Static and Dynamic 3D Meshes Processing using Spectral Methods

analysis and compression of signals and two-dimensional images. The popular
JPEG format projects the image pixels onto the 2D DCT basis and uses the
resulting spectral coefficients to achieve better compression ratios.

Spectral decomposition of 3D meshes was proposed by Karni and Gotsman in
SIGGRAPH 2000. This decomposition uses basis functions based only on the mesh
connectivity. As in the JPEG format, they projected the mesh geometry onto the
basis and used the resulting coefficients for progressive reconstruction. In
2004 Ben-Chen and Gotsman provided theoretical support for this method by
showing that the spectral basis is optimal for certain classes of irregular
meshes. Recently, Karni and Gotsman proposed to use spectral decomposition for
dynamic mesh compression. Motivated by the work of Alexa and Muller and by the
practical use of free vibration modes, they generated a spectral basis using
Principle Components Analysis of the dynamic mesh geometry, and encoded the
resulting coefficients using Linear Prediction Coding.

This talk will describe the fundamentals of 3D spectral decomposition on static
and dynamic meshes and explain why it works and how to apply it to mesh
geometry compression. The talk will detail the difficulties inherent in such
methods and finally introduce several techniques that overcome some of the
difficulties and make spectral methods more practical.