A Linear 3D Elastic Segmentation Model for Vector Fields. Application to the Heart Segmentation in MRI

In this paper a 3D elastic model for the segmentation of vector fields 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 force 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. Then the algorithm is applied to the segmentation of cardiac magnetic resonance imaging, and its efficiency is shown with two experiments.

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