Spectral Coding of Mesh Geometry with a Hierarchical Set Partitioning Algorithm

This work proposes a progressive mesh geometry coder, which expresses geometry information in terms of spectral coefficients obtained through a transformation and codes these coefficients using a hierarchical set partitioning algorithm that assigns right priorities to those coefficients at all bit planes. The spectral transformation used is the one proposed in (Karni Z. et al., 2000) where the spectral coefficients are obtained by projecting the mesh geometry on an orthonormal basis determined by mesh topology. The set partitioning method used in coding, treats spectral coefficients belonging to the three spatial coordinates with the right priority at all bit planes and realizes a truly embedded system by achieving implicit bit allocation via joint coding the zeroes of coefficients at the bit planes. The experiments performed on common irregular meshes reveal that the rate-distortion performance of the coder is significantly superior to the coding system proposed in (Karni Z. et al., 2000).