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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