How to normalize OpenCV Sobel filter given kernel size

Question

How to invoke OpenCV Sobel function to compute actual derivative of image given some kernel size? I.e. considering that image is a function of f(x, y) and x, y spans from [0, 0] to [width, height] in pixels?

dimg_x = cv2.Sobel(img, ddepth=-1, dx=1, dy=0, ksize=ksize)

Probably some scaling needs to be applied to gradient image, but I can't figure out how to compute it given kernel size.

Answer 1

You can use the scale argument of Sobel:

cv2.Sobel(img, dx=dx, dy=dy, ksize=ksize, scale=2**(2+dx+dy-ksize*2), ddepth=CV_32F)

When you scale the output that way, you typically do not want to have ddepth=-1 but rather get the result as floats or doubles.