Optimization techniques for geometric estimation: Beyond minimization

Abstract

We overview techniques for optimal geometric estimation from noisy observations for computer vision applications. We first describe estimation techniques based on minimization of given cost functions: least squares (LS), maximum likelihood (ML), which includes reprojection error minimization (Gold Standard) as a special case, and Sampson error minimization. We then formulate estimation techniques not based on minimization of any cost function: iterative reweight, renormalization, and hyper-renormalization. Showing numerical examples, we conclude that hyper-renormalization is robust to noise and currently is the best method. © 2012 Springer-Verlag Berlin Heidelberg.