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<title>Continuous scale invariant optical composite wavelet matched filters with adaptive wavelets</title>

Authors: Yunlong Sheng; Danny Roberge;

<title>Continuous scale invariant optical composite wavelet matched filters with adaptive wavelets</title>

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.

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
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