Recent advances of variational model in medical imaging and applications to computer aided surgery

Abstract

In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging: image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.