How is a convolution calculated on an image with three (RGB) channels?

Aragorn picture Aragorn · May 8, 2016 · Viewed 16.4k times · Source

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.

Answer

Muthukrishnan picture Muthukrishnan · Sep 2, 2018

Lets say we have a 3 Channel (RGB) image given by some matrix A


    A = [[[198 218 227]
          [196 216 225]
          [196 214 224]
          ...
          ...
          [185 201 217]
          [176 192 208]
          [162 178 194]]

and a blur kernal as


    K = [[0.1111, 0.1111, 0.1111],
         [0.1111, 0.1111, 0.1111],
         [0.1111, 0.1111, 0.1111]]

    #which is actually 0.111 ~= 1/9

The convolution can be represented as shown in the image below convolution of RGB channel

As you can see in the image, each channel is individually convoluted and then combined to form a pixel.