Wavelet coding of structured geometry data considering rate-distortion properties

In this paper we describe a wavelet coding method for geometry data structured on a triangular lattice. Efficient representations of a 3D object shape and its texture data have attracted wide attention for transmission of computer graphics data and for interactive design in manufacturing. Polygonal mesh data, which consists of connectivity information, geometry data and texture data, are often used for representing 3D objects in many applications. We propose a compression method for polygonal mesh data by structuring its connectivity data and geometry data on a triangular lattice. The structured geometry data is compressed by applying a 2D wavelet coding method. We obtain the wavelet coefficients by applying the shape-adaptive wavelet transform to the structured geometry data. By defining the parent-children dependencies as the set of wavelet coefficients from different bands that represent the same spatial region in a triangular lattice, the wavelet coefficients in the spatial tree are pruned optimally based on the rate-distortion properties of the geometry data. Comparison of the proposed wavelet coding with other coding schemes for polygonal mesh data shows that the proposed wavelet coding achieves better coding efficiency than other schemes adopted in the MPEG-4 standard.