Abstract. 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.