Optimal consensus set for digital plane fitting

Rita Zrour, Yukiko Kenmochi, Hugues Talbot, Lilian Buzer, Yskandar Hamam, Ikuko Shimizu, Akihiro Sugimoto

Abstract: This paper presents a method for fitting a digital plane to a given set of points in a 3D image in the presence of outliers. We present a new method that uses a digital plane model rather than the conventional continuous model. We show that such a digital model allows us to efficiently examine all possible consensus sets and to guarantee the solution optimality and exactness. Our algorithm has a time complexity O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> log N) together with a space complexity O(N) where N is the number of points.