3-D Mesh geometry compression with set partitioning in the spectral domain

This paper explains the development of a highly efficient progressive 3-D mesh geometry coder based on the region adaptive transform in the spectral mesh compression method. A hierarchical set partitioning technique, originally proposed for the efficient compression of wavelet transform coefficients in high-performance wavelet-based image coding methods, is proposed for the efficient compression of the coefficients of this transform. Experiments confirm that the proposed coder employing such a region adaptive transform has a high compression performance rarely achieved by other state of the art 3-D mesh geometry compression algorithms. A new, high-performance fixed spectral basis method is also proposed for reducing the computational complexity of the transform. Many-to-one mappings are employed to relate the coded irregular mesh region to a regular mesh whose basis is used. To prevent loss of compression performance due to the low-pass nature of such mappings, transitions are made from transform-based coding to spatial coding on a per region basis at high coding rates. Experimental results show the performance advantage of the newly proposed fixed spectral basis method over the original fixed spectral basis method in the literature that employs one-to-one mappings.This work was supported in part by the Scientific and Technological Research Council of Turkey, and conducted under Project 106E064Publisher's Versio

Adaptive Mesh Compression in 3D Computer Graphics using Multiscale Manifold Learning

This paper investigates compression of 3D objects in computer graphics using manifold learning. Spectral compression uses the eigenvectors of the graph Laplacian of an object’s topology to adaptively compress 3D objects. 3D compression is a challenging application domain: object models can have> 10 5 vertices, and reliably computing the basis functions on large graphs is numerically challenging. In this paper, we introduce a novel multiscale manifold learning approach to 3D mesh compression using diffusion wavelets, a general extension of wavelets to graphs with arbitrary topology. Unlike the “global ” nature of Laplacian bases, diffusion wavelet bases are compact, and multiscale in nature. We decompose large graphs using a fast graph partitioning method, and combine local multiscale wavelet bases computed on each subgraph. We present results showing that multiscale diffusion wavelets bases are superior to the Laplacian bases for adaptive compression of large 3D objects. 1