Modeling Wavelet Coefficients for Wavelet Subdivision Transforms of 3D Meshes

In this paper, a Laplacian Mixture (LM) model is proposed to accurately approximate the observed histogram of the wavelet coefficients produced by lifting-based subdivision wavelet transforms. On average, the proposed mixture model gives better histogram fitting for both normal and non-normal meshes compared to the traditionally used Generalized Gaussian (GG) distributions. Exact closed-form expressions for the rate and the distortion of the LM probability density function quantized using generic embedded deadzone scalar quantizer (EDSQ) are derived, without making high-rate assumptions. Experimental evaluations carried out on a set of 3D meshes reveals that, on average, the D-R function for the LM model closely follows and gives a better indication of the experimental D-R compared to the D-R curve of the competing GG model. Optimal embedded quantization for the proposed LM model is experimentally determined. In this sense, it is concluded that the classical Successive Approximation Quantization (SAQ) is an acceptable, but in general, not an optimal embedded quantization solution in wavelet-based scalable coding of 3D meshes.