Statistical Optimization for Geometric Estimation: Minimization vs. Non-minimization

We overview techniques for optimal geometric estimation from noisy observations for computer vision applications. We first describe techniques based on minimization of a given cost function: least squares (LS), maximum likelihood (ML), and Sampson error minimization. We then summarize techniques not based on minimization: one solves a given matrix equation. Different choices of the matrices in it result in different methods: LS, iterative reweight, the Taubin method, renormalization, HyperLS, and hyper-renormalization. Doing statistical analysis and conducting numerical examples, we conclude that hyper-renormalization is the best method in terms of accuracy and efficiency.