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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Tensor Field Interpolation with PDEs
verfasst von : Joachim Weickert, Martin Welk
Erschienen in: Visualization and Processing of Tensor Fields
Verlag: Springer Berlin Heidelberg
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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.