Normalization of gradient image

https://au.mathworks.com/help/images/ref/imgradient.html#bthgcil-method

imgradient does not normalize the gradient output. If the range of the gradient output image has to match the range of the input image, consider normalizing the gradient image, depending on the method argument used. For example, with a Sobel kernel, the normalization factor is 1/8, for Prewitt, it is 1/6, and for Roberts it is 1/2.

I'm confused with the last sentence. So excatly how to calculate the normalised gradient image with a sobel kernel for example?

Answer 1

[Shunichi Kusano]

For the case using sobel kernel, multiply 1/8 to the resulted values:

[Gmag,Gdir] = imgradient(I, 'sobel');
Gmag_normalized = Gmag / 8;

The window (kernel) used in sobel filter is:

w = [1 0 -1; 2 0 -2; 1 0 -1]; % for vertical edge detection

The sum of the absolute value is 8 (=abs(1+2+1)+abs(-1-2-1)). Hence, the resulted values are enhanced by this factor due to the convolution. One needs to compensate this for the normalization. The idea is the same as moving average.