The paper introduces VAD, a lightweight, network‑free method for computing Unsigned Distance Fields (UDFs) from unoriented point clouds. It assigns bi‑directional normals using two Voronoi‑based criteria, diffuses these normals to approximate a UDF gradient field, and then integrates to recover the final UDF. Experiments show VAD handles watertight, open, non‑manifold, and non‑orientable geometries efficiently and stably.
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...
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.
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.
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.
arXiv:2602. 07429v2 Announce Type: replace-cross Abstract: Boundary representation (B-rep) is the industry standard for computer-aided design (CAD).
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity. Expected Persistence Diagram (EPD) has been developed to reduce the time cost by studying the topology of multiple subsets of a point cloud and it serves as a distribution of topological features.
Implicit Neural Representations (INRs) have become the standard for continuous 2D shape modeling, but they suffer from black-box uneditability, vulnerability to noise, and high parameter counts that severely hinder deployment on edge devices. We introduce Fluid-SDF, a highly compressed, differentiable Constructive Solid Geometry (CSG) framework that models shapes using explicit geometric primitives blended via a smooth minimum function.
TriFlow introduces a generative method for creating compact 3D meshes with artist‑like triangle topology directly from input geometry such as signed distance fields. It represents mesh topology as a nearest‑vertex vector field (NVF) over the surface, trains a latent flow‑matching model to synthesize this field, and then clusters surface regions to guide a constrained quadric error metric simplification. The resulting meshes closely match the input geometry while exhibiting structured, artist‑like connectivity, achieving 90% lower Chamfer Distance and an 8× speedup over state‑of‑the‑art learning‑based approaches.
arXiv:2602. 10099v2 Announce Type: replace Abstract: Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis.
3D Gaussian Splatting (3DGS) has recently enabled real-time novel view synthesis with impressive quality. However, it struggles to recover accurate surfaces under limited viewpoints and due to the inherent irregularity of Gaussian primitives.