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16 February 2006 The discrete Gould transform and its applications
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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.
© (2006) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Hoang M. Le and Maurice Aburdene "The discrete Gould transform and its applications", Proc. SPIE 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, 60640I (16 February 2006); https://doi.org/10.1117/12.643278
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