Efficient representations of a 3-D object shape and its texture data have attracted wide attention for the transmission of computer graphics data and for the development of multi-view real image rendering systems on computer networks. Polygonal mesh data, which consist of connectivity information, geometry data, and texture data, are often used for representing 3-D objects in many applications. This paper presents a wavelet coding technique for coding the geometry data structured on a triangular lattice plane obtained by structuring the connectivity of the polygonal mesh data. Since the structured geometry data have an arbitrarily-shaped support on the triangular lattice plane, a shape-adaptive wavelet transform was used to obtain the wavelet coefficients, whose number is identical to the number of original data, while preserving the self-similarity of the wavelet coefficients across subbands. In addition, the wavelet coding technique includes extensions of the zerotree entropy (ZTE) coding for taking into account the rate-distortion properties of the structured geometry data. The parent-children dependencies are defined as the set of wavelet coefficients from different bands that represent the same spatial region in the triangular lattice plane, and the wavelet coefficients in the spatial tree are optimally pruned based on the rate-distortion properties of the geometry data. Experiments in which proposed wavelet coding was applied to some sets of polygonal mesh data showed that the proposed wavelet coding achieved better coding efficiency than the Topologically Assisted Geometry Compression scheme adopted in the MPEG-4 standard.

A simple embedded lossless wavelet-based image coding algorithm called Successive Partition Zero Coder (SPZC), which uses hybrid bit scanning and non-causal adaptive context modelling, is proposed. By successive partition the wavelet coefficients in the spatial-frequency domain, the coefficients are ordered based on their absolute range. The prioritized coefficients are quantized in a successive approximation manner to generate a binary sequence, which is divided into subsources and encoded by arithmetic coder with non-causal adaptive context modelling. This method is suited for progressive image transmission (PIT). Experimental results show that SPZC outperforms other state-of-the-art coders such as SPIHT, CREW and LJPEG, but slightly inferior to ECECOW and CALIC in lossless mode. SPZC is simple in both context modelling and implementation.