如何在具有三个(RGB)通道的图像上计算卷积?

问题描述

假设我们有一个单通道图片(5x5)

A = [ 1 2 3 4 5
      6 7 8 9 2
      1 4 5 6 3
      4 5 6 7 4
      3 4 5 6 2 ]

还有一个过滤器K(2x2)

K = [ 1 1
      1 1 ]

应用卷积的示例(让我们从A中获得第一个2x2)将是

1*1 + 2*1 + 6*1 + 7*1 = 16

这很简单.但是让我们为矩阵A(即具有3个通道甚至在深层网络中具有转换层的RGB图像)引入一个深度因子(深度可能为512).使用相同的滤波器如何进行卷积运算? 类似的练习对于RGB情况真的很有帮助.

解决方案

除了将获得三个矩阵而不是一个矩阵之外，它们与对单个通道图像进行处理的方式相同.这是有关CNN基础知识的讲义，我认为这可能对您有帮助. >

Say we have a single channel image (5x5)

A = [ 1 2 3 4 5
      6 7 8 9 2
      1 4 5 6 3
      4 5 6 7 4
      3 4 5 6 2 ]

And a filter K (2x2)

K = [ 1 1
      1 1 ]

An example of applying convolution (let us take the first 2x2 from A) would be

1*1 + 2*1 + 6*1 + 7*1 = 16

This is very straightforward. But let us introduce a depth factor to matrix A i.e., RGB image with 3 channels or even conv layers in a deep network (with depth = 512 maybe). How would the convolution operation be done with the same filter ? A similiar work out will be really helpful for an RGB case.

解决方案

They will be just the same as how you do with a single channel image, except that you will get three matrices instead of one.This is a lecture note about CNN fundamentals, which I think might be helpful for you.

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