Intuitive understanding of 1D, 2D, and 3D Convolutions in Convolutional Neural Networks

问题:

Can anyone please clearly explain the difference between 1D, 2D, and 3D convolutions in CNN (Deep Learning) with examples?

回答1:

I want to explain with picture from C3D.

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

↑↑↑↑↑ 1D Convolutions - Basic ↑↑↑↑↑

• 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

tf.nn.conv1d code Toy Example

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 Convolutions - Basic ↑↑↑↑↑

• 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

tf.nn.conv2d - Toy Example

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 Convolutions - Basic ↑↑↑↑↑

• 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

tf.nn.conv3d - Toy Example

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_depth, 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) 

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

• 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.

conv2d - LeNet, VGG, ... for 1 filter

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, ... for N filters

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) 

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

• 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.

tf.nn.conv2d - special case 1x1 conv

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) 

Animation (2D Conv with 3D-inputs)

- Original Link : LINK

- Twitter: @martin_gorner
- Google +: plus.google.com/+MartinGorne

Bonus 1D Convolutions with 2D input

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

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

• 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.

Bonus C3D

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_depth, 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() 

Input & Output in Tensorflow

Summary

文章来源: Intuitive understanding of 1D, 2D, and 3D Convolutions in Convolutional Neural Networks