Estimation of interband and intraband statistical dependencies in wavelet-based decomposition of meshes

This paper analyzes the statistical dependencies between wavelet coefficients in wavelet-based decompositions of 3D meshes. These dependencies are estimated using the interband, intraband and composite mutual information. For images, the literature shows that the composite and the intraband mutual information are approximat-ely equal, and they are both significantly larger than the interband mutual information. This indicates that intraband coding designs should be favored over the interband zerotree-based coding approaches, in order to better capture the residual dependencies between wavelet coefficients. This motivates the design of intraband wavelet-based image coding schemes, such as quadtree-limited (QT-L) coding, or the state-of-the-art JPEG-2000 scalable image coding standard. In this paper, we empirically investigate whether these findings hold in case of meshes as well. The mutual information estimation results show that, although the intraband mutual information is significantly larger than the interband mutual information, the composite case cannot be discarded, as the composite mutual information is also significantly larger than the intraband mutual information. One concludes that intraband and composite codec designs should be favored over the traditional interband zerotree-based coding approaches commonly followed in scalable coding of meshes.