Motion estimation is an important component of video codecs and various applications in computer vision. Especially in video compression the compact representation of motion fields is crucial, as modern video codecs use them for inter frame prediction. In recent years compression methods relying on diffusion-based inpainting have been becoming an increasingly competitive alternative to classical transform-based codecs. They perform particularly well on piecewise smooth data, suggesting that motion fields can be efficiently represented by such approaches. However, they have so far not been used for the compression of motion data. Therefore, we assess the potential of flow field compression based on homogeneous diffusion with a specifically designed new framework: Our codec stores only a few representative flow vectors and reconstructs the flow field with edge-aware homogeneous diffusion inpainting. Additionally stored edge data thereby ensure the accurate representation of discontinuities in the flow field. Our experiments show that this approach can outperform state-of-the-art codecs such as JPEG2000 and BPG HEVC intra.
Compression methods with diffusion-based inpainting were introduced by Gali ' c et al @cite_3 in 2005. Their method stores only a few selected pixels of an image and reconstructs missing data with edge-enhancing anisotropic diffusion @cite_10 . The R-EED algorithm of @cite_22 improves this idea with an efficient tree structure to adaptively encode mask pixels and can beat the quality of JPEG2000.
@cite_10 @cite_22 @cite_3
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Theoretical Foundations of Anisotropic Diffusion in Image Processing. A frequent problem in low-level vision consists of eliminating noise and small-scale details from an image while still preserving or even enhancing the edge structure. Nonlinear anisotropic diffusion filtering may be one possibility to achieve these goals. The objective of the present paper is to review the author’s results on a scale-space interpretation of a class of diffusion filters which comprises also several nonlinear anisotropic models. It is demonstrated that these models—which use an adapted diffusion tensor instead of a scalar diffusivity—offer advantages over isotropic filters. Most of the restoration and scale-space properties carry over from the continuous to the discrete case. Applications are presented ranging from preprocessing of medical images and postprocessing of fluctuating numerical data to visualizing quality relevant features for the grading of wood surfaces and fabrics. Although widely used standards such as JPEG and JPEG 2000 exist in the literature, lossy image compression is still a subject of ongoing research. (2008) have shown that compression based on edge-enhancing anisotropic diffusion can outperform JPEG for medium to high compression ratios when the interpolation points are chosen as vertices of an adaptive triangulation. In this paper we demonstrate that it is even possible to beat the quality of the much more advanced JPEG 2000 standard when one uses subdivisions on rectangles and a number of additional optimisations. They include improved entropy coding, brightness rescaling, diffusivity optimisation, and interpolation swapping. Experiments on classical test images are presented that illustrate the potential of our approach. While methods based on partial differential equations (PDEs) and variational techniques are powerful tools for denoising and inpainting digital images, their use for image compression was mainly focussing on pre- or postprocessing so far. In our paper we investigate their potential within the decoding step. We start with the observation that edge-enhancing diffusion (EED), an anisotropic nonlinear diffusion filter with a diffusion tensor, is well-suited for scattered data interpolation: Even when the interpolation data are very sparse, good results are obtained that respect discontinuities and satisfy a maximum–minimum principle. This property is exploited in our studies on PDE-based image compression. We use an adaptive triangulation method based on B-tree coding for removing less significant pixels from the image. The remaining points serve as scattered interpolation data for the EED process. They can be coded in a compact and elegant way that reflects the B-tree structure. Our experiments illustrate that for high compression rates and non-textured images, this PDE-based approach gives visually better results than the widely-used JPEG coding.