Wanli Ouyang, Renqi Zhang and Wai-Kuen Cham
Abstract This paper proposes a fast algorithm for Walsh Hadamard Transform on sliding windows which can be used to implement pattern matching most efficiently. The computational requirement of the proposed algorithm is about 1.5 additions per projection vector per sample, which is the lowest among existing fast algorithms for Walsh Hadamard Transform on sliding windows.
Wanli Ouyang and Wai-Kuen Cham, "The Segmented Gray-Code Kernels for Fast Pattern Matching", IEEE Trans. Image Processing, 22(4):1512-1525, Apr. 2013. [Full text *]
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Fig. 1 WHT in natural order and sequency order.
The Gray-Code Kernels (GCK) is a generalization of WHT. Our proposed Segmented Gray-Code Kernels (SegGCK) is a special case of GCK. SegGCK is a lapped orthogonal transform(LOT). SegGCK can be computed very efficiently. To project input data onto u basis vectors, we only need O(u/k) operations, a sub-linear computational complexity.
In this paper, we also propose an algorithm that computes the sliding WHT by 3/4 additions per basis vector, which is faster than our previous work in [d].
Many introductions of WHT and fast WHT algorithm in this webpage are directly copied from Wikipedia. To avoid annoyance, we did not provide reference to Wikipedia for all places.
[a] Fino, B.J., and Algazi, V.R., 1976, "Unified Matrix Treatment of the Fast Walsh-Hadamard Transform," IEEE Transactions on Computers 25: 1142-1146.
[b] Y. Hel-Or and H. Hel-Or, "Real Time Pattern Matching Using Projection Kernels," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 9, pp. 1430-1445, Sept. 2005.
[c] G. Ben-Artzi, H. Hel-Or, and Y. Hel-Or, "The Gray-Code Filter Kernels," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 3, pp. 382-393, Mar. 2007.
[d] Wanli Ouyang and Wai-Kuen Cham, "Fast algorithm for Walsh Hadamard transform on sliding windows", IEEE Trans. Pattern Anal. Mach. Intell., 32(1):165-171, Jan. 2010.
[e] Wanli Ouyang, Renqi Zhang and Wai-Kuen Cham, "Fast pattern matching using orthogonal Haar transform ", In Proc. IEEE CVPR 2010, Webpage and source code.
[f] Wanli Ouyang, Federico Tombari, Stefano Mattoccia, Luigi Di Stefano, and Wai- Kuen Cham, "Performance Evaluation of Full Search Equivalent Pattern Matching Algorithms," IEEE Trans. Pattern Anal. Mach. Intell., 34(1):127-143, Jan. 2012. Webpage and source code
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