Progressive Compression of 3D Mesh Geometry Using Sparse Approximations from Redundant Frame Dictionaries

Abstract

The proliferation of sophisticated techniques for 3D model acquisition and graphic design in recent years is resulting in a rapid increase in the number and complexity of 3D models being produced. At the same time, the need for exchanging 3D models is also rising due to new computing paradigms (e.g., cloud computing) and an increase in collaborative applications and online social networks. This has created a need for efficient compression techniques for 3D models, which are progressive, allow high quality or even lossless reconstruction, and minimize the amount of transferred data. Most of the research on 3D model compression to date has focused on the compression of triangular surface meshes, as this is the most common representation for 3D objects. In particular, progressive compression techniques for 3D mesh models have become very popular in recent years, as they allow a mesh to be reconstructed from coarse to fine levels of detail at the decoder while the bitstream of data is still being received. Currently the best-performing progressive compression techniques seem to be those that use transform coding ideas borrowed from traditional signal and image processing. The fundamental assumption behind such techniques is that the input data can be represented as some sparse linear combination of atoms taken from a representative dictionary of atoms that constitute the new representation domain. Traditionally, these dictionaries have been chosen to be orthogonal bases; however, recent research into alternative signal representations has shown that overcomplete dictionaries, or frames, may be able to produce even sparser representations than orthogonal bases can. In the field of 3D mesh compression, the idea of using redundant representations has only just started to surface. The main challenge here is currently the creation of a good overcomplete dictionary, particularly for mesh models with irregular connectivity that needs to be preserved. In light of this, the main objective of the work in this thesis is to develop a new method for constructing a frame, which can be applied to a manifold triangle mesh directly (i.e., with no requirement for a prior remeshing to a more regular domain) and can be used to obtain sparse approximations of the mesh geometry in a progressive compression scenario. This is the main contribution of this thesis. The frames that we propose are constructed from the unit-norm eigenvectors of a combinatorial mesh Laplacian matrix, plus a large number of redundant linear combinations of these eigenvectors. A sparse synthesis of the input mesh geometry is achieved by selecting atoms from the frame using the Matching Pursuit algorithm. The proposed frames can be applied directly to a manifold mesh with arbitrary topology and connectivity type, as long as the mesh can be represented as a connected graph. Our experimental results for a variety of different mesh models indicate that, for a given reconstruction quality, a sparser approximation of the input mesh geometry can be obtained with the proposed…