arXiv:2608.15933v1 Announce Type: cross
Abstract: Implicit surface representations have regained popularity because of their use in machine learning. A common component in optimization is regularizat...
By Tobias Djuren, Markus Worchel, Ugo Finnendahl, Marc Alexa
Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.
The paper introduces a differentiable voxelization technique that computes gradients of volumetric properties, such as winding numbers, with respect to surface mesh parameters. This method allows efficient optimization of triangle meshes using voxel-based volume samples on a regular grid. The authors demonstrate its utility in applications like resolving mesh intersections, designing manufacturable shapes for bandsaw cutting, and creating near-tiling 3D structures.
By Tobias Djuren, Ugo Finnendahl, Markus Worchel, Hendrik Meyer, Marc Alexa
arXiv:2607. 27126v1 Announce Type: new Abstract: Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity.
By Kaifeng Zhang, Kai Ming Ting
arXiv:2607. 01164v1 Announce Type: new Abstract: Recent work has shown that implicit neural representations (INRs) can be trained to effectively compress structured and unstructured volume data, allowing for direct data querying with a reduced memory footprint.
By Landon Dyken, Sharmistha Chakrabarti, Nathan Debardeleben, Steve Petruzza, Qi Wu, Will Usher, Sidharth Kumar
arXiv:2602. 07429v2 Announce Type: replace-cross Abstract: Boundary representation (B-rep) is the industry standard for computer-aided design (CAD).
By Yuanxu Sun, Yuezhou Ma, Haixu Wu, Guanyang Zeng, Muye Chen, Jianmin Wang, Mingsheng Long