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21 August 1987 Comparative Study Of Various Linear Mapping Algorithms For Hybrid Statistical Pattern Recognition
Q. Tian, Y. Fainman, Z. H. Gu, Sing H. Lee
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Proceedings Volume 0754, Optical and Digital Pattern Recognition; (1987) https://doi.org/10.1117/12.939981
Event: OE LASE'87 and EO Imaging Symposium, 1987, Los Angeles, CA, United States
Abstract
We study the relations among various linear mapping-based algorithms by formulating a more general unified pseudo-inverse algorithm. We show that the least-square linear mapping technique, the simplified least-square linear mapping technique, the synthetic discriminant function, the equal correlation peak method and the Caulfield-Maloney filter are in fact all special cases of the unified pseudo-inverse algorithm. When the total number of the training images (KM, where K is the number of classes and M is the number of training images in each class) is larger than the dimension of the images (N), the overdetermined case of the unified pseudo-inverse algorithm is the same as the least-square linear mapping technique, due to the fact that both algorithms are based on optimization processes of minimization of the least square error. When KM < N, the underdetermined case of the unified pseudo-inverse algorithm is the same as the least-square linear mapping technique and the synthetic discriminant function. Furthermore, when KM < N, the synthetic discriminant function method can be considered as the degenerated case of the least-square linear mapping technique. Experimental results on classification using the linear mapping-based algorithms are provided and show good agreement with the theoretical analysis.
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Q. Tian, Y. Fainman, Z. H. Gu, and Sing H. Lee "Comparative Study Of Various Linear Mapping Algorithms For Hybrid Statistical Pattern Recognition", Proc. SPIE 0754, Optical and Digital Pattern Recognition, (21 August 1987); https://doi.org/10.1117/12.939981
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KEYWORDS
Detection and tracking algorithms
Electronic filtering
Optical pattern recognition
Image filtering
Linear filtering
Image processing
Associative arrays
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