Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images

Antoine Bottenmuller, Florent Magaud, Arnaud Demortière, Etienne Decencière, Petr Dokladal

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.

Paper Citation

in Harvard Style

Bottenmuller A., Magaud F., Demortière A., Decencière E. and Dokladal P. (2025). Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images. In Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM; ISBN 978-989-758-730-6, SciTePress, pages 192-203. DOI: 10.5220/0013385600003905

in Bibtex Style

@conference{icpram25,
author={Antoine Bottenmuller and Florent Magaud and Arnaud Demortière and Etienne Decencière and Petr Dokladal},
title={Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images},
booktitle={Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM},
year={2025},
pages={192-203},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013385600003905},
isbn={978-989-758-730-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM
TI - Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images
SN - 978-989-758-730-6
AU - Bottenmuller A.
AU - Magaud F.
AU - Demortière A.
AU - Decencière E.
AU - Dokladal P.
PY - 2025
SP - 192
EP - 203
DO - 10.5220/0013385600003905
PB - SciTePress