Abstract: A fast marching algorithm is proposed to solve shape reconstruction problems and the general Eikonal equations. The mesh is dynamically refined according to the surface curvature. Hash table is used to quickly locate neighboring nodes. The causality condition is proven theoretically for first order differential. Experimental results show that the algorithm can improve numerical accuracy, intensify noise immunity and solve shape from shading problems.

Key words: Eikonal Equation, Shape Reconstruction, Fast Marching, Adaptive Mesh

摘要： 针对形状重建及Eikonal方程求解问题，提出一种根据曲面曲率动态地对网格进行细化的快速步进法，证明该方法在一阶差分情形下符合因果律，在实现中利用哈希表对邻接点进行快速定位。实验结果表明，该方法较已有方法计算误差小，对噪声适应力较强，可有效处理从明暗恢复形状问题。

关键词: 快速步进法, 自适应网格, Eikonal方程, 形状重建