NURBS representation for sets of spectral signatures

Abstract

In this study we demonstrate the representation of sets of spectral signatures such that the representation is optimal in the user-defined sense. The basis functions for the sets are defined by minimizing the reconstruction error using the user-defined metric. In our proposal the basis functions are non-uniform rational B-splines (NURBS). NURBS representation is compared to the respective representation from the principal component analysis (PCA). The optimization setting is defined such that the proposed NURBS representation is capable to provide parallel reconstruction quality as PCA representation. The experiments indicate that for a low number of basis functions, i.e. for one or two basis functions, NURBS representation gives mainly better results than PCA. When the number of basis functions gets larger, i.e. to three of four or more basis functions, then PCA representation is always better independent of the metric used. The drawback of the proposed procedure is the time consuming optimization in defining the control points for NURBS basis functions.