Statistical Optimization for Geometric Fitting: Theoretical Accuracy Bound and High Order Error Analysis

A rigorous accuracy analysis is given to various techniques for estimating parameters of geometric models from noisy data. First, it is pointed out that parameter estimation for vision applications is very different in nature from traditional statistical analysis and hence a different mathematical framework is necessary. After a general framework is formulated, typical numerical techniques are selected, and their accuracy is evaluated up to high order terms. As a byproduct, our analysis leads to a “hyperaccurate” method that outperforms existing methods.