论文标题
关于姿势估计神经网络的敏感性：旋转参数化，Lipschitz常数和可证明的边界
On the sensitivity of pose estimation neural networks: rotation parameterizations, Lipschitz constants, and provable bounds
论文作者
论文摘要
在本文中，我们应完成确定姿势估计神经网络灵敏度界限的任务。此任务特别具有挑战性，因为它需要表征3D旋转的灵敏度。我们开发了一种灵敏度度量，该度量描述了网络输出的最大旋转变化相对于其输入的变化。我们表明，这种度量是Lipschitz常数的一种类型，并且它受网络欧几里得Lipschitz常数的乘积和旋转参数化的内在特性的限制，我们称之为“距离比率常数”。我们得出了几个旋转参数化的距离比率常数，然后讨论为什么大多数参数化的结构使得难以构建具有可证明灵敏度界限的姿势估计网络。但是，我们表明，可以使用无约束的指数坐标来计算网络的灵敏度界限。然后，我们构建和训练这样的网络并计算其灵敏度界限。
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.
