Triangle mesh compression and homological spanning forests

Abstract

Triangle three-dimensional meshes have been widely used to represent 3D objects in several applications. These meshes are usually surfaces that require a huge amount of resources when they are stored, processed or transmitted. Therefore, many algorithms proposing an efficient compression of these meshes have been developed since the early 1990s. In this paper we propose a lossless method that compresses the connectivity of the mesh by using a valence-driven approach. Our algorithm introduces an improvement over the currently available valence-driven methods, being able to deal with triangular surfaces of arbitrary topology and encoding, at the same time, the topological information of the mesh by using Homological Spanning Forests. We plan to develop in the future (geo-topological) image analysis and processing algorithms, that directly work with the compressed data.