A distribution-dependent Mumford-Shah model for unsupervised hyperspectral image segmentation
This work addresses the challenge of unsupervised segmentation for hyperspectral images, which is crucial due to the difficulty of obtaining labeled data, but it is incremental as it builds on existing methods like MNF and Mumford-Shah.
The authors tackled unsupervised hyperspectral image segmentation by developing a framework that integrates a novel distribution-dependent indicator function into the Mumford-Shah model, achieving competitive results that outperform three state-of-the-art methods on three out of four benchmark datasets.
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.