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.
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.
For RGB-like inputs, the filter is actually 2*2*3, each filter corresponse to one color channel, resulting three filter response. These three add up to one flowing by bias and activation. finally, this is one pixel in the output map.
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
As you can see in the image, each channel is individually convoluted and then combined to form a pixel.
来源：https://stackoverflow.com/questions/37095783/how-is-convolution-done-with-rgb-channel