Fast ADMM L1 minimization by applying SMW formula and multi-row simultaneous estimation for Light Transport Matrix acquisition*
Fast ADMM L1 minimization by applying SMW formula and multi-row simultaneous estimation for Light Transport Matrix acquisition*
复制标题
通过应用 SMW 公式和多行同时估计进行光传输矩阵采集，实现快速 ADMM L1 最小化*
DOI：
10.1109/robio49542.2019.8961736
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Koichi Hashimoto
中科院分区：
文献类型：
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作者：
Naoya Chiba;Akira Imakura;Koichi Hashimoto
光传输矩阵（LTM）是投影仪-相机系统的光传播的基本表达。该矩阵包括从投影仪传输到相机的光线的所有特征，用于场景重新照明，理解光路和3D测量。特别是，即使场景中包含金属或半透明物体，LTM也可以实现强大的3D测量;因此它已经用于机器人视觉。由于LTM有大量的元素，因此通常通过最小化来估计LTM。利用乘子交替方向法（ADMM）的最小化方法可以减少观测值的数量。此外，一个强大的扩展ADMM的最小化方法称为饱和ADMM，它可以估计在饱和条件下的LTM，也存在。在本文的研究中，我们减少了计算成本的ADMM的最小化，通过应用谢尔曼-莫里森-伍德伯里（SMW）公式。此外，我们提出了“多行同时LTM估计”，这是一种新的方法，以提高计算效率。本文的贡献是提出使用这两种方法来加速LTM估计，并证明我们的方法在理论上减少了计算成本，在实践中减少了计算时间。实验结果表明，我们的方法加速ADMM_1最小化高达4.64倍，饱和ADMM_1最小化高达2.54倍，与原来的方法相比。
The Light Transport Matrix (LTM) is a fundamental expression of the light propagation of the projector-camera system. The matrix includes all the characteristics of light rays transferred from the projector to the camera, and it is used for scene relighting, understanding the light path, and 3D measurement. Especially, LTM enables robust 3D measurement even if the scene includes metallic or semi-transparent objects; thus it is already used for robot vision. The LTM is often estimated by ℓ1minimization because the LTM has a huge number of elements. ℓ1minimization methods, which utilize the Alternating Direction Method of Multipliers (ADMM), can reduce the number of observations. In addition, a powerful extended ADMM ℓ1minimization method named Saturation ADMM, which can estimate the LTM under saturated conditions, also exists. In the study presented in this paper, we reduce the computational cost of ADMM ℓ1minimization by applying the Sherman-Morrison-Woodbury (SMW) formula. Furthermore, we propose "multi-row simultaneous LTM estimation," which is a new method to improve the computational efficiency. The contribution of this paper is to propose the use of these two methods to speed up LTM estimation and demonstrate that our methods reduce the computational cost in theory and the calculation time in practice. Experiments indicate that our method accelerates ADMM ℓ1minimization by up to 4.64 times, and Saturation ADMM ℓ1minimization by up to 2.54 times compared to the original methods.