Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images
This addresses spectral image analysis for applications like remote sensing and battery monitoring, offering a more robust alternative to linear unmixing.
The paper tackles the problem of estimating abundance maps from spectral images when linear unmixing approaches fail due to limited bands or correlated spectra, by presenting a novel approach using Euclidean distance to convex polyhedra; it demonstrates state-of-the-art performance on the Samson dataset and validates generality on Lithium-ion battery images.
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.