Preconditioned Deformation Grids

Abstract: Dynamic surface reconstruction of objects from point cloud sequences is a challenging field in computer graphics. Existing approaches either require multiple regularization terms or extensive training data which, however, lead to compromises in reconstruction accuracy as well as over-smoothing or poor generalization to unseen objects and motions. To address these lim- itations, we introduce Preconditioned Deformation Grids, a novel technique for estimating coherent deformation fields directly from unstructured point cloud sequences without requiring or forming explicit correspondences. Key to our approach is the use of multi-resolution voxel grids that capture the overall motion at varying spatial scales, enabling a more flexible deformation representation. In conjunction with incorporating grid-based Sobolev preconditioning into gradient-based optimization, we show that applying a Chamfer loss between the input point clouds as well as to an evolving template mesh is sufficient to obtain accurate deformations. To ensure temporal consistency along the object surface, we include a weak isometry loss on mesh edges which complements the main objective without constraining deformation fidelity. Extensive evaluations demonstrate that our method achieves superior results, particularly for long sequences, compared to state-of-the-art techniques.