Polyhedral Unmixing: Bridging Semantic Segmentation with Hyperspectral Unmixing via Polyhedral-Cone Partitioning

A team from the Centre de Morphologie Mathématique (CMM), PSL, and STIM has published a novel method called 'Polyhedral Unmixing' that formally connects two core problems in spectral image analysis: semantic segmentation and hyperspectral unmixing. The research demonstrates that under the linear mixing model, classifying pixels by their dominant material creates distinct polyhedral-cone regions in the spectral space. This fundamental insight allows the team to propose a new, direct pipeline where any semantic segmentation result can be used to perform 'blind' hyperspectral unmixing—estimating pure material spectra (endmembers) and their abundances without prior spectral knowledge.

The pipeline is deterministic and lightweight. It works by constructing a polyhedral-cone partition that best fits the labeled pixels from a segmentation. It then computes signed distances, transforms them via a change of basis, and projects them onto a probability simplex to get an initial abundance estimate. This estimate is used to extract endmembers and recover final abundances via matrix pseudo-inversion. Crucially, because the segmentation method is a free choice, users gain explicit control over the unmixing process, improving interpretability. The paper reports that experiments on three real datasets show the approach's effectiveness, especially when paired with appropriate clustering algorithms, and that it delivers consistent improvements over recent deep and non-deep state-of-the-art methods.