MATLAB Toolbox for Fast Marching Algorithm in Level Set Methods

The level set method is a powerful mathematical tool for handling interface evolution problems, and the Fast Marching algorithm serves as one of its core numerical solutions with mature toolbox implementations available in MATLAB. These toolboxes typically contain the following key functional modules: Initialization and Distance Function Computation The toolbox provides multiple methods to initialize the level set function, including signed distance function generation based on binary images. Users can quickly convert segmentation targets or geometric shapes into initial conditions suitable for Fast Marching algorithm processing. Implementation typically involves functions like bwdist() for distance transform and subfunctions for sign assignment. Customizable Speed Field Support for user-defined propagation speed functions, which constitute the core parameter of the Fast Marching algorithm. The toolbox may include common speed models (such as constant speed, gradient-dependent speed, etc.) while allowing custom logic injection through function handles. Code implementation often involves creating speed functions that accept coordinates and return propagation values. Efficient Narrow Band Implementation Optimized computation using heap data structures, updating only the narrow band region near the interface rather than the entire grid, significantly improving computational efficiency. Some toolboxes provide visualization capabilities for the narrow band evolution process. The algorithm typically maintains a priority queue for efficient front propagation. Multi-Dimensional Problem Support Not only applicable to 2D image segmentation but also capable of handling 3D volume data or higher-dimensional level set evolution problems, which is crucial for applications like medical image analysis. The code structure usually uses ndgrid or meshgrid functions to handle different dimensions consistently. Post-processing and Visualization Includes tools for isosurface extraction and evolution animation generation to help users intuitively understand algorithm results. Some advanced toolboxes also integrate regularization functions like curvature flow to improve result smoothness. Visualization may involve isosurface() and patch() functions for 3D rendering. These toolboxes are commonly applied in image segmentation, computational geometry, and path planning domains. Users should balance grid resolution and speed function design—overly coarse grids may lead to accuracy loss, while complex speed functions might present numerical stability challenges. The implementation often requires careful tuning of time steps and convergence criteria for optimal performance.