Prediction schemes for meshes with regular connectivity

This paper introduces two novel geometry prediction schemes, called Hexagon and Quad Tromino, designed to enhance lossless geometry compression for meshes with triangular and quadrilateral faces, respectively. These prediction schemes exploit regular mesh connectivities, where vertices are connected to six edges in triangular meshes and four edges in quad meshes. The proposed prediction schemes capture similarities in nearby grid line curvatures and spacings, as well as shape similarities of nearby parallelograms or quads. The Hexagon prediction scheme predicts a target vertex based on the known positions of five neighboring vertices in a regular triangular grid. Similarly, the Quad Tromino scheme predicts a vertex using seven neighboring vertices in a regular quad grid. Both methods extrapolate from known nearby vertices and apply corrections from known nearby edges to predict the target vertex. The schemes are more effective when vertex positions are accurate and contain more geometric signal compared to quantization noise. Results show that the biggest impact is achieved for meshes with high position quantization. For meshes with regular connectivity and 16 bit position quantization, the introduction of the Hexagon and the Quad Tromino predictors (to a codec that also uses simpler predictors like Parallelogram and multi-way) yielded an average position compression gain of 5.7% and 6.4%, respectively.