Multiresolution analysis relying on Beta wavelet transform and multi-mother wavelet network for a novel 3D mesh alignment and deformation technique

Abstract

In this paper, we propose a new 3D high mesh deformation technique to extract intuitive and interpretable deformation and alignment components. Our framework is based on a fast Beta wavelet transform for a multi-resolution analysis relying on multi-library wavelet neural network architecture. The main drawback of 3D high mesh deformation is the large number of triangles necessary to characterize a smooth surface; the majority of these techniques impose a very high computational cost. Our approach is based on the idea of combining the decomposition technique of multi-resolution analysis by Beta wavelet transform for each level of deformation process and a multi-mother wavelet network structure to construct an effective 3D alignment algorithm. We use, in our experiment, only the approximation coefficients at a chosen decomposition level to reduce the complexity of the mesh and to facilitate the alignment until reaching the target mesh, for the purpose of improving various executions and obtaining an optimal solution while reducing the error between the original and the reconstructed object to create a well-formed object. Then, to enhance the performance of wavelet networks, a novel learning algorithm based on multi-mother wavelet neural network architecture using trust region spherical is employed as an approximation tool for feature alignment between the source and the target models. This network architecture ensures the use of several mother wavelets to solve the problem of high mesh deformation utilizing the best wavelet mother that well models the object. Extensive experimental results demonstrate that the progressive deformation processes aim at avoiding the weaknesses of traditional approaches such as the slowness and the difficulty of finding an exact reconstruction.