A distribution-dependent Mumford-Shah model for unsupervised hyperspectral image segmentation

TL;DR

This paper introduces a novel unsupervised hyperspectral image segmentation method that combines denoising, dimensionality reduction, and a distribution-dependent Mumford-Shah model, achieving superior results on benchmark datasets.

Contribution

It proposes a new distribution-dependent Mumford-Shah functional with a fixed point optimization scheme for hyperspectral segmentation, addressing spectral variability and noise challenges.

Findings

Outperforms three state-of-the-art methods on three benchmark datasets

Effective handling of spectral variability and noise in hyperspectral data

Competitive segmentation results demonstrated on public datasets

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 acquisition of labeled training data is very time-consuming, unsupervised methods become crucial in hyperspectral image analysis. The spectral variability and noise in hyperspectral data make this task very challenging and define special requirements for such methods. Here, we present a novel unsupervised hyperspectral segmentation framework. It starts with a denoising and dimensionality reduction step by the well-established Minimum Noise Fraction (MNF) transform. Then, the Mumford-Shah (MS) segmentation functional is applied to segment the data. We equipped the MS functional with a novel robust distribution-dependent indicator function designed to handle the characteristic challenges of hyperspectral data. To optimize our objective function with respect to the parameters for which no closed form solution is available, we propose an efficient fixed point iteration scheme. Numerical experiments on four public benchmark datasets show that our method produces competitive results, which outperform three state-of-the-art methods substantially on three of these datasets.