 10.2500, 10.7500, 11.2500, 11.7500,9.0000],[ 8.2500, 11.2500, 11.7500, 12.2500, 12.7500, 13.2500, 13.7500,10.5000],[ 6.7500,  9.1875,  9.5625,  9.9375, 10.3125, 10.6875, 11.0625,8.4375]]]]

附录3： F.grid_sample 双线性插值实现：4×4 到8×8

import torch.nn.functional as F
import torch
inputv = torch.arange(4*4).view(1, 1, 4, 4).float()
print(inputv.shape)
'''
输出尺寸为(1,1,4,4)
输出为：tensor([[[[ 0.,  1.,  2.,  3.],[ 4.,  5.,  6.,  7.],[ 8.,  9., 10., 11.],[12., 13., 14., 15.]]]])
'''
# 生成grid，这个grid大小为(1,8,8,2)，空间尺寸而言是原输入图片的两倍。
d = torch.linspace(-1,1, 8)
meshx, meshy = torch.meshgrid((d, d))
grid = torch.stack((meshy, meshx), 2)
grid = grid.unsqueeze(0) # add batch dim
print(grid.shape)# inputv.shape : [B,C,H_in,W_in]
# grid.shape: [B,H_out,W_out,2]
# output: [B,C,H_out,W_out]
# 进行双线性采样，其中指定align_corners=True保证了输出的整个图片的角边像素与原输入的一致性。
output = F.grid_sample(inputv, grid,align_corners=True)
print(output)
output = torch.nn.functional.upsample_bilinear(inputv,  scale_factor=2)
print(output.shape)output = F.interpolate(inputv, scale_factor=2, mode='bilinear', align_corners=True)
print(output)

结果有差异？？？

tensor([[[[ 0.0000,  0.4286,  0.8571,  1.2857,  1.7143,  2.1429,  2.5714,3.0000],[ 1.7143,  2.1429,  2.5714,  3.0000,  3.4286,  3.8571,  4.2857,4.7143],[ 3.4286,  3.8571,  4.2857,  4.7143,  5.1429,  5.5714,  6.0000,6.4286],[ 5.1429,  5.5714,  6.0000,  6.4286,  6.8571,  7.2857,  7.7143,8.1429],[ 6.8571,  7.2857,  7.7143,  8.1429,  8.5714,  9.0000,  9.4286,9.8571],[ 8.5714,  9.0000,  9.4286,  9.8571, 10.2857, 10.7143, 11.1429,11.5714],[10.2857, 10.7143, 11.1429, 11.5714, 12.0000, 12.4286, 12.8571,13.2857],[12.0000, 12.4286, 12.8571, 13.2857, 13.7143, 14.1429, 14.5714,15.0000]]]])

1×512×1×1 使用反卷积实现双线性插值到 1×512×32×32

欢迎指正错误：

from torch import nn
from torch.nn import init
from torch.autograd import Variable
import torchimport numpy as np
def get_bilinear_filter(filter_shape, upscale_factor):##filter_shape is [width, height, num_in_channels, num_out_channels]kernel_size = 2*upscale_factor - upscale_factor%2### Centre location of the filter for which value is calculatedif kernel_size % 2 == 1:centre_location = upscale_factor - 1else:centre_location = upscale_factor - 0.5bilinear = np.zeros([filter_shape[0], filter_shape[1]], dtype='float32')for x in range(filter_shape[0]):for y in range(filter_shape[1]):##Interpolation Calculationvalue = (1 - abs((x - centre_location)/ upscale_factor)) * (1 - abs((y - centre_location)/ upscale_factor))bilinear[x, y] = valuereturn bilinear# kernel_size=2∗upscale_factor−upscale_factor%2
upscale_factor =32
bilinear = get_bilinear_filter([64,64,1,1,],upscale_factor)
print(bilinear)
inputv = torch.arange(512*1*1).view(1, 512, 1, 1).float()
print(inputv.shape)# inputv = N,Cin,Hin,Win
dconv = nn.ConvTranspose2d(in_channels=1, out_channels= 1,  kernel_size=64, stride=1, padding=16,output_padding=0, bias= False,padding_mode='zeros')# Hout=(Hin−1)×stride[0]−2×padding[0]+dilation[0]×(kernel_size[0]−1)+output_padding[0]+1
# https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.htmlbilinear = torch.reshape(torch.from_numpy (bilinear), [1, 1, 64, 64])#NHWC
print(bilinear.shape) # 先创建一个自定义权值的Tensor，这里为了方便将所有权值设为1
dconv.weight=torch.nn.Parameter(bilinear)
print(dconv.weight.shape)save = torch.arange(512*32*32).view(1, 512, 32, 32).float()
for i in range(512):inputvsin = torch.reshape(inputv[0][i], [1, 1, 1, 1])#NHWC# print(inputvsin)# print(dconv(inputvsin).shape) # torch.Size([1, 1, 8, 8])# print(dconv(inputvsin)) # torch.Size([1, 1, 8, 8])save[0][i]=dconv(inputvsin)
print(save)
print(save.shape)import torch.nn.functional as F
output = F.interpolate(inputv, scale_factor=32, mode='bilinear', align_corners=False)# : nearest | linear | bilinear | bicubic | trilinear (got near)
print(output)
print(output.shape)

和pytorch的api的结果有较大差异

ConvTranspose2d 使用 0 padding，一般的线性插值由边界的像素点决定padding数值。所以ConvTranspose2d 的计算结果和interpolate的计算结果不同。

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参考

目标