A morphological gradient binary edge enhancement operator is defined by the formula: Using a 1-D model of an edge, or otherwise, show that this will give wide edges in binary images. If grayscale...

A morphological gradient binary edge enhancement operator is defined by the formula:

Using a 1-D model of an edge, or otherwise, show that this will give wide edges in binary images. If grayscale dilation (") is equated to taking a local maximum of the intensity function within a 3 × 3 window, and grayscale erosion (~) is equated to taking a local minimum within a 3 × 3 window, sketch the result of applying the operator G. Show that it is similar in effect to a Sobel edge enhancement operator, if edge orientation effects are ignored by taking the Sobel magnitude: