Level Set Methods

Abstract

The level set method for capturing moving fronts was introduced in 1987 by Osher and Sethian {$[$}401{$]$}. It has proven to be phenomenally successful as a numerical device. For example, as of June 2002, typing in ``Level Set Methods''on Google's search engine gives roughly 2800 responses and the original article has been cited over 530 times (according to web of science). Applications range from capturing multiphase fluid dynamical flows, to graphics, e.g. special effects in Hollywood, to visualization, image processing, control, epitaxial growth, computer vision and include many others. In this chapter we shall give an overview of the numerical technology and of applications in imaging science. These will include surface interpolation, solving PDE's on manifolds, visibility, ray tracing, segmentation (including texture segmentation) and restoration.