Level Set Methods and Their Applications in Image Science

In this article, we discuss the question “What Level Set Methods can do for image science”. We examine the scope of these techniques in image science, in particular in image segmentation, and introduce some relevant level set techniques that are potentially useful for this class of applications. We will show that image science demands multi-disciplinary knowledge and flexible but still robust methods. That is why the Level Set Method has become a thriving technique in this field. We begin by reviewing some typical PDE based applications in image processing. In typical PDE methods, images are assumed to be continuous functions sampled on a grid. We will show that these methods all share a common feature, which is the emphasis on processing the level lines of the underlying image. The importance of level lines has been known for some time. See e.g., [2]. This feature places our slightly general definition of the level set method for image science in context. In section two, we describe the building blocks of a typical level set method in the continuum setting. Each important task that one needs to do is formulated as the solution to certain PDEs. Then, in section three, we quickly describe the finite difference methods developed to construct approximate solutions to these PDEs. In section four, we discuss the Chan-Vese segmentation algorithm and two new fast implementation methods. Finally, in section five, we describe some new techniques developed in the level set community as our prospectus for the future.