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

arXiv: https://arxiv.org/abs/2603.29438 · HTML: https://mlsanity.com/paper/2603.29438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 87 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and Survey](https://mlsanity.com/paper/1708.05125/) (2017)
- [Building Instance Classification Using Street View Images](https://mlsanity.com/paper/1802.09026/) (2018)
- [EndNet: Sparse AutoEncoder Network for Endmember Extraction and Hyperspectral Unmixing](https://mlsanity.com/paper/1708.01894/) (2017)
- [Endmember-Guided Unmixing Network (EGU-Net): A General Deep Learning Framework for Self-Supervised Hyperspectral Unmixing](https://mlsanity.com/paper/2105.10194/) (2021)
- [Spectral Unmixing via Data-guided Sparsity](https://mlsanity.com/paper/1403.3155/) (2014)
- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Multi-Band Image Fusion Based on Spectral Unmixing](https://mlsanity.com/paper/1603.08720/) (2016)
- [Entropic Descent Archetypal Analysis for Blind Hyperspectral Unmixing](https://mlsanity.com/paper/2209.11002/) (2022)
- [SUnAA: Sparse Unmixing using Archetypal Analysis](https://mlsanity.com/paper/2308.04771/) (2023)
- [Hyperspectral vs. RGB for Pedestrian Segmentation in Urban Driving Scenes: A Comparative Study](https://mlsanity.com/paper/2508.11301/) (2025)
- [Fast Spectral Unmixing based on Dykstra's Alternating Projection](https://mlsanity.com/paper/1505.01740/) (2015)
- [SISAL Revisited](https://mlsanity.com/paper/2107.00386/) (2021)
- [CEU-Net: Ensemble Semantic Segmentation of Hyperspectral Images Using Clustering](https://mlsanity.com/paper/2203.04873/) (2022)
- [Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images](https://mlsanity.com/paper/2503.20328/) (2025)

## Abstract (arXiv)

Semantic segmentation and hyperspectral unmixing are two central problems in spectral image analysis. The former assigns each pixel a discrete label corresponding to its material class, whereas the latter estimates pure material spectra, called endmembers, and, for each pixel, a vector representing material abundances in the observed scene. Despite their complementarity, these two problems are usually addressed independently. This paper aims to bridge these two lines of work by formally showing that, under the linear mixing model, pixel classification by dominant materials induces polyhedral-cone regions in the spectral space. We leverage this fundamental property to propose a direct segmentation-to-unmixing pipeline that performs blind hyperspectral unmixing from any semantic segmentation by constructing a polyhedral-cone partition of the space that best fits the labeled pixels. Signed distances from pixels to the estimated regions are then computed, linearly transformed via a change of basis in the distance space, and projected onto the probability simplex, yielding an initial abundance estimate. This estimate is used to extract endmembers and recover final abundances via matrix pseudo-inversion. Because the segmentation method can be freely chosen, the user gains explicit control over the unmixing process, while the rest of the pipeline remains essentially deterministic and lightweight. Beyond improving interpretability, experiments on three real datasets demonstrate the effectiveness of the proposed approach when associated with appropriate clustering algorithms, and show consistent improvements over recent deep and non-deep state-of-the-art methods. The code is available at: https://github.com/antoine-bottenmuller/polyhedral-unmixing