We proposed an algorithm for solving Hamilton-Jacobi equation associated to
an optimal trajectory problem for a vehicle moving inside the pre-specified
domain with the speed depending upon the direction of the motion and current
position of the vehicle. The dynamics of the vehicle is defined by an ordinary
differential equation, the right hand of which is given by product of control(a
time dependent fuction) and a function dependent on trajectory and control. At
some unspecified terminal time, the vehicle reaches the boundary of the
pre-specified domain and incurs a terminal cost. We also associate the
traveling cost with a type of integral to the trajectory followed by vehicle.
We are interested in a numerical method for finding a trajectory that minimizes
the sum of the traveling cost and terminal cost. We developed an algorithm
solving the value function for general trajectory optimization problem. Our
algorithm is closely related to the Tsitsiklis's Fast Marching Method and J. A.
Sethian's OUM and SLF-LLL[1-4] and is a generalization of them. On the basis of
these results, We applied our algorithm to the image processing such as
fingerprint verification.

本文提出了一种解决 Hamilton-Jacobi 方程的算法，用于优化车辆在指定区域内行驶的最佳轨迹问题，旨在利用数值方法来找到最小化行驶成本和终端成本的轨迹，并将此算法应用于图像处理领域。