FeatureZ : A General Framework for Feature-Preserving Compression via Pointwise Bounds and Star Classification

Sparse cubical complexes for efficient topology-preservation in image data

Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segmentation, where preservation of topological structures is important. However, despite its general applicability across dimensionality, domains, and target structures, the r...

Minkowski Tensors as a Lightweight and Interpretable Representation for Three-Dimensional Morphology

Quantitative analysis of biological shape is central to understanding how form encodes function. Despite rapid advances in volumetric imaging and segmentation, analysis and of three-dimensional morphology remains challenging due to complex geometries and topologies found in biology. Existing approaches either rely on h...

A structure-preserving diffusion model for point cloud upsampling

Area-Preserving Parameterization: Variational Principle, Gradient Flow, and Discrete Approximation

Area-preserving parameterizations are used in applications where relative surface areas must be preserved. We study this problem through the stretch energy. For orientation-preserving diffeomorphisms between compact Riemannian 2-manifolds of equal total area, we show that the stretch energy is characterized by the vari...

HieFormer: Leveraging hyperbolic geometry to overcome the hierarchical expressiveness limitation of transformers.

3D instance segmentation requires fine-grained geometric discrimination together with an effective representation of the hierarchical organization of real-world objects and scenes. Conventional transformer architectures, however, operate predominantly in Euclidean space, whose polynomial volume growth can be poorly mat...

Heat Field Signatures: From Point Clouds to Smooth Geometry

HFS turns a classical heat field into a practical interface for multiscale geometric analysis in modern point-cloud learning, and introduces the Heat Dimension Spectrum (HDS), a compact summary of multiscale geometric composition.