Progressive Coding of 3-D Objects Based on Overcomplete Decompositions

This paper presents a progressive coding scheme for 3-D objects, based on overcomplete signal expansions on the 2-D sphere. Due to increased freedom in the basis construction, redundant expansions have shown interesting approximation properties in the decomposition of signals with multidimensional singularities organized along embedded submanifolds. We propose to map simple 3-D models on 2-D spheres and then to decompose the signal over a redundant dictionary of oriented and anisotropic atoms living on the sphere. The signal expansion is computed iteratively with a matching pursuit algorithm, which greedily selects the most prominent components of the 3-D model. The decomposition therefore inherently represents a progressive stream of atoms, which is advantageously used in the design of scalable representations. An encoder is proposed that compresses the stream of atoms by adaptive coefficient quantization and entropy coding of atom indexes. Experimental results show that the novel coding strategy outperforms state-of-the-art progressive coders in terms of distortion, mostly at low bit rates. Furthermore, since the dictionary is built on structured atoms, the proposed representation simultaneously offers an increased flexibility for easy stream manipulations. We finally illustrate that advantage in the design of a view-dependent transmission scheme