具有非线性测量方程的$\operatorname{SE}_3$二阶最小能量滤波
Second Order Minimum Energy Filtering on $\operatorname{SE}_3$ with Nonlinear Measurement Equations
摘要：
准确的摄像机运动估计是许多计算机视觉算法的基本构建块。为了提高鲁棒性，通常通过使用随机滤波器向前传播运动信息来假设平移和旋转相机速度的时间一致性。然而，经典的随机滤波器，使用线性逼近的非线性观测器模型和非线性结构的基本李群$\operatorname{SE}_3$，并近似未知的后验分布。在本文中，我们采用了一个非线性测量模型的摄像机运动估计问题，结合了多个观测方程。我们解决了潜在的过滤问题，使用一种新的最小能量滤波器的$\operatorname{SE}_3$，并给出明确的表达式的最佳状态变量。在具有挑战性的KITTI基准测试上的实验表明，虽然只采用了一个简单的运动模型，但我们的方法提高了旋转速度估计，并且在其他方面与最先进的方法不相上下。
英文摘要：
Accurate camera motion estimation is a fundamental building block for many Computer Vision algorithms. For improved robustness, temporal consistency of translational and rotational camera velocity is often assumed by propagating motion information forward using stochastic filters. Classical stochastic filters, however, use linear approximations for the non-linear observer model and for the non-linear structure of the underlying Lie Group $\operatorname{SE}_3$ and have to approximate the unknown posteriori distribution. In this paper we employ a non-linear measurement model for the camera motion estimation problem that incorporates multiple observation equations. We solve the underlying filtering problem using a novel Minimum Energy Filter on $\operatorname{SE}_3$ and give explicit expressions for the optimal state variables. Experiments on the challenging KITTI benchmark show that, although a simple motion model is only employed, our approach improves rotational velocity estimation and otherwise is on par with the state-of-the-art.
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