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. 2006:43:365-396.
doi: 10.1090/s0273-0979-06-01104-9.

MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

Sigurd Angenent  1 , Eric Pichon, Allen Tannenbaum
Affiliations

MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

Sigurd Angenent et al. Bull New Ser Am Math Soc. 2006.

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.

Keywords: Medical imaging; artificial vision; registration; segmentation; smoothing.

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Figures

Figure 3.1
Figure 3.1
X-ray radiography at the end of the 19th century.
Figure 3.2
Figure 3.2
Examples of different image modalities.
Figure 5.1
Figure 5.1
Linear smoothing smears the edges.
Figure 5.2
Figure 5.2
Optimal Warping of Myocardium from Diastolic to Systolic in Cardiac Cycle. These static images become much more vivid when viewed as a short animation. (Available at http://www.bme.gatech.edu/groups/minerva/publications/papers/medicalBAMS2005.html).
Figure 5.3
Figure 5.3
Result of two edge detectors on a heart MRI image.
Figure 5.4
Figure 5.4
A conformal active contour among unstable manifolds.
Figure 5.5
Figure 5.5
Ventricle segmentation in MRI heart image via shrinking conformal active contour.
Figure 5.6
Figure 5.6
Myocardium segmentation in MRI heart image with two merging expanding conformal active contours.
Figure 5.7
Figure 5.7
Cyst segmentation in ultrasound breast image with three merging expanding conformal active contours.
Figure 5.8
Figure 5.8
Bone segmentation in CT image with splitting shrinking conformal active contour.
See this image and copyright information in PMC

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