In the square root velocity framework, the computation of shape space distances and the registration of curves requires solution of a non-convex variational problem. In this paper, we present a new PDE-based method for solving this problem numerically. The method is constructed from numerical approximation of the Hamilton-Jacobi-Bellman equation for the variational problem, and has quadratic complexity and global convergence for the distance estimate. In conjunction, we propose a backtracking scheme for approximating solutions of the registration problem, which additionally can be used to compute shape space geodesics. The methods have linear numerical convergence, and improved efficiency compared previous global solvers.
翻译:在平方根速度框架内,计算形状空间距离和曲线登记要求解决非曲线变异问题。在本文中,我们提出了一个新的基于PDE的数值方法来解决这个问题。该方法根据汉密尔顿-Jacobi-Bellman等方程式的数值近似值来构建,对变异问题,对距离估计具有二次复杂度和全球趋同性。同时,我们提出一个近似登记问题解决办法的回溯跟踪方案,还可以用来计算空间大地测量学的形状。这种方法具有线性数字趋同性,与以前的全球解算器相比,效率也有所提高。