Sparse Localized Decomposition of Deformation Gradients

Sparse localized decomposition is a useful technique to extract meaningful deformation components out of a training set of mesh data. However, existing methods cannot capture large rotational motion in the given mesh dataset. In this paper we present a new decomposition technique based on deformation gradients. Given a mesh dataset, the deformation gradient field is extracted, and decomposed into two groups: rotation field and stretching field, through polar decomposition. These two groups of deformation information are further processed through the sparse localized decomposition into the desired components. These sparse localized components can be linearly combined to form a meaningful deformation gradient field, and can be used to reconstruct the mesh through a least squares optimization step. Our experiments show that the proposed method addresses the rotation problem associated with traditional deformation decomposition techniques, making it suitable to handle not only stretched deformations, but also articulated motions that involve large rotations.