Application of inhomogeneous diffusion to image and video coding

Ford, Gary E.

doi:10.1109/acssc.1996.599080

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…[67,40]) or as a postprocessing tool for removing coding artifacts (see e.g. [31,2]). The papers [32,33] as well as our present work differs from these strategies by the fact that we use a PDE within encoding and decoding rather than applying it before encoding or after decoding.…”

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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“…In the context of image compression, PDEs and related variational techniques have mainly been used as a preprocessing step before coding images or videos [18,29,30,41,66] or as a postprocessing tool for removing coding artifacts [1,26,29,33,53,72,73]. Our work differs from these papers by the fact that we use a PDE within the encoding and decoding step rather than applying it before encoding or after decoding.…”

Section: Related Workmentioning

confidence: 54%

Image Compression with Anisotropic Diffusion

et al. 2008

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Compression is an important field of digital image processing where well-engineered methods with high performance exist. Partial differential equations (PDEs), however, have not much been explored in this context so far. In our paper we introduce a novel framework for image compression that makes use of the interpolation qualities of edge-enhancing diffusion. Although this anisotropic diffusion equation with a diffusion tensor was originally proposed for image denoising, we show that it outperforms many other PDEs when sparse scattered data must be interpolated. To exploit this property for image compression, we consider an adaptive triangulation method for remov- ing less significant pixels from the image. The remaining points serve as scattered interpolation data for the diffusion process. They can be coded in a compact way that reflects the B-tree structure of the triangulation. We supplement the coding step with a number of amendments such as error threshold adaptation, diffusion-based point selection, and specific quantisation strategies. Our experiments illustrate the usefulness of each of these modifications. They demonstrate that for high compression rates, our PDE-based approach does not only give far better results than the widelyused JPEG standard, but can even come close to the quality of the highly optimised JPEG2000 codec.

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“…This means that we do not discuss the numerous PDE-based or variational techniques that have been advocated as a preprocessing step before coding images or videos (see e.g. [78,128]) or as a postprocessing tool for removing coding artifacts (such as [3,16,52]).…”

Section: A Review Of Pde-based Image Compressionmentioning

confidence: 99%

“…Similar considerations apply to the parameter η in (52): The nonlinear dynamics of the Jacobian suggests to use small values for η in order to approximate the derivative well. On the other side, if η is too small, numerical problems can arise, since both the numerator and the denominator in (52) approach zero. Table 6 shows how an appropriate selection of the parameters α and η can be used to optimise the reconstruction quality for EED-based inpainting.…”

Section: Optimising Tonal Datamentioning

confidence: 99%

2. Optimizing spatial and tonal data for PDE-based inpainting

Hoeltgen¹,

Mainberger²,

Hoffmann³

et al. 2016

Variational Methods

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Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. Apart from these specific contributions, we also give an extensive literature survey on PDE-based image compression methods. Summary and ConclusionsThe contributions of our work are twofold: On the one hand we gave a comprehensive survey on the state-of-the-art in PDE-based image compression.

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Application of inhomogeneous diffusion to image and video coding

Cited by 3 publications

References 13 publications

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

Understanding, Optimising, and Extending Data Compression with Anisotropic Diffusion

Image Compression with Anisotropic Diffusion

2. Optimizing spatial and tonal data for PDE-based inpainting

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