Efficient Algorithm for Level Set Method Preserving Distance Function

摘要

The level set method (31) is a popular technique for tracking moving interfaces in several disciplines including computer vision and fluid dynamics. However, despite its high edibility, the original level set method is limited by two important numerical issues. Firstly, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features s.a. the curvature or the contour normal. Secondly, the level set algorithm is slow because the time step is limited by the standard CFL condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods (4, 3) and continuous convex relaxation methods (7, 5, 16) provide powerful alternatives to the level set method for image processing problems because they are fast, accurate and guaranteed to nd the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method.