A fast C++ Template Library for Total Variation Minimization of manifold-valued two and three-dimensional Images
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Author
Date
2015-10-01Type
- Master Thesis
ETH Bibliography
yes
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Abstract
In this thesis, a versatile, multi-threaded C++ template library for total variation (TV) minimization of manifold-valued image data is introduced. The library implements two minimizers: the iteratively reweighted least squares (IRLS) algorithm using the Riemannian Newton method for the optimization step and the proximal point algorithm. Pixels can take values in Euclidean space, on the Sphere, the special orthogonal group, the set of positive definite matrices and the Grassmann manifold while images can be either two- or three-dimensional. Some semi-analytic expressions for the derivatives of the squared distance functions using Kronecker products and a short overview about the relevant Grassmann manifold theory is provided along with a high level documentation of the library and its design concepts. The last part demonstrates the library’s capabilities on different applications in image and video processing, medical imaging and computer vision. Performance is measured and compared for the IRLS and the proximal point implementations. Lastly the influence of the noisy original data on the the minimizer is investigated. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000657180Publication status
publishedPublisher
ETH ZurichSubject
total variation minimization; manifold-valued data; iteratively reweighted least squares; proximal point algorithm; Riemannian Newton methodOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
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Is cited by: http://hdl.handle.net/20.500.11850/290582
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ETH Bibliography
yes
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