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Do you achieve anything different if you blur each channel independently?

I saw in a tutorial (cant remember where the tutorial was) where someone split a 3 channel image (BGR) into its single channels, median blurred each single channel, performed Canny edge detection on each blurred channel image then joined the 3 resulting edges together. I was thinking, why not just median blur the 3 channel image then use Canny to get the edges instead of splitting first?

My question is; is there any significant difference in results by doing things their way vs mine? Does it do something different that I'm not aware of? Maybe it does something useful I need to learn.

*I'm pretty sure the tutorial was a PyImageSearch one but I cannot find which one.