Compressing Mesh Geometry using Spectral Methods and a Set Partitioning Approach

We propose a mesh geometry coder that utilizes spectral methods and a set partitioning approach for coding the spectral coefficients. The spectral method of [1] not only achieved high rate-distortion performance on irregular meshes, but also allowed progressive transmission of meshes by truncating the coefficient vector and performing reconstruction with a small subset of coefficients that contain most of the total energy. In this paper, mesh geometry is projected onto an orthonormal basis that is derived from the mesh topology as in [1], and the spectral coefficients are coded with the set partitioning sorting algorithm of [2]. Since the method achieves implicit bit allocation to the spectral coefficients of the three coordinates and efficiently codes the significant coefficient location information by jointly coding the zeroes in the bit planes of these coefficients the rate-distortion performance of the proposed method is superior to that of [1] as demonstrated by our experiments on common irregular meshes. The generated bit stream is also truly embedded.