Optimized Butterfly-based lifting scheme for semi-regular meshes

Abstract

To cite this version: ABSTRACTIn this paper, we propose an optimization of the lifted Butterfly scheme for semi-regular meshes. This optimization consists in adapting the predict and update steps at each level of resolution for a given semi-regular mesh. The motivation is the improvement of the multiresolution analysis in order to increase the compression performances of the subsequent geometry coder. We first compute an optimized prediction scheme that minimizes the L1-norm of the wavelet coefficients for each level of resolution, independently. We then compute the update scheme in order to preserve the data average (0 th moment) at the lower resolution. Experimental results shows that our technique globally reduces the entropy of the wavelet coefficients of any semi-regular mesh. Consequently our contribution also improves the compression performances of the zerotree coder PGC.

Sparsity-based optimization of two lifting-based wavelet transforms for semi-regular mesh compression

“…The idea of adapting the prediction step of the Butterfly-based scheme has been already introduced in [31]. The main contributions of the current paper are:…”

“…• A more robust method for computing the update operator for this scheme. The reason is that the technique proposed in [31] sometimes fails because of a potential null divisor;…”

“…In this section we present our optimization algorithm for adapting the Butterfly-based lifting scheme to the input mesh. This algorithm consists in finding for each resolution the optimal operators P such as the sparsity of the wavelet coefficients is maximized [31]. This algorithm produces new stencils for each level of resolution.…”

“…In this work, we choose to compute γ such as to preserve the average between V j and V j−1 . Contrary to [31], we prefer using the robust method proposed in [32]. The principle is to put all the vertices of V j−1 and all the coefficients of C j to zero, except one coefficient of C j put to 1 (see Figure 8).…”