Multiphase Object Detection and Image Segmentation

Abstract

This chapter presents a class of techniques for object detection and image segmentation, using variational models formulated in a level set approach. We consider in particular Mumford and Shah like energies, whose minimizers are in the space of special functions of bounded variation. For such functions, all points are of two types: points where the functions have an approximate gradient, and points of discontinuities along curves or edges. The set of discontinuities is represented implicitly, using the level set method. Minimizing these energies in a level set formulation, yields coupled curve evolution and diffusion equations, which can be used for object detection and image segmentation. Finally, the proposed methods are validated by various numerical results in two dimensions.