A new interpretation of the compass gradient edge operators

✍ Scribed by Rae-Hong Park; Woo Young Choi

• Book ID: 104343518
• Publisher: Elsevier Science
• Year: 1989
• Weight: 322 KB
• Volume: 47
• Category: Article
• ISSN: 0734-189X
• DOI: 10.1016/s0734-189x(89)80010-6

✦ Synopsis

Two-dimensional 3 • 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 • 3 mask. We show that 8-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 the above two relations, we present the new interpretation of compass gradient operators such as Sobel, Prewitt, and Kirsch operators.