From Homepage of Andreas Arnold

Work: Additional note concerning paper "Towards an automatic denoising of underwater optical images"

When considering the ratio S of the magnitude of the gradient, it is important to note that this ratio can be computed without actually having to compute the gradients. This can be seen by using equation (6) in equation (15). Thus, the "magic" result is that S is in fact equal to the low pass image (after suitable normalization by factor 1/G of the raw low pass image, where G is described by equation (3) of our first paper concerning underwater vision).

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