We summarize techniques for optimal geometric estimation from noisy observations for computer
vision applications. We first discuss the interpretation of optimality and point out that geometric
estimation is different from the standard statistical estimation. We also describe our noise
modeling and a theoretical accuracy limit called the KCR lower bound. Then, we formulate estimation
techniques based on minimization of a given cost function: least squares (LS), maximum
likelihood (ML), which includes reprojection error minimization as a special case, and Sampson
error minimization. We describe bundle adjustment and the FNS scheme for numerically solving
them and the hyperaccurate correction that improves the accuracy of ML. Next, we formulate
estimation techniques not based on minimization of any cost function: iterative reweight, renormalization,
and hyper-renormalization. Finally, we show numerical examples to demonstrate that
hyper-renormalization has higher accuracy than ML, which has widely been regarded as the most
accurate method of all. We conclude that hyper-renormalization is robust to noise and currently is
the best method
