Optimal Consensus set for digital line and plane fitting

Rita Zrour (1) , Yukiko Kenmochi (2) , Hugues Talbot (2) , Lilian Buzer (2) , Yskandar Hamam (2, 3) , Ikuko Shimizu (4) , Akihiro Sugimoto (5)

1 SIC
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 F’SATI - French South African Institute of Technology
4 TUAT - Tokyo University of Agriculture and Technology
5 NII - National Institute of Informatics

This article presents a new method for fitting a digital line or plane to a given set of points in a 2D or 3D image in the presence of noise by maximizing the number of inliers, namely the consensus set. By using a digital model instead of a continuous one, we show that we can generate all possible consensus sets for model fitting. We present a deterministic algorithm that efficiently searches the optimal solution with time complexity O(Nd log N) for dimension d, where d = 2,3, together with space complexity O(N) where N is the number of points.

Mots clés: line fitting; plane fitting; digital geometry; discrete optimization; consensus set

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Géométrie algorithmique [cs.CG]

Rita Zrour, Yukiko Kenmochi, Hugues Talbot, Lilian Buzer, Yskandar Hamam, et al.. Optimal Consensus set for digital line and plane fitting. International Journal of Imaging Systems and Technology, 2011, 21 (1), pp.45-57. ⟨10.1002/ima.20269⟩. ⟨hal-00493415⟩