3D winding number: theory and application to medical imaging

Authors:
Alessandro Becciu;Andrea Fuster;Mark Pottek;Bart van den Heuvel;Bart ter Haar Romeny;Hans van Assen
Affiliations:
Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Biology, Kaiserslautern University of Technology, Kaiserslautern, Germany;Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
Journal of Biomedical Imaging - Special issue on modern mathematics in biomedical imaging
Year:
2011

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Abstract

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 ourmethod 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.