The reliability of RANSAC method when estimating the parameters of geometric object

Abstract

The RANSAC (RANdom SAmple Consensus) is often used to identify points belonging to the objects whose shape can be modeled with geometric primitives. These points, called inliers, are of great interest in some applications but often the goal is also to estimate the parameters of geometric shape and their accuracies. The quality of RANSAC results is rarely analysed. The accuracies of estimated parameters are usually calculated based only on the residuals of inliers, selected by RANSAC, from a mathematical model. However, the analysis does not indicate if the right points were selected. The result of RANSAC depends on the random selection of the minimum number of points that uniquely describe a mathematical model; in the case of multiple repetitions of the method, the results are not necessarily the same. This paper presents an analysis of RANSAC reliability based on repeating the selection of points from the point cloud by RANSAC one hundred times. A standard deviation of one hundred parameter values is used to estimate the parameters’ accuracies. An analysis is made for three different examples of geometric objects: a sphere, a cone, and a plane. Finally, we suggest repeating the algorithm several times and checking the consistency of the results to obtain a more reliable estimation of parameters and their accuracies.

Keywords

• RANSAC
• reliability
• point cloud
• geometric object