MATLAB Toolbox for Classical Level Set Methods

The level set method is a powerful numerical technique widely applied in image segmentation, interface tracking, and geometric evolution problems. Its core concept involves implicitly representing curves or surfaces (such as zero-level set functions) to avoid topological constraints associated with parameterization. The MATLAB implementation typically utilizes signed distance functions (SDFs) to track evolving interfaces through partial differential equations (PDEs).

The MATLAB toolbox provides convenient implementations for these computations, encapsulating the following key functionalities: Initialization Processing: Supports generating signed distance functions (SDFs) from binary masks or explicit coordinates as initial conditions for level set evolution. The code typically involves Euclidean distance transformations and sign assignments to create proper SDF initializations. PDE Solving: Built-in classical re-initialization algorithms and mean curvature flow schemes ensure numerical stability during evolution. The implementation often uses finite difference methods with upwind schemes for gradient calculations. Speed Term Extension: Allows user-defined image-driven forces (such as edge-based gradient information or regional statistics) and external force terms (like dilation/contraction coefficients). Custom speed functions can be integrated through callback mechanisms in the toolbox. Visualization Tools: Real-time display of contour evolution for level set functions facilitates debugging and result analysis. The toolbox typically includes functions for plotting intermediate results using contour or isosurface visualizations.

When using such toolboxes, two critical considerations are necessary: First, time step selection must satisfy the CFL condition to ensure convergence, which is typically handled through adaptive time-stepping algorithms. Second, for specific applications (like medical image segmentation), weighting parameters in speed terms may require adjustment through empirical testing or automated parameter optimization techniques.