Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.27958

From Proper Scoring Rules and Edge Biases to Mumford-Shah Models: Robust Unsupervised Hyperspectral Image Segmentation

Fabian Conrad·Benjamin Berkels
View original source ↗Read source document ↗Export metadata ↓

Abstract

Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the availability of labeled hyperspectral images is limited and the acquisition of labeled training data is time-consuming, unsupervised segmentation methods are important in hyperspectral image segmentation. Spectral variability, mixed pixels, noise as well as high correlation between neighboring spectral bands make this task challenging. We present a feature-agnostic, unsupervised hyperspectral segmentation framework based on the piecewise-constant Mumford-Shah functional. Our framework turns a strictly proper scoring rule and a family of parametric probability distributions into an indicator function for the Mumford-Shah functional, and we naturally generalize some previous Mumford-Shah based models for image segmentation this way. Our focus will be on heavy-tailed elliptical distributions, the negative log-likelihood score and the score based on the beta-divergence to deal with the heavy outliers in hyperspectral imaging. Using the interplay between the calculus of variations and statistics, we also propose a robustness step to estimate the statistical parameters of these heavy-tailed elliptical distributions. In addition, an edge bias, which contains prior boundary information, is incorporated into both the data fidelity term and the perimeter term of the Mumford-Shah functional. Numerical experiments show that, to the best of our knowledge, our method achieves the highest overall accuracy among fully unsupervised methods on three of the four standard benchmarks (Indian Pines, Kennedy Space Center, Pavia University and Salinas) evaluated on the full scenes. It also improves upon our previous Mumford-Shah based model.

Explore related subjects

cs.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Fabian Conrad, Benjamin Berkels. 2026-10-20. From Proper Scoring Rules and Edge Biases to Mumford-Shah Models: Robust Unsupervised Hyperspectral Image Segmentation. https://arxiv.org/abs/2610.27958

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Taskonomy: Disentangling Task Transfer Learning

Do visual tasks have a relationship, or are they unrelated? For instance, could having surface normals simplify estimating the depth of an image? Intuition answers these questions positively, implying existence of a structure among visual tasks. Knowing this structure has notable values; it is the concept underlying transfer learning and provides a principled way for identifying redundancies across tasks, e.g., to seamlessly reuse supervision among related tasks or solve many tasks in one system without piling up the complexity. We proposes a fully computational approach for modeling the structure of space of visual tasks. This is done via finding (first and higher-order) transfer learning dependencies across a dictionary of twenty six 2D, 2.5D, 3D, and semantic tasks in a latent space. The product is a computational taxonomic map for task transfer learning. We study the consequences of this structure, e.g. nontrivial emerged relationships, and exploit them to reduce the demand for labeled data. For example, we show that the total number of labeled datapoints needed for solving a set of 10 tasks can be reduced by roughly 2/3 (compared to training independently) while keeping the performance nearly the same. We provide a set of tools for computing and probing this taxonomical structure including a solver that users can employ to devise efficient supervision policies for their use cases.

cs.CV↗
arXiv2026

WildPPG: A Real-World PPG Dataset of Long Continuous Recordings

Reflective photoplethysmography (PPG) has become the default sensing technique in wearable devices to monitor cardiac activity via a person's heart rate (HR). However, PPG-based HR estimates can be substantially impacted by factors such as the wearer's activities, sensor placement and resulting motion artifacts, as well as environmental characteristics such as temperature and ambient light. These and other factors can significantly impact and decrease HR prediction reliability. In this paper, we show that state-of-the-art HR estimation methods struggle when processing \emph{representative} data from everyday activities in outdoor environments, likely because they rely on existing datasets that captured controlled conditions. We introduce a novel multimodal dataset and benchmark results for continuous PPG recordings during outdoor activities from 16 participants over 13.5 hours, captured from four wearable sensors, each worn at a different location on the body, totaling 216\,hours. Our recordings include accelerometer, temperature, and altitude data, as well as a synchronized Lead I-based electrocardiogram for ground-truth HR references. Participants completed a round trip from Zurich to Jungfraujoch, a tall mountain in Switzerland over the course of one day. The trip included outdoor and indoor activities such as walking, hiking, stair climbing, eating, drinking, and resting at various temperatures and altitudes (up to 3,571\,m above sea level) as well as using cars, trains, cable cars, and lifts for transport -- all of which impacted participants' physiological dynamics. We also present a novel method that estimates HR values more robustly in such real-world scenarios than existing baselines.

cs.CV↗
arXiv2026

Scene-R1: Video-Grounded Large Language Models for 3D Scene Reasoning with Lightweight Annotations

Large language models are increasingly being applied to 3D scene understanding. However, existing 3D-aware LLMs largely operate as black boxes: they produce bounding boxes or textual responses without exposing the reasoning process, and they typically depend on pre-trained 3D detectors for object proposals. We present Scene-R1, a video-grounded framework for 3D scene reasoning that avoids both pre-trained 3D object detectors and dense point-cloud backbones. The framework combines reinforcement-learning-based reasoning with a two-stage grounding pipeline. In the first stage, Scene-R1 performs temporal grounding by identifying the video segments most relevant to an open-ended query. In the second stage, it grounds the target in image space by predicting a 2D bounding box. This prediction is then refined into a precise 3D localization using high-quality candidates from a zero-shot segmentation module, enabling fine-grained geometric reasoning without detector-based proposals. Scene-R1 can also be adapted to 3D visual question answering, generating free-form answers directly from RGB-D video. Our training pipeline uses lightweight 2D supervision projected from sparse scans, avoiding the computational overhead required to train 3D instance segmentation models. Across multiple datasets, Scene-R1 outperforms existing open-vocabulary baselines while also providing interpretable intermediate reasoning steps. These results suggest that reinforcement-learning-based reasoning over RGB-D video can support accurate 3D scene understanding with task-level supervision. The training, inference, and 3D refinement code is available at https://github.com/819346675/Scene-R1.

cs.CV↗