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Preprint (Vorabdruck) zugänglich unter
Tensor field interpolation with PDEs
URN: urn:nbn:de:bsz:291-scidok-45110
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4511/
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Dokument 1.pdf (1.547 KB)
Freie Schlagwörter (Englisch):
matrix-valued images , inpainting , scattered data interpolation , regularisation
Institut:
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer:
142
Sprache:
Englisch
Erstellungsjahr:
2005
Publikationsdatum:
25.01.2012
Kurzfassung auf Englisch:
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.
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