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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Mathematical methods in medical image processing
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by Sigurd Angenent, Eric Pichon and Allen Tannenbaum PDF
Bull. Amer. Math. Soc. 43 (2006), 365-396 Request permission

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
  • MR Author ID: 26245
  • ORCID: 0000-0003-3515-4539
  • 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.
  • 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.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 43 (2006), 365-396
  • MSC (2000): Primary 92C55, 94A08, 68T45; Secondary 35K55, 35K65
  • DOI: https://doi.org/10.1090/S0273-0979-06-01104-9
  • MathSciNet review: 2223011