Nonparametric Estimation of Multiple Structures with Outliers

Common problem encountered in the analysis of dynamic scene is the problem of simultaneous estimation of the number of models and their parameters. This problem becomes difficult as the measurement noise in the data increases and the data are further corrupted by outliers. This is especially the case in a variety of motion estimation problems, where the displacement between the views is large and the process of establishing correspondences is difficult. In this paper we propose a novel nonparametric sampling based method for estimating the number of models and their parameters. The main novelty of the proposed method lies in the analysis of the distribution of residuals of individual data points with respect to the set of hypotheses, generated by a RANSAC-like sampling process. We will show that the modes of the residual distributions directly reveal the presence of multiple models and facilitate the recovery of the individual models, without making any assumptions about the distribution of the outliers or the noise process. The proposed approach is capable of handling data with a large fraction of outliers. Experiments with both synthetic data and image pairs related by different motion models are presented to demonstrate the effectiveness of the proposed approach.