Geodesic Active Contours using Level Set Method with MATLAB Implementation

This text introduces a MATLAB implementation of geodesic active contours using the level set method, designed for extracting multiple object boundaries from images. The algorithm handles noisy images effectively through its robust edge-stopping function and curvature-based regularization, which prevents leakage at weak boundaries. However, the partial differential equation (PDE) solving process involves computationally intensive operations like reinitialization and narrow-band implementations. Several optimization approaches can address these computational demands. Hardware acceleration using GPUs or multicore processors can significantly reduce processing time through parallelized finite difference calculations. Algorithmic improvements may include implementing sparse field methods for efficient narrow-band computation or incorporating additive operator splitting (AOS) schemes for stable PDE solutions. Code optimization techniques like vectorizing convolution operations for Gaussian smoothing and optimizing the curvature calculation function can further enhance performance. The core implementation typically involves key functions such as: - Edge indicator function using image gradient magnitude - Curvature term calculation for contour regularization - Level set evolution equation with time step constraints - Reinitialization procedure to maintain signed distance property This MATLAB-based geodesic active contour framework provides a powerful tool for complex image analysis tasks, enabling precise extraction of structural information from challenging visual data while maintaining topological flexibility through its level set formulation.