Voronoi-based geometry estimator for 3D digital surfaces

Louis Cuel (1) , Jacques-Olivier Lachaud (1) , Boris Thibert (2)

1 LAMA - Laboratoire de Mathématiques
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

We propose a robust estimator of geometric quantities such as normals, curvature directions and sharp features for 3D digital surfaces. This estimator only depends on the digitisation gridstep and is defined using a digital version of the Voronoi Covariance Measure, which exploits the robust geometric information contained in the Voronoi cells. It has been proved that the Voronoi Covariance Measure is resilient to Hausdorff noise. Our main theorem explicits the conditions under which this estimator is multigrid convergent for digital data. Moreover, we determine what are the parameters which maximise the convergence speed of this estimator, when the normal vector is sought. Numerical experiments show that the digital VCM estimator reliably estimates normals, curvature directions and sharp features of 3D noisy digital shapes.

Mots clés: DigitalGeometrie; normal estimation; multigrid convergence; curvature

Domaines: Mathématique discrète [cs.DM]

Louis Cuel, Jacques-Olivier Lachaud, Boris Thibert. Voronoi-based geometry estimator for 3D digital surfaces. [Research Report] LJK. 2014. ⟨hal-00990169⟩