arXiv Computer Vision
Sep 3

Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting

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.

By Romy Williamson, Niloy Mitra
arXiv Machine Learning
Aug 31

Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification

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.

By Alexandre L. M. Levada