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.
CITATION STYLE
Weickert, J., & Welk, M. (2006). Tensor field interpolation with PDEs. In Mathematics and Visualization (Vol. 0, pp. 315–325). Springer Heidelberg. https://doi.org/10.1007/3-540-31272-2_19
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