In this paper a 3D elastic model for the segmentation of cardiac magnetic resonance imaging has been proposed and analyzed. Elastic models for segmentation usually involve minimization of internal and external energy. A problem we observed with standard internal and external energy is that the local or the global reached minima do not impose the external energy to be zero. To eliminate this difficulty, we propose introducing a constraint. The constraint problem is proved to be mathematically well posed, and a simple algorithm which avoids computing the Lagrange multiplier is provided. This algorithm is proved to be convergent. Finally the efficiency of the method is shown with numerical experiments.
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