Improving accuracy of geometric parameter estimation using projected score method

A fundamental problem in computer vision (CV) is the estimation of geometric parameters from multiple observations obtained from images; examples of such problems range from ellipse fitting to multi-view structure from motion (SFM). The maximum likelihood (ML) method is widely used to estimate the parameters in such problems, assuming Gaussian noises to be present in the observations, for example, bundle adjustment for SFM. According to the theory of statistics, the ML estimates are nearly optimal for these problems, provided that the variance of the observation noises is sufficiently small. This implies that when noises are not small, more accurate estimates can be derived as compared to the ML estimates. In this study, we propose the application of a method called the projected score method, developed in statistics for computing higher-accuracy estimates, to the CV problems. We describe how it can be customized to solve the CV problems and propose a numerical algorithm to implement the method. We show that the method works effectively for such problems.