Level Set Method: Theory and Implementation

Level Set Methods are mathematical techniques originally proposed by Sethian and Osher in 1988, which have seen extensive development and application in recent years. These methods find broad utility across multiple domains, particularly in image segmentation applications. For instance, they can be effectively implemented for facial contour segmentation and license plate recognition tasks. The core algorithm operates through curve evolution using partial differential equations, where the zero-level set of a higher-dimensional function represents the moving interface. Implementation typically involves discretizing the Hamilton-Jacobi equation using upwind schemes and incorporating regularization terms for stability. By evolving the level set function through iterative updates, these methods can accurately segment different objects or regions within images, providing superior segmentation results compared to traditional techniques. Beyond image segmentation, Level Set Methods play significant roles in medical image processing, computer vision, and machine learning applications, where they are often implemented with narrow-band methods for computational efficiency and coupled with shape priors for robust performance.