Optimal Consensus set for nD Fixed Width Annulus Fitting

International audienceThis paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solution(s) within a time complexity O(N n+1 log N) for dimension n, N being the number of points. Our algorithm guarantees optimal solution(s) and has lower complexity than previous known methods

Representation of Imprecise Digital Objects

International audienceIn this paper, we investigate a new framework to handle noisy digital objects. We consider digital closed simple 4-connected curves that are the result of an imperfect digital conversion (scan, picture, etc), and call digital imprecise contours such curves for which an imprecision value is known at each point. This imprecision value stands for the radius of a ball around each point, such that the result of a perfect digitization lies in the union of all the balls. In the first part, we show how to define an imprecise digital object from such an imprecise digital contour. To do so, we define three classes of pixels : inside, outside and uncertain pixels. In the second part of the paper, we build on this definition for a volumetric analysis (as opposed to contour analysis) of imprecise digital objects. From so-called toleranced balls, a filtration of objects, called λ-objects is defined. We show how to define a set of sites to encode this filtration of objects

Digital hyperplane fitting

International audienceThis paper addresses the hyperplane fitting problem of discrete points in any dimension (i.e. in Z d). For that purpose, we consider a digital model of hyperplane, namely digital hyperplane, and present a combinatorial approach to find the optimal solution of the fitting problem. This method consists in computing all possible digital hyperplanes from a set S of n points, then an exhaustive search enables us to find the optimal hyperplane that best fits S. The method has, however, a high complexity of O(n d), and thus can not be applied for big datasets. To overcome this limitation, we propose another method relying on the Delaunay triangulation of S. By not generating and verifying all possible digital hyperplanes but only those from the elements of the triangula-tion, this leads to a lower complexity of O(n d 2 +1). Experiments in 2D, 3D and 4D are shown to illustrate the efficiency of the proposed method

Optimal consensus set for digital line and plane fitting

This paper presents a method for fitting a digital line (resp. plane) to a given set of points in a 2D (resp. 3D) image in the presence of outliers. One of the most widely used methods is Random Sample Consensus (RANSAC). However it is also known that RANSAC has a drawback: as maximum iteration number must be set, the solution may not be optimal. To overcome this problem, we present a new method that uses a digital geometric model for lines and planes in a discrete space. Such a digital model allows us to efficiently examine all possible consensus sets, which guarantees the solution optimality and exactness. 1