我想用 C3D 的图片进行解释a>.

I want to explain with picture from C3D.

概括地说，卷积方向& 输出形状很重要！

In a nutshell, convolutional direction & output shape is important!

↑↑↑↑↑ 一维卷积-基本 ↑↑↑↑↑

↑↑↑↑↑ 1D Convolutions - Basic ↑↑↑↑↑

• 只需 1 方向(时间轴)即可计算转化
• 输入= [W]，过滤器= [k]，输出= [W]
• ex)输入= [1,1,1,1,1]，过滤器= [0.25,0.5,0.25]，输出= [1,1,1,1,1]
• 输出形状是一维数组
• 示例)图形平滑

• just 1-direction (time-axis) to calculate conv
• input = [W], filter = [k], output = [W]
• ex) input = [1,1,1,1,1], filter = [0.25,0.5,0.25], output = [1,1,1,1,1]
• output-shape is 1D array
• example) graph smoothing

import tensorflow as tf
import numpy as np

sess = tf.Session()

ones_1d = np.ones(5)
weight_1d = np.ones(3)
strides_1d = 1

in_1d = tf.constant(ones_1d, dtype=tf.float32)
filter_1d = tf.constant(weight_1d, dtype=tf.float32)

in_width = int(in_1d.shape[0])
filter_width = int(filter_1d.shape[0])

input_1d   = tf.reshape(in_1d, [1, in_width, 1])
kernel_1d = tf.reshape(filter_1d, [filter_width, 1, 1])
output_1d = tf.squeeze(tf.nn.conv1d(input_1d, kernel_1d, strides_1d, padding='SAME'))
print sess.run(output_1d)

↑↑↑↑↑ 2D卷积-基本 ↑↑↑↑↑

↑↑↑↑↑ 2D Convolutions - Basic ↑↑↑↑↑

• 2 方向(x，y)计算转化率
• 输出形状为 2D 矩阵
• 输入= [W，H]，过滤器= [k，k]输出= [W，H]
• 示例) Sobel Egde Fllter

• 2-direction (x,y) to calculate conv
• output-shape is 2D Matrix
• input = [W, H], filter = [k,k] output = [W,H]
• example) Sobel Egde Fllter

ones_2d = np.ones((5,5))
weight_2d = np.ones((3,3))
strides_2d = [1, 1, 1, 1]

in_2d = tf.constant(ones_2d, dtype=tf.float32)
filter_2d = tf.constant(weight_2d, dtype=tf.float32)

in_width = int(in_2d.shape[0])
in_height = int(in_2d.shape[1])

filter_width = int(filter_2d.shape[0])
filter_height = int(filter_2d.shape[1])

input_2d   = tf.reshape(in_2d, [1, in_height, in_width, 1])
kernel_2d = tf.reshape(filter_2d, [filter_height, filter_width, 1, 1])

output_2d = tf.squeeze(tf.nn.conv2d(input_2d, kernel_2d, strides=strides_2d, padding='SAME'))
print sess.run(output_2d)

↑↑↑↑↑ 3D卷积-基本 ↑↑↑↑↑

↑↑↑↑↑ 3D Convolutions - Basic ↑↑↑↑↑

• 3 方向(x，y，z)计算转化率
• 输出形状为 3D 体积
• 输入= [W，H， L ]，过滤器= [k，k， d ]输出= [W，H，M]
• d< L 很重要！用于输出音量
• 示例)C3D

• 3-direction (x,y,z) to calcuate conv
• output-shape is 3D Volume
• input = [W,H,L], filter = [k,k,d] output = [W,H,M]
• d < L is important! for making volume output
• example) C3D

ones_3d = np.ones((5,5,5))
weight_3d = np.ones((3,3,3))
strides_3d = [1, 1, 1, 1, 1]

in_3d = tf.constant(ones_3d, dtype=tf.float32)
filter_3d = tf.constant(weight_3d, dtype=tf.float32)

in_width = int(in_3d.shape[0])
in_height = int(in_3d.shape[1])
in_depth = int(in_3d.shape[2])

filter_width = int(filter_3d.shape[0])
filter_height = int(filter_3d.shape[1])
filter_depth = int(filter_3d.shape[2])

input_3d   = tf.reshape(in_3d, [1, in_depth, in_height, in_width, 1])
kernel_3d = tf.reshape(filter_3d, [filter_depth, filter_height, filter_width, 1, 1])

output_3d = tf.squeeze(tf.nn.conv3d(input_3d, kernel_3d, strides=strides_3d, padding='SAME'))
print sess.run(output_3d)

↑↑↑↑↑ 具有3D输入的2D卷积 -LeNet，VGG，...，↑↑↑↑↑

↑↑↑↑↑ 2D Convolutions with 3D input - LeNet, VGG, ..., ↑↑↑↑↑

• 事件输入为3D，例如)224x224x3、112x112x32
• 输出形状不是 3D 体积，而是 2D 矩阵
• 因为过滤器深度= L 必须与输入通道= L
匹配
• 2 方向(x，y)计算转换！不是3D
• 输入= [W，H， L ]，过滤器= [k，k， L ]输出= [W，H]
• 输出形状为 2D 矩阵
• 如果我们要训练N个过滤器(N是过滤器数)
• 然后，输出形状为(堆叠2D) 3D = 2D x N 矩阵.

• Eventhough input is 3D ex) 224x224x3, 112x112x32
• output-shape is not 3D Volume, but 2D Matrix
• because filter depth = L must be matched with input channels = L
• 2-direction (x,y) to calcuate conv! not 3D
• input = [W,H,L], filter = [k,k,L] output = [W,H]
• output-shape is 2D Matrix
• what if we want to train N filters (N is number of filters)
• then output shape is (stacked 2D) 3D = 2D x N matrix.

in_channels = 32 # 3 for RGB, 32, 64, 128, ... 
ones_3d = np.ones((5,5,in_channels)) # input is 3d, in_channels = 32
# filter must have 3d-shpae with in_channels
weight_3d = np.ones((3,3,in_channels)) 
strides_2d = [1, 1, 1, 1]

in_3d = tf.constant(ones_3d, dtype=tf.float32)
filter_3d = tf.constant(weight_3d, dtype=tf.float32)

in_width = int(in_3d.shape[0])
in_height = int(in_3d.shape[1])

filter_width = int(filter_3d.shape[0])
filter_height = int(filter_3d.shape[1])

input_3d   = tf.reshape(in_3d, [1, in_height, in_width, in_channels])
kernel_3d = tf.reshape(filter_3d, [filter_height, filter_width, in_channels, 1])

output_2d = tf.squeeze(tf.nn.conv2d(input_3d, kernel_3d, strides=strides_2d, padding='SAME'))
print sess.run(output_2d)

conv2d-LeNet，VGG ...用于N个过滤器

in_channels = 32 # 3 for RGB, 32, 64, 128, ... 
out_channels = 64 # 128, 256, ...
ones_3d = np.ones((5,5,in_channels)) # input is 3d, in_channels = 32
# filter must have 3d-shpae x number of filters = 4D
weight_4d = np.ones((3,3,in_channels, out_channels))
strides_2d = [1, 1, 1, 1]

in_3d = tf.constant(ones_3d, dtype=tf.float32)
filter_4d = tf.constant(weight_4d, dtype=tf.float32)

in_width = int(in_3d.shape[0])
in_height = int(in_3d.shape[1])

filter_width = int(filter_4d.shape[0])
filter_height = int(filter_4d.shape[1])

input_3d   = tf.reshape(in_3d, [1, in_height, in_width, in_channels])
kernel_4d = tf.reshape(filter_4d, [filter_height, filter_width, in_channels, out_channels])

#output stacked shape is 3D = 2D x N matrix
output_3d = tf.nn.conv2d(input_3d, kernel_4d, strides=strides_2d, padding='SAME')
print sess.run(output_3d)

↑↑↑↑↑ 在CNN中获得1x1转化奖励 -GoogLeNet，...，↑↑↑↑↑

↑↑↑↑↑ Bonus 1x1 conv in CNN - GoogLeNet, ..., ↑↑↑↑↑

当您将其视为像sobel这样的2D图像滤镜时，
• 1x1转换会令人困惑
• 对于CNN中的1x1转换，输入为3D形状，如上图所示.
• 它计算深度过滤
• 输入= [W，H，L]，过滤器= [1,1，L] 输出= [W，H]
• 输出堆叠形状为 3D = 2D x N 矩阵.

• 1x1 conv is confusing when you think this as 2D image filter like sobel
• for 1x1 conv in CNN, input is 3D shape as above picture.
• it calculate depth-wise filtering
• input = [W,H,L], filter = [1,1,L] output = [W,H]
• output stacked shape is 3D = 2D x N matrix.

in_channels = 32 # 3 for RGB, 32, 64, 128, ... 
out_channels = 64 # 128, 256, ...
ones_3d = np.ones((1,1,in_channels)) # input is 3d, in_channels = 32
# filter must have 3d-shpae x number of filters = 4D
weight_4d = np.ones((3,3,in_channels, out_channels))
strides_2d = [1, 1, 1, 1]

in_3d = tf.constant(ones_3d, dtype=tf.float32)
filter_4d = tf.constant(weight_4d, dtype=tf.float32)

in_width = int(in_3d.shape[0])
in_height = int(in_3d.shape[1])

filter_width = int(filter_4d.shape[0])
filter_height = int(filter_4d.shape[1])

input_3d   = tf.reshape(in_3d, [1, in_height, in_width, in_channels])
kernel_4d = tf.reshape(filter_4d, [filter_height, filter_width, in_channels, out_channels])

#output stacked shape is 3D = 2D x N matrix
output_3d = tf.nn.conv2d(input_3d, kernel_4d, strides=strides_2d, padding='SAME')
print sess.run(output_3d)

动画(具有3D输入的2D转换)

-原始链接:

Animation (2D Conv with 3D-inputs)

- Original Link : LINK
- The author: Martin Görner
- Twitter: @martin_gorner
- Google +: plus.google.com/+MartinGorne

↑↑↑↑↑ 具有1D输入的1D卷积 ↑↑↑↑↑

↑↑↑↑↑ 1D Convolutions with 1D input ↑↑↑↑↑

↑↑↑↑↑ 具有2D输入的一维卷积 ↑↑↑↑↑

↑↑↑↑↑ 1D Convolutions with 2D input ↑↑↑↑↑

• 事件输入为2D，例如20x14
• 输出形状不是 2D ，而是 1D 矩阵
• 因为过滤器高度= L 必须与输入高度= L
相匹配
• 1 -方向(x)计算转换！不是2D
• 输入= [W， L ]，过滤器= [k， L ]输出= [W]
• 输出形状为 1D 矩阵
• 如果我们要训练N个过滤器(N是过滤器数)
• 然后，输出形状为(堆叠1D) 2D = 1D x N 矩阵.

• Eventhough input is 2D ex) 20x14
• output-shape is not 2D , but 1D Matrix
• because filter height = L must be matched with input height = L
• 1-direction (x) to calcuate conv! not 2D
• input = [W,L], filter = [k,L] output = [W]
• output-shape is 1D Matrix
• what if we want to train N filters (N is number of filters)
• then output shape is (stacked 1D) 2D = 1D x N matrix.

in_channels = 32 # 3, 32, 64, 128, ... 
out_channels = 64 # 3, 32, 64, 128, ... 
ones_4d = np.ones((5,5,5,in_channels))
weight_5d = np.ones((3,3,3,in_channels,out_channels))
strides_3d = [1, 1, 1, 1, 1]

in_4d = tf.constant(ones_4d, dtype=tf.float32)
filter_5d = tf.constant(weight_5d, dtype=tf.float32)

in_width = int(in_4d.shape[0])
in_height = int(in_4d.shape[1])
in_depth = int(in_4d.shape[2])

filter_width = int(filter_5d.shape[0])
filter_height = int(filter_5d.shape[1])
filter_depth = int(filter_5d.shape[2])

input_4d   = tf.reshape(in_4d, [1, in_depth, in_height, in_width, in_channels])
kernel_5d = tf.reshape(filter_5d, [filter_depth, filter_height, filter_width, in_channels, out_channels])

output_4d = tf.nn.conv3d(input_4d, kernel_5d, strides=strides_3d, padding='SAME')
print sess.run(output_4d)

sess.close()

输入&在Tensorflow中输出