  Outlier-robust estimation is a fundamental problem and has been extensively
investigated by statisticians and practitioners. The last few years have seen a
convergence across research fields towards "algorithmic robust statistics",
which focuses on developing tractable outlier-robust techniques for
high-dimensional estimation problems. Despite this convergence, research
efforts across fields have been mostly disconnected from one another. This
monograph bridges recent work on certifiable outlier-robust estimation for
geometric perception in robotics and computer vision with parallel work in
robust statistics. In particular, we adapt and extend recent results on robust
linear regression (applicable to the low-outlier regime with << 50% outliers)
and list-decodable regression (applicable to the high-outlier regime with >>
50% outliers) to the setup commonly found in robotics and vision, where (i)
variables (e.g., rotations, poses) belong to a non-convex domain, (ii)
measurements are vector-valued, and (iii) the number of outliers is not known a
priori. The emphasis here is on performance guarantees: rather than proposing
radically new algorithms, we provide conditions on the input measurements under
which modern estimation algorithms (possibly after small modifications) are
guaranteed to recover an estimate close to the ground truth in the presence of
outliers. These conditions are what we call an "estimation contract". Besides
the proposed extensions of existing results, we believe the main contributions
of this monograph are (i) to unify parallel research lines by pointing out
commonalities and differences, (ii) to introduce advanced material (e.g.,
sum-of-squares proofs) in an accessible and self-contained presentation for the
practitioner, and (iii) to point out a few immediate opportunities and open
questions in outlier-robust geometric perception.
