6533b836fe1ef96bd12a1cb2
RESEARCH PRODUCT
The “λ-medial axis”
André LieutierFrédéric Chazalsubject
HomotopyMinimum distanceMathematical analysisOpen setComputer Graphics and Computer-Aided DesignCritical point (mathematics)CombinatoricsHausdorff distanceMedial axisModeling and SimulationHausdorff dimensionPhysics::Atomic and Molecular ClustersGeometry and TopologyPhysics::Chemical PhysicsSoftwareMathematicsdescription
Medial axis is known to be unstable for nonsmooth objects. For an open set O, we define the weak feature size, wfs, minimum distance between Oc and the critical points of the function distance to Oc. We introduce the "lambda-medial axis" Mλ of O, a subset of the medial axis of O which captures the homotopy type of O when λ < wfs. We show that, at least for some "regular" values of λ, Mλ remains stable under Hausdorff distance perturbations of Oc.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-07-01 | Graphical Models |