Level set and fast marching methods in image processing and computer vision

Abstract

Level set methods have been used in a variety of settings for problems in computer vision and image processing. A related numerical methodology, known as marching has been developed to solve static Hamilton-Jacobi equations extremely quickly; the techniques rely on conversion to a static problem, and are based on a marriage between narrow band techniques for level set methods and fast sorting algorithms. We show the application of these techniques to a collection of problems, including image denoising and enhancement schemes based on curvature-controlled diffusion with automatic stopping and hierarchical scales, extremely fast shape-from-shading schemes, and shape recovery in medical imaging. Level set methods have also been applied to problems in image denoising and enhancement through curvature-controlled diffusion schemes. An extension of these techniques, known as fast marching methods, has been developed to solve static Hamilton-Jacobi equations which arise in aspects of computer vision. We discuss advances in both of these techniques for such problems.