Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 918510, 11 pages
http://dx.doi.org/10.1155/2012/918510
Research Article

Iterative Methods for Obtaining Energy-Minimizing Parametric Snakes with Applications to Medical Imaging

Alexandru Ioan Mitrea,1 Radu Badea,2 Delia Mitrea,3 Sergiu Nedevschi,3 Paulina Mitrea,3 Dumitru Mircea Ivan,1 and Octavian Mircia Gurzău1

1Department of Mathematics, Technical University of Cluj-Napoca, George Baritiu Street, no. 25, 400020 Cluj-Napoca, Romania
2Department of Ultrasonography, University of Medicine and Pharmacy “Iuliu Haţieganu” Cluj-Napoca, Victor Babeş Street, no. 8, 400079 Cluj-Napoca, Romania
3Department of Computer Science, Technical University of Cluj-Napoca, George Baritiu Street, no. 26-28, 400027 Cluj-Napoca, Romania

Received 30 September 2011; Accepted 8 November 2011

Academic Editor: Maria Crisan

Copyright © 2012 Alexandru Ioan Mitrea 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.

Abstract

After a brief survey on the parametric deformable models, we develop an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes. We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm, then we discuss its convergence, consistency, and stability. Some aspects regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.