Please use this identifier to cite or link to this item: doi:10.22028/D291-26291
Title: Tensor field interpolation with PDEs
Author(s): Weickert, Joachim
Welk, Martin
Language: English
Year of Publication: 2005
Free key words: matrix-valued images
scattered data interpolation
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: We present a unified framework for interpolation and regularisation of scalar- and tensor-valued images. This framework is based on elliptic partial differential equations (PDEs) and allows rotationally invariant models. Since it does not require a regular grid, it can also be used for tensor-valued scattered data interpolation and for tensor field inpainting. By choosing suitable differential operators, interpolation methods using radial basis functions are covered. Our experiments show that a novel interpolation technique based on anisotropic diffusion with a diffusion tensor should be favoured: It outperforms interpolants with radial basis functions, it allows discontinuity-preserving interpolation with no additional oscillations, and it respects positive semidefiniteness of the input tensor data.
Link to this record: urn:nbn:de:bsz:291-scidok-45110
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 142
Date of registration: 25-Jan-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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