Abstract Time‐varying meshes (TVMs), that is mesh sequences with varying connectivity, are a greatly versatile representation of shapes evolving in time, as they allow a surface topology to change or details to appear or disappear at any time during the sequence. This, however, comes at the cost of large storage size. Since 2003, there have been attempts to compress such data efficiently. While the problem may seem trivial at first sight, considering the strong temporal coherence of shapes represented by the individual frames, it turns out that the varying connectivity and the absence of implicit correspondence information that stems from it makes it rather difficult to exploit the redundancies present in the data. Therefore, efficient and general TVM compression is still considered an open problem. We describe and categorize existing approaches while pointing out the current challenges in the field and hint at some related techniques that might be helpful in addressing them. We also provide an overview of the reported performance of the discussed methods and a list of datasets that are publicly available for experiments. Finally, we also discuss potential future trends in the field.

A new method for encoding a sequence of integers, named Binary Adaptive Sequential Coding with Return to Bias, is proposed in this paper. It extends the compressing pipeline for chain codes’ compression consisting of Burrows Wheeler Transform, Move-To-Front Transform, and Adaptive Arithmetic Coding. We also explain when to include the Zero-Run Transform into the above-mentioned pipeline. The Zero-Run Transform generates a sequence of integers corresponding to the number of zero-runs. This sequence is encoded by Golomb coding, Binary Adaptive Sequential Coding, and the new Binary Adaptive Sequential Coding with Return to Bias. Finally, a comparison is performed with the two state-of-the-art methods. The proposed method achieved similar compression efficiency for the Freeman chain code in eight directions. However, for the chain codes with shorter alphabets (Freeman chain code in four directions, Vertex Chain Code, and Three-OrThogonal chain code), the introduced method outperforms the referenced ones.