Continuous scale invariant optical composite wavelet matched filters with adaptive wavelets

Danny Roberge; Yunlong Sheng

doi:10.1117/12.205410

6 April 1995 Continuous scale invariant optical composite wavelet matched filters with adaptive wavelets

Danny Roberge, Yunlong Sheng

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205410
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

The wavelet transform (WT) can be used for pattern recognition. One scheme is to extract the wavelet features in the 4-D space-scale joint representation of the 2-D pattern for statistical pattern recognition. Another scheme is the wavelet matched filters (WMF), that uses the WT to enhance the edge features and make correlation between the WT of the input image and the WT of the reference image. This approach uses the optical shift invariant continuous WT and implements the WT and the matching of two WTs in a single step of the correlation. Several adaptive WTs and the matching pursuits have been proposed that use the best basis functions to the signal decomposition. The basis is selected from a library of dictionary waveforms to minimize an energy or an entropy in such a way that the signal expansion with those bases is the best for signal representation or classification. Pattern recognition emphasizes the classification. Fast numerical algorithms are given for the signal expansion with the best adaptive discrete orthogonal bases. Most approaches use a fixed shape basic wavelet with varying shift and dilation parameters. Szu et al., proposed adaptive wavelets that are linear combination of wavelets, called the `super-wavelet.' The super-wavelets can be continuous and redundant. The shape of the super-wavelets can be adaptively changed for the particular applications. They show the adaptive WT of the 1-D speech signals. In this paper we show the adaptive WT with continuous 2-D wavelets, whose shape is adaptively changed to achieve the pattern recognition invariant to continuous shift and scale changes. We show why such an adaptive WT is needed and how to construct the composite wavelet matched filter (CWMF) with the adaptive super-wavelet for the continuous scale invariant pattern recognition. The real-time complex valued optical filters implementation is reported in this paper.

Citation Download Citation

Danny Roberge and Yunlong Sheng "Continuous scale invariant optical composite wavelet matched filters with adaptive wavelets", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205410

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