Principal components analysis: extension to scaling for application to images acquired at various ranges

Gerald Cook; Gary F. O'Brien

doi:10.1117/12.364066

29 September 1999 Principal components analysis: extension to scaling for application to images acquired at various ranges

Gerald Cook, Gary F. O'Brien

Author Affiliations +

Proceedings Volume 3810, Radar Processing, Technology, and Applications IV; (1999) https://doi.org/10.1117/12.364066
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

This paper builds on the method of Principal Components Analysis and its use for obtaining from a set of training image vectors a basis in which the members are rank ordered in terms of importance. The particular focus of this research is situations where the training vectors arise from images acquired at one range, call it the base range, and the image under question has been acquired at a different range. A natural question is whether one must train for all possible ranges. It is shown that, under certain assumptions, the eigenvectors for the data corresponding to ranges other than the base range may be approximated by performing a simple transformation on the eigenvectors derived from the training set at the base range. This is an important result, tending to obviate the need for acquisition of additional training patterns or for additional complex computations. It is also shown that under these assumptions the eigenvalues remain approximately constant over the different ranges even though pixel size is changed. Bounds for the errors of approximation introduced by the method are derived.

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Gerald Cook and Gary F. O'Brien "Principal components analysis: extension to scaling for application to images acquired at various ranges", Proc. SPIE 3810, Radar Processing, Technology, and Applications IV, (29 September 1999); https://doi.org/10.1117/12.364066

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