Reconstruction Algorithms as a Suitable Basis for Mesh Connectivity Compression

Abstract

During a highly productive period running from 1995 to about 2002, the research in lossless compression of surface meshes mainly consisted in a hard battle for the best bitrates. However, for a few years, compression rates seem stabilized around 1.5 bit per vertex for the connectivity coding of usual triangular meshes, and more and more work is dedicated to remeshing, lossy compression, or gigantic mesh compression, where memory access and CPU optimizations are the new priority. However, the size of 3D models keeps growing, and many application fields keep requiring lossless compression. In this paper, we present a new contribution for single-rate lossless connectivity compression, which first brings improvement over current state of the art bitrates, and second, does not constraint the coding of the vertex positions, offering therefore a good complementarity with the best performing geometric compression methods. The initial observation having motivated this work is that very often, most of the connectivity part of a mesh can be automatically deduced from its geometric part using reconstruction algorithms. This has already been used within the limited framework of projectable objects (essentially, terrain models and GIS), but finds here its first generalization to arbitrary triangular meshes, without any limitation regarding the topological genus, the number of connected components, the manifoldness or the regularity. This can be obtained by constraining and guiding a Delaunay-based reconstruction algorithm so that it outputs the initial mesh to be coded. The resulting rates seem extremely competitive when the meshes are fully included in Delaunay, and are still good compared to the state-of-the-art in the case of scanned models.Note to Practitioners-A 3D triangle mesh is composed of a geometric part (the vertex coordinates) and a connectivity part (the description of the triangles). In this paper, we show how to reencode such surface meshes in order to obtain near zero connectivity cost for some class of surface meshes (and very good rates in the general case), while guaranteeing in the same time state-of-the-art geometry encoding cost. This method can be useful in all application areas where the mesh size is a bottleneck (typically network or storage applications). The best results are obtained for meshes made from 3D scans (in contrast to CAD meshes). The main current limitations of the method are the computing times (about 1 s per 1000 points part of the mesh, for compression which can be done offline) and the memory footprint.

Priority‐based encoding of triangle mesh connectivity for a known geometry

“…For highly regular data, Chaine et al. [CGR09] proposed a connectivity coding approach based on surface reconstruction. Both the encoder and the decoder perform an iterative surface reconstruction algorithm, and the encoder signals the differences between the actual and the reconstructed surface.…”