Parametric model fitting: from inlier characterization to outlier detection

Parametric models play an important role in broad areas of science and technology. This paper presents a novel framework for the fitting of multiple parametric models. It comprises of a module for parameter estimation based on a solution for generalized least squares problems and of a procedure for error propagation, which takes both the geometric arrangement of the input data points and their precision into account. The results from error propagation are used to complement each model parameter with a precision estimate, to assign an inlier set of data points supporting the fit to each extracted model, and to determine the a priori unknown total number of meaningful models in the data. Although the models are extracted sequentially, the final result is almost independent of the extraction order. This is achieved by further statistical processing which controls the mutual exchange of inlier data between the models. Consequently, sound data classification as well as robust fitting are guaranteed even in areas where different models intersect or touch each other. Apart from the input data and its precision, the framework relies on only one additional control parameter: the confidence level on which the various statistical tests for data and model classification are carried out. We demonstrate the algorithmic performance by fitting straight lines in: 2D and planes in 3D with applications to problems of computer vision and pattern recognition. Synthetic data is used to show the robustness and accuracy of the scheme. Image data and range data are used to illustrate its applicability and relevance in respect of real-world problems, e.g., in the domain of image feature extraction.