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In this paper, we approach the task of determining sensitivity bounds forpose estimation neural networks. This task is particularly challenging as itrequires characterizing the sensitivity of 3D rotations. We develop asensitivity measure that describes the maximum rotational change in a network'soutput with respect to a Euclidean change in its input. We show that thismeasure is a type of Lipschitz constant, and that it is bounded by the productof a network's Euclidean Lipschitz constant and an intrinsic property of arotation parameterization which we call the "distance ratio constant". Wederive the distance ratio constant for several rotation parameterizations, andthen discuss why the structure of most of these parameterizations makes itdifficult to construct a pose estimation network with provable sensitivitybounds. However, we show that sensitivity bounds can be computed for networkswhich parameterize rotation using unconstrained exponential coordinates. Wethen construct and train such a network and compute sensitivity bounds for it.

On the sensitivity of pose estimation neural networks: rotation parameterizations, Lipschitz constants, and provable bounds