What the fourier transform can really bring to clustering

摘要

The general philosophy and motivations of extracting classification information from histograms have been developed in a previously published paper.(1) The content of the present paper deals with an optimum signal theory implementation of the same concepts by appropriate Fourier filtering of the data histogram. This strategy was developed to cluster remotely sensed multispectral imagery.First, the theoretical foundations of clustering are explained in terms of Watanabe's ‘Ugly Duckling’ theorem on classification. A brief outline of the clustering strategy detailed in Leboucher and Lowitz is then given for the sake of clarity. In the following sections the clustering methodology is explained in terms of signal detection and signal filtering. The mathematical model is then refined and optimized using the prolate spheroidal wave function expansions of Slepian et al.Computer simulations of this new strategy were conducted on test multispectral imagery and some clustering results are presented.