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Proceedings Paper

The discrete Gould transform and its applications
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Paper Abstract

We present a new discrete transform, the Gould transform (DGT). The transform has many interesting mathematical properties. For example, the forward and inverse transform matrices are both lower triangular, with constant diagonals and sub-diagonals and both can be factored into the product of binary matrices. The forward transform can be used to detect edges in digital images. If G is the forward transform matrix and y is the image, then the two dimensional DGT, GyGT can be used directly to detect edges. Ways to improve the edge detection technique is to use the "combination of forward and backward difference", GT(Gy) to better identify the edges. For images that tend to have vertical and horizontal edges, we can further improve the technique by shifting rows (or columns), and then use the technique to detect edges, essentially applying the transform in the diagonal directions.

Paper Details

Date Published: 16 February 2006
PDF: 12 pages
Proc. SPIE 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, 60640I (16 February 2006); doi: 10.1117/12.643278
Show Author Affiliations
Hoang M. Le, Bucknell Univ. (United States)
Maurice Aburdene, Bucknell Univ. (United States)

Published in SPIE Proceedings Vol. 6064:
Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning
Nasser M. Nasrabadi; Edward R. Dougherty; Jaakko T. Astola; Syed A. Rizvi; Karen O. Egiazarian, Editor(s)

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