A Framework for Object Characterization and Matching in Multi--and Hyperspectral Imaging Systems

Abstract

The idea of shape has been a field of scientific study since the time of Galileo. Most shapes that have been studied until now have been those that are 'conceivable' by the human mind. This has restricted the study of shape by the image processing community to the visible range of the spectrum (an otherwise very small range). Perception of shape in the realm of the spectrum outside of the visible range has not received much attention. However with the recent advancement in imaging systems (multi--and hyperspectral) that can capture images over a wide spectral range, it is only natural to expect this field to receive notice by the imaging community. In this work, the idea of 'shape' in the multi--and hyperspectral imaging scenarios is studied and its paradigms explored. Notions of the hyperspectral cube are borrowed from the remote sensing community as a means of representation of this high dimensional data.

In this work, edges of two types are used, one that makes use of the vector valued data in the image and another that treats each spectral band individually. The edge-sets are used to extract spatio-spectral shape signatures of objects which are in turn used for extracting canonical views of objects and also to perform classification using three dimensionality reduction techniques, Principal Component Analysis, Independent Component Analysis and Non-negative Matrix Factorization. As an extension to edge-based decompositions, we also use view-based techniques for classification. The results obtained by using a combination of spatial and spectral information are compared with those resulting from conventional single-band techniques, showing considerable improvement.

Issues regarding noisy data have been addressed using two approaches -- increasing the dimensionality of the eigensystem and estimating the new eigensystem under noisy conditions using approximations of results using perturbation theory. The former approach gives a measure of the number of basis vectors that need to be included additionally based upon the strength of the noise. It develops a system that adds dimensions (Noise Equivalent Dimensions) to the original eigensystem that compensates for the energy contributed by the noise. The latter approach determines the manner in which the eigenviews of an eigensystem change in the presence of noise by using first-order approximations from perturbation theory. Both approaches are compared using reconstruction error in the original and noisy data.