Adaptive Interpolatory Curve Subdivision with Learned Local Angles
Read the original on arXiv Computer Vision →The Flow has not summarised this story yet — read it at arXiv Computer Vision.
The Flow has not summarised this story yet — read it at arXiv Computer Vision.
arXiv:2509. 03758v5 Announce Type: replace Abstract: We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations.
Blended Chart Surfaces present a compact, network‑free, explicit surface representation that is smooth by construction and anchored to user‑provided topology. The method jointly optimizes polynomial maps at proxy mesh vertices to fit an implicit target shape, then fuses neighboring maps with a smooth one‑ring coordinate blending scheme, decoupling coarse geometry from fine details. The resulting surface is globally smooth, fully differentiable, and equivariant to rigid motions and scaling, enabling reliable access to differential quantities and surface energies while avoiding seam artifacts common in other explicit neural maps.
arXiv:2606. 18759v1 Announce Type: cross Abstract: The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically.
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN) is a geometry-driven framework that adapts the spatial support of each neighborhood based on local geometric complexity. It estimates intrinsic dimensionality with TwoNN, builds an intrinsic representation via PCA, and uses a shape-operator-based estimate of local mean curvature to shrink the radius in highly curved regions while keeping a broader support in flatter areas. Experiments on over 70 OpenML datasets show that CARSANN consistently outperforms standard k‑NN and rivals other adaptive nearest‑neighbor methods, achieving a mean balanced accuracy increase from 0.6506 to 0.7528 and statistically significant improvements on most datasets.
Mesh subdivision is a fundamental operation for converting coarse, editable meshes into high-resolution surfaces, with broad applications in digital asset creation. Classical rule-based schemes rely on fixed local refinement rules and often produce over-smoothed surfaces.
arXiv:2606. 00139v1 Announce Type: cross Abstract: Curvature-penalized geodesic models have proven their effectiveness in image segmentation by computing globally optimal curves.