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International Journal of Biomedical Imaging
Volume 2011, Article ID 516942, 13 pages
Research Article

3D Winding Number: Theory and Application to Medical Imaging

1Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
2Department of Biology, Kaiserslautern University of Technology, 67653 Kaiserslautern, Germany

Received 2 June 2010; Revised 20 September 2010; Accepted 1 November 2010

Academic Editor: Yangbo Ye

Copyright © 2011 Alessandro Becciu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a new formulation, mathematically elegant, to detect critical points of 3D scalar images. It is based on a topological number, which is the generalization to three dimensions of the 2D winding number. We illustrate our method by considering three different biomedical applications, namely, detection and counting of ovarian follicles and neuronal cells and estimation of cardiac motion from tagged MR images. Qualitative and quantitative evaluation emphasizes the reliability of the results.