Optimal instantaneous rigid motion estimation insensitive to local minima

A novel method is introduced for optimal estimation of rigid camera motion from instantaneous velocity measurements. The error surface associated with this problem is highly complex and existing algorithms suffer heavily from local minima. Repeated minimization with different random initializations and selection of the minimum-cost solution are a common (albeit ad hoc) procedure to increase the likelihood of finding the global minimum. We instead show that the optimal estimation problem can be transformed into one of arbitrary complexity, which allows for a gradual regularization of the error function. A simple reweighting scheme is presented that smoothly increases the problem complexity at each iteration. We show that the resulting method retains all the desirable properties of optimal algorithms, such as unbiasedness and minimal variance of the parameter estimates, but is substantially more robust to local minima. This robustness comes at the expense of a slightly increased computational complexity.