论文标题
量子Levenberg-用于捆绑调整的优化算法
Quantum Levenberg--Marquardt Algorithm for optimization in Bundle Adjustment
论文作者
论文摘要
在本文中，我们开发了一种量子优化算法，并使用它来解决模拟量子计算机的捆绑调整问题。束调整是优化相机姿势和传感器属性的过程，以最好地重建三维结构和查看参数。通常，使用Levenberg--Marquardt算法的某种实现来解决此问题。在这种情况下，我们实现了一种量子算法来求解正常方程式的线性系统，该方程计算Levenberg-marquardt中的优化步骤。此过程是束调整算法复杂性中的当前瓶颈。提出的量子算法大大降低了相对于点数的复杂性。 我们研究了9种玩具模型的配置，用于捆绑调整，限制为10分和2个相机。通过使用稀疏的Levenberg-Marquardt算法和我们的量子实现来解决此优化问题。提出了所得的解决方案，显示了收敛速度的提高，以及对理论速度提高的分析以及成功运行算法在当前量子计算机上的概率。 提出的量子算法是使用量子计算算法的开创性实现，以解决计算机视觉中的复杂优化问题，尤其是束调整，这提供了几种进一步研究的途径。
In this paper we develop a quantum optimization algorithm and use it to solve the bundle adjustment problem with a simulated quantum computer. Bundle adjustment is the process of optimizing camera poses and sensor properties to best reconstruct the three-dimensional structure and viewing parameters. This problem is often solved using some implementation of the Levenberg--Marquardt algorithm. In this case we implement a quantum algorithm for solving the linear system of normal equations that calculates the optimization step in Levenberg--Marquardt. This procedure is the current bottleneck in the algorithmic complexity of bundle adjustment. The proposed quantum algorithm dramatically reduces the complexity of this operation with respect to the number of points. We investigate 9 configurations of a toy-model for bundle adjustment, limited to 10 points and 2 cameras. This optimization problem is solved both by using the sparse Levenberg-Marquardt algorithm and our quantum implementation. The resulting solutions are presented, showing an improved rate of convergence, together with an analysis of the theoretical speed up and the probability of running the algorithm successfully on a current quantum computer. The presented quantum algorithm is a seminal implementation of using quantum computing algorithms in order to solve complex optimization problems in computer vision, in particular bundle adjustment, which offers several avenues of further investigations.
