Tensor Field Interpolation with PDEs
نویسندگان
چکیده
We present a unified framework for interpolation and regularisation of scalarand 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.
منابع مشابه
Sparse tensor discretizations of elliptic PDEs with random input data
We consider a stochastic Galerkin and collocation discretization scheme for solving elliptic PDEs with random coefficients and forcing term, which are assumed to depend on a finite, but possibly large number of random variables. Both methods consist of a hierarchic wavelet discretization in space and a sequence of hierarchic approximations to the law of the random solution in probability space....
متن کاملExtrapolation of Sparse Tensor Fields: Application to the Modeling of Brain Variability
Modeling the variability of brain structures is a fundamental problem in Neurosciences. In this paper, we start from a dataset of precisely delineated anatomical structure: sulcal lines. We propose an original method to compute the average sulcal curves, which constitute the mean anatomy in this context. The second order moment of the sulcal distribution can be modeled as a sparse field of cova...
متن کاملPDEs for Tensor Image Processing
Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters...
متن کاملTensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs
We investigate the convergence rate of approximations by finite sums of rank-1 tensors of solutions of multi-parametric elliptic PDEs. Such PDEs arise, for example, in the parametric, deterministic reformulation of elliptic PDEs with random field inputs, based for example, on the M -term truncated Karhunen-Loève expansion. Our approach could be regarded as either a class of compressed approxima...
متن کاملTensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation
Interpolation is an essential step in the visualization process. While most data from simulations or experiments are discrete many visualization methods are based on smooth, continuous data approximation or interpolation methods. We introduce a new interpolation method for symmetrical tensor fields given on a triangulated domain. Differently from standard tensor field interpolation, which is ba...
متن کامل