Partial Differential Equations for Interpolation and Compression of Surfaces

Bae, Egil; Weickert, Joachim

doi:10.1007/978-3-642-11620-9_1

Cited by 14 publications

(16 citation statements)

References 16 publications

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“…[68] or [14]. A generalisation of image compression ideas with homogeneous diffusion to the compression of surfaces is studied in [6]. The second part of our manuscript extends preliminary results of a conference paper [59].…”

Section: Introductionmentioning

confidence: 74%

“…It is more challenging to adapt our methods to the efficient compression of image sequences and surface data, see e.g. [6]. A more advanced handling of colour images and shapes is also on our agenda.…”

Section: Resultsmentioning

confidence: 99%

“…Interestingly there is a relatively simple remedy for all these problems: In [6] it is proposed to perform an additional inpainting step in which the role of known and unknown pixels is swapped. That is, after reconstructing the image with inpainting, one regards the reconstructed points in Ω \ K as known and the specified points in K as unknown.…”

Section: Interpolation Swappingmentioning

confidence: 99%

“…Here we propose a modification that extends the interpolation swapping of [6]: Instead of only recomputing the known points, we also allow the possibility to recompute more points. More precisely, we reconstruct all points within a certain radius around the saved mask points.…”

Section: Interpolation Swappingmentioning

confidence: 99%

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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: 74%

Section: Resultsmentioning

confidence: 99%

Section: Interpolation Swappingmentioning

confidence: 99%

Section: Interpolation Swappingmentioning

confidence: 99%

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Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

et al. 2014

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“…Research on PDE-based data compression suffers from poverty, but enjoys liberty [1,2,8,18]: Unlike in pure inpainting research [14,3], one has an extremely tight pixel budget for reconstructing some given image. However, one is free to choose where and how one spends this budget.…”

Section: Introductionmentioning

confidence: 99%

Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

Mainberger

Hoffmann

Weickert

et al. 2012

Lecture Notes in Computer Science

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Abstract. Finding optimal inpainting data plays a key role in the field of image compression with partial differential equations (PDEs). In this paper, we optimise the spatial as well as the tonal data such that an image can be reconstructed with minimised error by means of discrete homogeneous diffusion inpainting. To optimise the spatial distribution of the inpainting data, we apply a probabilistic data sparsification followed by a nonlocal pixel exchange. Afterwards we optimise the grey values in these inpainting points in an exact way using a least squares approach. The resulting method allows almost perfect reconstructions with only 5% of all pixels. This demonstrates that a thorough data optimisation can compensate for most deficiencies of a suboptimal PDE interpolant.

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Partial Differential Equations for Interpolation and Compression of Surfaces

Cited by 14 publications

References 16 publications

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

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