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For early image preprocessing tasks, normalization is not mandatory, as long as they only add a common multiplication factors for all images. Indeed, one is mostly interested in relative "importance" of features, or in detection, localization. As much as "integer" pixel values are somewhat arbitrary, multiplying them a constant often does ...


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The answer is simple, the Sobel Filter is a composition of Lows Pass Filter (LPF) and High Pass Filter (HPF). The composition is done by convolution. Now, indeed the LPF presented above $ {\left[ 1, 2, 1 \right]}^{T} $ has amplification in the DC value (Its sum is 4 so the amplification is 4). Yet it is convolved with an HPF filter which rejects the DC ...


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