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TY - THES AU - Cohrs, Jan-Christopher TI - Mumford–Shah type models for unsupervised hyperspectral image segmentation PB - RWTH Aachen University VL - Dissertation CY - Aachen M1 - RWTH-2025-10634 SP - 1 Online-Ressource : Illustrationen PY - 2025 N1 - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2026 N1 - Dissertation, RWTH Aachen University, 2025 AB - Hyperspectral sensors provide images that are rich in information by accurately resolving the incoming spectra with a high sampling rate. The idea is that, by resolving the spectra with a sufficiently high level of detail, each constituent in the captured scene or specimen can be identified by its unique spectral fingerprint, the so-called spectral signature. This allows for a differentiation of the contributing constituents on a pixel level and, thus, leads to high quality image segmentations. However, some special characteristic properties of hyperspectral images like the strong noise and the spectral variability adversely affect the quality of the segmentations of such images. Several approaches for hyperspectral image segmentation have been proposed. A shortcoming of supervised methods is that the process of generating labeled training data is expensive and time-consuming, making unsupervised methods an important tool to solve the hyperspectral segmentation task. While different methods for unsupervised hyperspectral image segmentation have been introduced, an accurate description of the data despite the spectral variability and noise remains a decisive challenge. In this thesis, we propose and investigate a novel segmentation framework and three new models for unsupervised hyperspectral image segmentation. The framework comprises a preprocessing for noise and dimensionality reduction by the minimum noise fraction transform, an alternating optimization approach to minimize the objective functional and a stopping criterion. The three introduced models, ϵAMS, ϕAMS and kMS, are based on the Mumford-Shah segmentation functional. The models ϵAMS and ϕAMS aim to directly model the spectra with first- and second-order statistics, while kMS maps the spectra into a higher-dimensional Hilbert space to describe the data there. To ensure that ϵAMS and ϕAMS remain always feasible, we propose a regularization of the covariance matrices for each of the models. Furthermore, we prove the existence of minimizers for both models. Additionally, we investigate the importance of the regularization parameter of ϵAMS rigorously: we prove the Γ-convergence of the corresponding functional to a Γ-limit and see that we lose the guarantee of a minimizer in the limit with a counterexample. We solve the problem of the lack of closed-form solutions for the model-specific parameters of ϵAMS and ϕAMS for optimization by introducing fixed point iteration schemes. Furthermore, we derive a closed-form solution for the model-specific parameters of kMS. Extensive numerical experiments on four publicly available datasets show the great potential of all three methods. In particular, ϵAMS and ϕAMS show consistently the best performances and provide segmentations of the highest qualities among all competing methods, which include state-of-the-art methods for unsupervised hyperspectral image segmentation. An evaluation of the effect of the preprocessing by the minimum noise fraction transform on the segmentation results shows that the preprocessing has a clear positive effect but the main contribution comes from the models themselves. Finally, we test ϵAMS also on multispectral Sentinel-2 data taken over the Arctic region and find out that the model is able to derive complex sea ice states from these images. The models presented in this thesis are able to produce segmentations of high quality and have a great potential to enhance techniques used in practice that apply hyperspectral segmentation methods. Additionally, the theoretical analysis of the models provides a solid understanding of them and yields starting points for further improvements. LB - PUB:(DE-HGF)11 DO - DOI:10.18154/RWTH-2025-10634 UR - https://publications.rwth-aachen.de/record/1023351 ER -