Topological Data Analysis (TDA) is a recent and fast growing field providing a set of new
topological and geometric tools to infer relevant features for possibly complex data. This …

Geometric and topological inference deals with the retrieval of information about a geometric
object using only a finite set of possibly noisy sample points. It has connections to manifold …

Data often comes in the form of a point cloud sampled from an unknown compact subset of
Euclidean space. The general goal of geometric inference is then to recover geometric and …

We present an efficient and robust method for extracting curvature information, sharp
features, and normal directions of a piecewise smooth surface from its point cloud sampling …

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis.
Even though PH has been used in many different types of applications, the reasons behind …

CGALmesh is the mesh generation software package of the Computational Geometry
Algorithm Library (CGAL). It generates isotropic simplicial meshes—surface triangular …

The estimation of differential quantities on oriented point cloud is a classical step for many
geometry processing tasks in computer graphics and vision. Even if many solutions exist to …

Motivated by a broad range of potential applications in topological and geometric inference,
we introduce a weighted version of the k-nearest neighbor density estimate. Various …

We show that geometric inference of a point cloud can be calculated by examining its kernel
density estimate with a Gaussian kernel. This allows one to consider kernel density …

The convexity of a set can be generalized to the two weaker notions of positive reach and r-
convexity; both describe the regularity of a set's boundary. For any compact subset of R d …