Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces. A family of box- splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box-spline, the optimal positioning of the wire-frame nodes is determined for each level of the hierarchical wire-frame decomposition. Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution level. This is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible. The application of the proposed scheme to the hierarchical coding of 3D wire meshes is experimentally evaluated.

Date Published: 30 October 1997
PDF: 12 pages
Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); doi: 10.1117/12.292808

Published in SPIE Proceedings Vol. 3169:
Wavelet Applications in Signal and Image Processing V
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)