arXiv:2604.16512v2 Announce Type: replace-cross Abstract: 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 tr
This paper represents continued academic advancement in the foundational techniques for 3D reconstruction and understanding, crucial for robotics and simulation.
Improved methods for generating Signed Distance Functions (SDFs) can lead to more accurate 3D models from point clouds, benefiting areas like digital twins, medical imaging, and robotics perception.
The proposed variational method for SDF computation offers a more accurate global representation, potentially enhancing the precision and efficiency of 3D environmental mapping.
- · Robotics researchers
- · Computer graphics developers
- · Medical imaging
More robust and detailed 3D environmental representations become possible.
Advanced SDFs can improve simulation fidelity and the capabilities of autonomous systems.
These foundational improvements contribute to the long-term feasibility and sophistication of areas like humanoid robotics and digital manufacturing.
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