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Abstract
In this article, we propose a new segmentation model including geometric constraints, namely interpolation conditions, to detect objects in a given image sequence. We propose to apply the deformable models to an explicit function to avoid the problem of parameterization (see Gout, C. and Vieira-Testé, S. (2003). An algorithm for segmentation under interpolation conditions using deformable models. Int. J. Comput. Math., 80(1), 47–54.). A problem of energy minimization on a closed subspace of a Hilbert space is defined, and introducing Lagrange multipliers enables us to formulate the corresponding variational problem with interpolation conditions. We apply this method in order to ouline the cross-sectional area (CSA) of a great thoracic vessel, namely the main pulmonary artery, in order to non-invasively assess pulmonary arterial hypertension (see Laffon, E., Vallet, C., Bernard, V., Montaudon, M., Ducassou, D., Laurent, F. and Marthan, R. (2003). A computed method for non-invasive MRI assessment of pulmonary arterial hypertension. J. Appl. Physiol. (in press); Laffon, E., Laurent, F., Bernard, V., De Boucaud, L., Ducassou, D. and Marthan, R. (2001). Noninvasive assessment of pulmonary arterial hypertension by MR phase-mapping method. J. Appl. Physiol., 90(6), 2197–2202; Laffon, E., Bernard, V., Montaudon, M., Marthan, R., Barat, J. L. and Laurent, F. (2001). Tuning of pulmonary arterial circulation evidenced by MR phase mapping in healthy volunteers. J. Appl. Physiol., 90(2), 469–474, for more details).
Acknowledgement
This work was supported in part by CHU of Bordeaux (grant from ‘appel d'offre interne 2000’ n° 01-06).