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@PHDTHESIS{Cohrs:1023351,
author = {Cohrs, Jan-Christopher},
othercontributors = {Berkels, Benjamin and Grasedyck, Lars},
title = {{M}umford–{S}hah type models for unsupervised
hyperspectral image segmentation},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2025-10634},
pages = {1 Online-Ressource : Illustrationen},
year = {2025},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2026; Dissertation, RWTH Aachen University, 2025},
abstract = {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, $\epsilon$AMS, $\phi$AMS and kMS, are
based on the Mumford-Shah segmentation functional. The
models $\epsilon$AMS and $\phi$AMS 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 $\epsilon$AMS and
$\phi$AMS 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 $\epsilon$AMS rigorously:
we prove the $\Gamma$-convergence of the corresponding
functional to a $\Gamma$-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 $\epsilon$AMS and
$\phi$AMS 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, $\epsilon$AMS and $\phi$AMS 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 $\epsilon$AMS 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.},
cin = {111410 / 110000},
ddc = {510},
cid = {$I:(DE-82)111410_20170801$ / $I:(DE-82)110000_20140620$},
pnm = {GRK 2379 - GRK 2379: Hierarchische und hybride Ansätze
für moderne inverse Probleme (333849990)},
pid = {G:(GEPRIS)333849990},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2025-10634},
url = {https://publications.rwth-aachen.de/record/1023351},
}
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