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Bulletin of the American Mathematical Society

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Mathematical methods in medical image processing


Authors: Sigurd Angenent, Eric Pichon and Allen Tannenbaum
Journal: Bull. Amer. Math. Soc. 43 (2006), 365-396
MSC (2000): Primary 92C55, 94A08, 68T45; Secondary 35K55, 35K65
Published electronically: April 28, 2006
MathSciNet review: 2223011
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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.


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Additional Information

Sigurd Angenent
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email: angenent@math.wisc.edu

Eric Pichon
Affiliation: Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250
Email: eric@ece.gatech.edu.

Allen Tannenbaum
Affiliation: Departments of Electrical and Computer and Biomedical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250
Email: tannenba@ece.gatech.edu.

DOI: http://dx.doi.org/10.1090/S0273-0979-06-01104-9
Keywords: Medical imaging, artificial vision, smoothing, registration, segmentation
Received by editor(s): June 15, 2005
Received by editor(s) in revised form: September 22, 2005
Published electronically: April 28, 2006
Additional Notes: The authors would like to thank Steven Haker, Ron Kikinis, Guillermo Sapiro, Anthony Yezzi, and Lei Zhu for many helpful conversations on medical imaging and to Bob McElroy for proofreading the final document.
This research was supported by grants from the NSF, NIH (NAC P41 RR-13218 through Brigham and Women’s Hospital), and the Technion, Israel Institute of Technology. This work was done under the auspices of the National Alliance for Medical Image Computing (NAMIC), funded by the National Institutes of Health through the NIH Roadmap for Medical Research, Grant U54 EB005149.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.