Camera-Pose Estimation via Projective Newton Optimization on the Manifold
Camera-Pose Estimation via Projective Newton Optimization on the Manifold
复制标题
DOI：
10.1109/tip.2011.2177845
复制
发表时间：
2012-04
影响因子：
10.6
通讯作者：
M. Sarkis;K. Diepold
中科院分区：
文献类型：
--
作者：
M. Sarkis;K. Diepold
运动摄像机的姿态确定是计算机视觉中的一项重要任务。本文提出了一种基于流形的投影牛顿算法来改进摄像机的姿态估计。主要思想是利用三维刚体运动是由特殊的欧几里得群描述的这一事实，欧几里得群是一个黎曼流形。后者具有由相应的李代数定义的切空间。这使我们能够在流形的切空间上的投影牛顿格式的每次迭代中计算优化方向，即梯度和Hessian。然后，通过在流形本身上投影回变量来更新运动。我们还推导了另一种采用同胚参数化的特殊欧几里得群算法。我们在几个模拟和真实图像数据集上测试了该算法。与标准牛顿最小化方案相比，我们现在能够获得Hessian的完整数值公式，计算复杂度降低了60%。与Levenberg-Marquardt相比，得到的结果更精确，但复杂度相当。
Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.