4 papers
Continuity of the normal cycle with respect to topologies
David Cohen-Steiner, Antoine Commaret
We show that the generalized curvatures and more specifically the normal cycle of a compact subset of are continuous under weak notions of convergence, assuming an a…
Modeling high dimensional point clouds with the spherical cluster model
Frédéric Cazals, Antoine Commaret, Louis Goldenberg
A parametric cluster model is a statistical model providing geometric insights onto the points defining a cluster. The {\em spherical cluster model} (SC) approximates a finite poin…
Persistent Intrinsic Volumes
David Cohen-Steiner, Antoine Commaret
We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset of from a set that is close in the Hausdorff dist…
Generalized Morse theory for tubular neighborhoods
Antoine Commaret
We define a notion of Morse function and establish Morse theory-like theorems over offsets of any compact set in a Euclidean space at regular values of their distance function. Usi…