✍ Scribed by A.L.D Beckers; A.W.M Smeulders
No coin nor oath required. For personal study only.
Two-dimensional 3 X 3 compass gradient operators are commonly used in the edge detection and usually detect eight compass directional components. In this paper, we present a new interpretation of the relationship between the resulting eight gradient components and the eight intensity values of neighboring pixels which are covered by the 2-dimensional 3 X 3 mask. We show that X-directional edge values can be expressed by using a circulant matrix. And a circulant matrix can be diagonalized by using the Fourier transform matrix. By using above two relations, we present the new interpretation of compass gradient operators, such as, Sobel, Prewitt. and Kirsch operators.
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