This paper introduces two new methods of registering 2D point sets over rigid transformations when the registration error is based on a robust loss function. In contrast to previous work, our methods are guaranteed to compute the optimal transformation, and at the same time, the worst-case running times are bounded by a low-degree polynomial in the number of correspondences. In practical terms, this means that there is no need to resort to ad-hoc procedures such as random sampling or local descent methods that cannot guarantee the quality of their solutions.
We have tested the methods in several different settings, in particular, a thorough evaluation on two benchmarks of microscopic images used for histologic analysis of prostate cancer has been performed. Compared to the state-of-the-art, our results show that the methods are both tractable and reliable despite the presence of a significant amount of outliers.