Angenent Sigurd, Pichon Eric, Tannenbaum Allen
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706,
Bull New Ser Am Math Soc. 2006;43:365-396. doi: 10.1090/s0273-0979-06-01104-9.
In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation.
在本文中，我们描述了医学成像中的一些核心数学问题。由于更好的硬件和软件，该领域一直在经历快速变革。许多软件基于新颖的方法，这些方法将几何偏微分方程与标准信号/图像处理技术以及促进人机交互的计算机图形学结合起来。作为这项工作的一部分，研究人员一直试图将生物医学工程原理建立在严格的数学基础上，以开发可集成到完整治疗输送系统中的软件方法。这些系统支持更有效地进行许多图像引导的程序，如放射治疗、活检和微创手术。我们将展示数学如何影响该领域的一些主要问题，包括图像增强、配准和分割。
