Connectivity regularization for triangular meshes

This paper introduces novel connectivity regularization techniques for triangle-dominated meshes aimed at improving lossless compression efficiency. It addresses the irregular connectivity that arises from the triangulation of quad meshes, where vertex degrees typically range from four to eight. The proposed regularization detects triangle pairs that constitute the original quads and applies one of two regularization techniques. The first technique flips diagonal edges of certain quads to achieve consistent diagonal edge orientations. The second technique restores the original quads by removing their diagonal edges. This results in a connectivity where most vertices are surrounded either by six triangles or by four quads. To ensure lossless compression, the affected edge data can be encoded in the bitstream, allowing the decoder to restore the input mesh connectivity. The results demonstrate compression gains for meshes with position, texture coordinate, and normal attributes. Adaptively applying the two techniques yielded an average compression gain of 1.9% when preserving the affected edge data for lossless compression and 5.9% when discarding the affected edge data.