Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images
Journal:
arXiv
Published Date:
Mar 26, 2025
Abstract
With the aim of estimating the abundance map from observations only, linear
unmixing approaches are not always suitable to spectral images, especially when
the number of bands is too small or when the spectra of the observed data are
too correlated. To address this issue in the general case, we present a novel
approach which provides an adapted spatial density function based on any
arbitrary linear classifier. A robust mathematical formulation for computing
the Euclidean distance to polyhedral sets is presented, along with an efficient
algorithm that provides the exact minimum-norm point in a polyhedron. An
empirical evaluation on the widely-used Samson hyperspectral dataset
demonstrates that the proposed method surpasses state-of-the-art approaches in
reconstructing abundance maps. Furthermore, its application to spectral images
of a Lithium-ion battery, incompatible with linear unmixing models, validates
the method's generality and effectiveness.
