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.
 Traditional video compression methods obtain a compact representation for image frames by computing coarse motion fields defined on patches of pixels called blocks, in order to compensate for the motion in the scene across frames. This piecewise constant approximation makes the motion field efficiently encodable, but it introduces block artifacts in the warped image frame. In this paper, we address the problem of estimating dense motion fields that, while accurately predicting one frame from a given reference frame by warping it with the field, are also compressible. We introduce a representation for motion fields based on wavelet bases, and approximate the compressibility of their coefficients with a piecewise smooth surrogate function that yields an objective function similar to classical optical flow formulations. We then show how to quantize and encode such coefficients with adaptive precision. We demonstrate the effectiveness of our approach by comparing its performance with a state-of-the-art wavelet video encoder. Experimental results on a number of standard flow and video datasets reveal that our method significantly outperforms both block-based and optical-flow-based motion compensation algorithms. In image compression, codecs that rely on interpolation with partial differential equations (PDEs) are becoming increasingly popular. However, there have not been many attempts to transfer this concept to video compression. Since real-time performance is challenging for PDE-based reconstruction, first efficient approaches work on a frame-by-frame basis and focus on parallel implementations without considering coding quality. So far, there is no fully PDE-based video codec that exploits temporal redundancies. As a remedy, we propose a modular framework that combines PDE-based compression with motion compensation: Intra frames are predicted with PDE-based inpainting and inter frames with dense optic flow fields. We use this framework to develop a proof-of-concept codec that combines homogeneous diffusion inpainting with the variational optic flow model of (2004). Even without sophisticated parallelisation, we are able to perform real-time decompression of colour videos for the first time in PDE-based video compression.