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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 278479, 16 pages
Research Article

Fitting Continuous Parametric Surfaces to Frontiers Delimiting Physiologic Structures

1L’Institut de Rythmologie et Modélisation Cardiaque, Université de Bordeaux, 166 Cours de l’Argonne, 33000 Bordeaux, France
2Department of Bioengineering, Binghamton University, P.O. Box 6000, Binghamton, NY 13902, USA
3Department of Pharmacology, SUNY Upstate Medical University, 3135 Weiskotten Hall, 750 East Adams Street, Syracuse, NY 13210, USA

Received 7 October 2013; Revised 16 January 2014; Accepted 23 January 2014; Published 24 March 2014

Academic Editor: Linwei Wang

Copyright © 2014 Jason D. Bayer 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 present a technique to fit continuous parametric surfaces to scattered geometric data points forming frontiers delimiting physiologic structures in segmented images. Such mathematical representation is interesting because it facilitates a large number of operations in modeling. While the fitting of continuous parametric curves to scattered geometric data points is quite trivial, the fitting of continuous parametric surfaces is not. The difficulty comes from the fact that each scattered data point should be assigned a unique parametric coordinate, and the fit is quite sensitive to their distribution on the parametric plane. We present a new approach where a polygonal (quadrilateral or triangular) surface is extracted from the segmented image. This surface is subsequently projected onto a parametric plane in a manner to ensure a one-to-one mapping. The resulting polygonal mesh is then regularized for area and edge length. Finally, from this point, surface fitting is relatively trivial. The novelty of our approach lies in the regularization of the polygonal mesh. Process performance is assessed with the reconstruction of a geometric model of mouse heart ventricles from a computerized tomography scan. Our results show an excellent reproduction of the geometric data with surfaces that are continuous.