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

TL;DR

This paper develops a framework for analyzing the sensitivity of pose estimation neural networks to rotational changes, introducing bounds based on Lipschitz constants and rotation parameterizations, and demonstrates this with a network using exponential coordinates.

Contribution

The paper introduces a sensitivity measure for pose estimation networks, derives bounds based on rotation parameterizations, and constructs a network with provable sensitivity bounds using exponential coordinates.

Findings

Sensitivity bounds can be computed for networks with exponential coordinate parameterization.

Most rotation parameterizations make it difficult to establish provable sensitivity bounds.

A new sensitivity measure related to Lipschitz constants is proposed.

Abstract

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