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 est imation 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 p oints supporting the fit to each extracted model, and to determine the a priori unknown total number of meaningful models in the data. Altho ugh the models are extracted sequentially, the final result is almost independent of the extraction order. This is achieved by further stati stical processing which controls the mutual exchange of inlier data be tween the models. Consequently, sound data classification as well as r obust fitting are guaranteed even in areas where different models inte rsect or touch each other. Apart from the input data and its precision , the framework relies on only one additional control parameter: the c onfidence level on which the various statistical tests for data and mo del classification are carried out. We demonstrate the algorithmic per formance by fitting straight lines in 2D and planes in 3D with applica tions to problems of computer vision and pattern recognition. Syntheti c data is used to show the robustness and accuracy of the scheme. Imag e data and range data are used to illustrate its applicability and rel evance in respect of real-world problems, e.g., in the domain of image feature extraction.