Implementation and Manipulation of Fast Marching Algorithms in 2D and 3D

This article provides a comprehensive overview of the tool's objectives and implementation methodology. The primary focus is on manipulating the fast marching algorithm in both two-dimensional and three-dimensional spaces. The implementation features a priority queue system for efficient front propagation and incorporates gradient computation for optimal path reconstruction. Key applications include shortest path extraction for scenarios such as road network tracking and tubular structure identification in medical imaging datasets. The algorithm calculates minimal geodesic paths by solving partial differential equations using upwind finite difference schemes. Additional capabilities extend to shape statistics analysis through geodesic distance matrices and mesh processing via geodesic-aware remeshing techniques. The technical discussion covers practical implementation aspects including initialization of distance maps, handling of boundary conditions, and acceleration methods using narrow band approaches. Readers will learn to integrate this tool into their workflows for enhanced efficiency in spatial analysis and computational geometry tasks, with particular emphasis on medical imaging and computer vision applications.