The discrete Gould transform and its applications

Hoang M. Le; Maurice Aburdene

doi:10.1117/12.643278

16 February 2006 The discrete Gould transform and its applications

Hoang M. Le, Maurice Aburdene

Proceedings Volume 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning; 60640I (2006) https://doi.org/10.1117/12.643278
Event: Electronic Imaging 2006, 2006, San Jose, California, United States

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, GyG^T can be used directly to detect edges. Ways to improve the edge detection technique is to use the "combination of forward and backward difference", G^T(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.

Citation Download Citation

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

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available