An axiomatic approach to image interpolation

Caselles, V.; Morel, Jean‐Michel; Sbert, Catalina

doi:10.1109/83.661188

Cited by 287 publications

(116 citation statements)

References 17 publications

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“…The interpolation qualities of PDEs have become evident by an axiomatic analysis [20], by applying them to image inpainting [51,10,22,12,66,11] and by utilising them for upsampling digital images [49,7,8,3,73,58]. Extending this to image compression drives inpainting to the extreme: Only a small set of specifically selected pixels is stored, while the remaining image is reconstructed using the filling-in effect of PDE-based interpolation.…”

Section: Introductionmentioning

confidence: 99%

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

et al. 2014

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Galić et al. [33] have shown that compression based on edge-enhancing anisotropic diffusion (EED) can outperform the quality of JPEG for medium to high compression ratios when the interpolation points are chosen as vertices of an adaptive triangulation. However, the reasons for the good performance of EED remained unclear, and they could not outperform the more advanced JPEG 2000. The goals of the present paper are threefold: Firstly, we investigate the compression qualities of various partial differential equations. This sheds light on the favourable properties of EED in the context of image compression. Secondly, we demonstrate that it is even possible to beat the quality of JPEG 2000 with EED if one uses specific subdivisions on rectangles and several important optimisations. These amendments include improved entropy coding, brightness and diffusivity optimisation, and interpolation swapping. Thirdly, we demonstrate how to extend our approach to 3-D and shape data. Experiments on classical test images and 3-D medical data illustrate the high potential of our approach.

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Section: Introductionmentioning

confidence: 99%

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

et al. 2014

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“…If the data are not available on a regular grid, scattered data interpolation techniques have been proposed [7,15]. More recently, also interpolation methods based on variational formulations and nonlinear partial differential equations (PDEs) have been advocated [4,11], in particular for so-called inpainting methods [12,5,9], where the image data are only corrupted in specific areas. Nonlinear PDEs allow to design discontinuity-preserving interpolants.…”

Section: Introductionmentioning

confidence: 99%

Tensor Field Interpolation with PDEs

Weickert

Welk

2006

Mathematics and Visualization

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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.

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“…Early works include [CMS98], where an approach on image interpolation was introduced, a level lines-based method presented in [MM98], and the work of [BSCB00], which we already stated above. They can be seen as pioneering works.…”

Section: Geometry-oriented Methodsmentioning

confidence: 99%