Before leaving the subject of edge detection, two additional matters need to be mentioned.
First, in toto edges are in general characterised not only by luminance (or brightness) differences, but also by chrominance (or colour) differences. In fact, strictly speaking there are three dimensions of local changes which matter - luminance changes, chroma changes along a R/G (i.e. reddish to greenish) axis and chroma changes along a B/Y (i.e. bluish to yellowish) axis. A simple diagrammatic representation is shown to the right. Important points to note from this are that pure blue has no intrinsic luminance and that pure yellow has the same luminance as white - these being because in human vision luminance (brightness) sensation is derived solely from R & G receptors. The representation of luminance & colour on three axes is discussed at some length in Chapter 14 of ‘Computer Vision ...’.
Human vision is able to analyse luminance & R/G differences both separately & combined at very high resolution, but it can only analyse B/Y differences at a much lower resolution (leading to so-called ‘blue blindness’ or small field tritanopia for very small objects - see Chapters 14.2 & 15.5.3 of ‘Computer Vision ...’).