中文摘要：

在这份报纸，我们在医药图象处理考察一些数学模型。由于在当模特儿和计算的优势，变化方法被证明了是强大的技术，它在过去的二十年极其流行、戏剧性地改进。一方面，许多模型被建议了为将近各种应用。在另一方面，很多模型能全球性被优化，也，许多计算工具被介绍了。在变化框架下面，我们在医药成像集中于二个基本问题：图象恢复和分割，它是为有点特定的任务的核心部件。为图象恢复，我们在添加剂和趋于增加的噪音上讨论一些模型。为图象分割，我们在两个上考察一些模型整个图象分割和特定的目标描述，与以后是，在计算机的关键步帮助了外科。另外，我们肝描述上的现在的一些模型并且把他们的应用给生活施主肝移植。

英文摘要：

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.