Dimensionality reduction and information-theoretic divergence between sets of LADAR images

Abstract

This paper presents a preliminary study of information-theoretic divergence between sets of LADAR image data. This study has been motivated by the hypothesis that despite the huge dimensionality of raw image space, related images actually lie on embedded manifolds within this set of all possible images and can be represented in much lowerdimensional sub-spaces. If these low-dimensional representations can be found, information theoretic properties of the images can be exploited while circumventing many of the problems associated with the so-called "curse of dimensionality." In this study, PCA techniques are used to find a low-dimensional sub-space representation of LADAR image sets. A real LADAR image data set was collected using the AFSTAR sensor and a synthetic image data set was created using the Irma LADAR image modeling program. One unique aspect of this study is the use of an entirely synthetic data set to find a sub-space representation that is reasonably valid for both the synthetic data set and the real data set. After the sub-space representation is found, an information-theoretic density divergence measure (Cauchy- Schwarz divergence) is computed using Parzen window estimation methods to find the divergence between and among the sets of synthetic and real target classes. These divergence measures can then be used to make target classification decisions for sets of images. In practice, this technique could be used to make classification decisions on multiple images collected from a moving sensor platform or from a geographically distributed set of cooperating sensor platforms operating in a target region.