Medial Axis Aware Learning of Signed Distance Functions
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...
| Authors | Samuel Weidemaier, Christoph Norden-Smoch, Martin Rumpf |
|---|---|
| Primary category | cs.CV |
| Published | 15 April 2026 |
| Last updated at source | 8 June 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.