Permuting and Lifting Wavelet Coding for Structured Geometry Data of 3-D Polygonal Mesh

Akira KAWANAKA  Shuji WATANABE  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E90-D   No.9   pp.1439-1447
Publication Date: 2007/09/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.9.1439
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computer Graphics
Keyword: 
lifting wavelet,  permutation,  polygonal mesh,  geometry data,  2-D structuring,  triangular lattice plane,  

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Summary: 
This paper presents a lifting wavelet coding technique with permutation and coefficient modification processes for coding the structured geometry data of 3-D polygonal mesh model. One promising method for coding 3-D geometry data is based on the structure processing of a 3-D model on a triangle lattice plane, while maintaining connectivity. In the structuring process, each vertex may be assigned to several nodes on the triangular lattice plane. One of the nodes to which a vertex is assigned is selected as a representative node and the others are called expanded nodes. Only the geometry data of the vertices at the representative nodes are required for reconstructing the 3-D model. In this paper we apply a lifting wavelet transform with a permutation process for an expanded node at an even location in each decomposition step and the neighboring representative node. This scheme arranges more representative nodes into the lower frequency band. Also many representative nodes separated from the connective expanded nodes are made to adjoin each other in lower frequency bands, and the correlation between the representative nodes will be reduced by the following decomposition process. A process is added to use the modified coefficients obtained from the coefficients of the adjacent representative nodes instead of the original coefficients in the permutation process. This has the effect of restraining increases in the decomposed coefficients with larger magnitude. Some experiments in which the proposed scheme was applied to structured geometry data of a 3-D model with complex connectivity show that the proposed scheme gives better coding performance and the reconstructed models are more faithful to the original in comparison with the usual schemes.