A Distribution-Dependent Mumford–Shah Model for Unsupervised Hyperspectral Image Segmentation

IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1–21

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.

Authors 3

1. Jan-Christopher Cohrs Aachen Aachen Institute for Advanced Study in Computational Engineering Science (AICES)

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Aachen, Germany

2. Chandrajit Bajaj

   The University of Texas at Austin

   Affiliation as printed

   Oden Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, TX, USA

3. Benjamin Berkels Aachen Aachen Institute for Advanced Study in Computational Engineering Science (AICES)

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Aachen, Germany