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This is because edge detection tries to find out significant transitions in luminosity/brightness in an image. Therefore grayscale images are used, since in grayscale the brightness of an image is modeled.

You can of course use other characteristics of a pixel (like the red color) if the scene is illuminated in red or if the edges to be detected belong to objects that reflect the red color specter most.

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Q: Why you use gray image for edge detection?
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