论文标题
有效的平面束调整算法
An Efficient Planar Bundle Adjustment Algorithm
论文作者
论文摘要
本文使用点对平面成本为最小二乘问题提出了一种有效的算法，该算法旨在共同优化3D重建的深度传感器姿势和平面参数。由于此问题与视觉重建中的原始捆绑捆绑调整（BA）之间的相似性，因此我们称此最小二乘问题\ textbf {平面束调整}（PBA）。由于飞机在人造环境中存在普遍存在，因此它们通常用作各种深度传感器的猛击算法中的地标。 PBA对于减少漂移和提高地图的质量很重要。但是，直接在视觉重建中采用良好的BA框架将导致PBA的效率非常低。这是因为一个3D点在相机姿势上只有一个观察结果。相比之下，深度传感器一次可以在平面中记录数百个点，即使在一个小规模的空间中，也会导致非常大的非线性最小二乘问题。幸运的是，我们发现存在PBA问题的特殊结构。我们引入了减少的Jacobian矩阵和降低的残留载体，并证明它们可以替代普遍采用的Levenberg-Marquardt（LM）算法中原始的Jacobian矩阵和残留载体。这大大降低了计算成本。此外，当平面与3D重建的其他功能结合在一起时，减少的Jacobian矩阵和残留矢量也可以替换从平面中得出的相应零件。我们的实验结果验证了使用传统的BA框架与解决方案相比，我们的算法可以显着减少计算时间。此外，与使用平面至平面成本相比，我们的算法更快，更准确，对初始化错误更强
This paper presents an efficient algorithm for the least-squares problem using the point-to-plane cost, which aims to jointly optimize depth sensor poses and plane parameters for 3D reconstruction. We call this least-squares problem \textbf{Planar Bundle Adjustment} (PBA), due to the similarity between this problem and the original Bundle Adjustment (BA) in visual reconstruction. As planes ubiquitously exist in the man-made environment, they are generally used as landmarks in SLAM algorithms for various depth sensors. PBA is important to reduce drift and improve the quality of the map. However, directly adopting the well-established BA framework in visual reconstruction will result in a very inefficient solution for PBA. This is because a 3D point only has one observation at a camera pose. In contrast, a depth sensor can record hundreds of points in a plane at a time, which results in a very large nonlinear least-squares problem even for a small-scale space. Fortunately, we find that there exist a special structure of the PBA problem. We introduce a reduced Jacobian matrix and a reduced residual vector, and prove that they can replace the original Jacobian matrix and residual vector in the generally adopted Levenberg-Marquardt (LM) algorithm. This significantly reduces the computational cost. Besides, when planes are combined with other features for 3D reconstruction, the reduced Jacobian matrix and residual vector can also replace the corresponding parts derived from planes. Our experimental results verify that our algorithm can significantly reduce the computational time compared to the solution using the traditional BA framework. Besides, our algorithm is faster, more accuracy, and more robust to initialization errors compared to the start-of-the-art solution using the plane-to-plane cost
