Medial Axis Aware Learning of Signed Distance Functions
For 3D shape reconstruction and geometry processing, this method provides a more accurate SDF by incorporating medial axis information, though it is an incremental improvement over existing variational approaches.
The paper introduces a variational method for computing accurate signed distance functions (SDFs) from unoriented point clouds by explicitly modeling the medial axis via a phase field approximation. Experiments show improved accuracy in both near-field and global SDF compared to existing methods.
We propose a novel variational method to compute a highly accurate global signed distance function (SDF) to a given point cloud. To this end, the jump set of the gradient of the SDF, which coincides with the medial axis of the surface, is explicitly taken into account through a higher-order variational formulation that enforces linear growth along the gradient direction away from this discontinuity set. The eikonal equation and the zero-level set of the SDF are enforced as constraints. To make this variational problem computationally tractable, a phase field approximation of Ambrosio-Tortorelli type is employed. The associated phase field function implicitly describes the medial axis. The method is implemented for surfaces represented by unoriented point clouds using neural network approximations of both the SDF and the phase field. Experiments demonstrate the method's accuracy both in the near field and globally. Quantitative and qualitative comparisons with other approaches show the advantages of the proposed method.