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.

Compressing piecewise smooth images is important for many data types such as depth maps in 3D videos or optic flow fields for motion compensation. Specialised codecs that rely on explicitly stored segmentations excel in this task since they preserve discontinuities between smooth regions. However, current approaches rely on ad hoc segmentations that lack a clean interpretation in terms of energy minimisation. As a remedy, we derive a generic region merging algorithm from the Mumford-Shah cartoon model. It adapts the segmentation to arbitrary reconstruction operators for the segment content. In spite of its conceptual simplicity, our framework can outperform previous segment-based compression methods as well as BPG by up to 3 dB.

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