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23 November 2011 Fast algorithm of (k, k-1) type discrete Walsh-Haar transformation and application in image edge detection
Li Lu, Bao-Chang Shi
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Proceedings Volume 8006, MIPPR 2011: Remote Sensing Image Processing, Geographic Information Systems, and Other Applications; 80062N (2011) https://doi.org/10.1117/12.902816
Event: Seventh International Symposium on Multispectral Image Processing and Pattern Recognition (MIPPR2011), 2011, Guilin, China
Abstract
Walsh-Haar function system that was first introduced by us is a new kind of function systems, and has a good global / local property. This function system is called Walsh ordering function system since its generation kernel functions belong to Walsh ordering Walsh function system. We worked out a recursive property of the matrix WH KR m+1 WH corresponding to the first KR m+1 Walsh-Haar functions in Walsh-Haar function system, and proved that Walsh-Haar function system is perfect and orthogonal similar to Walsh function system and Haar function system. Thus, discrete Walsh-Haar transformation (DW-HT) is an orthogonal transformation that can be widely used in signal processing. In this paper, using the recursive property of the matrix WH KRm+1 WH and the fast algorithm of discrete Walsh transformation in Walsh ordering, we have designed a fast algorithm of Walsh ordering (k, k-1) type DW-HT based on the bisection technique. As one of its applications, we use it to detect image edges. Compare with some edge-detecting methods, the method in this paper detects more details of image edge. The idea and method used to design the fast algorithm in this paper can be used to design fast algorithms of other ordering (k, k-1) type DW-HTs and other discrete orthogonal transformations.
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Li Lu and Bao-Chang Shi "Fast algorithm of (k, k-1) type discrete Walsh-Haar transformation and application in image edge detection", Proc. SPIE 8006, MIPPR 2011: Remote Sensing Image Processing, Geographic Information Systems, and Other Applications, 80062N (23 November 2011); https://doi.org/10.1117/12.902816
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KEYWORDS
Edge detection
Detection and tracking algorithms
Geographic information systems
Image processing
Algorithms
Digital filtering
Fast wavelet transforms
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