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-Test, 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).*

dominique.apprato@univ-pau.fr†

medecine-nucleaire.ducassou@chu-bordeaux.fr§

elaffon@u-bordeaux2.fr¶

carole.leguyader@laposte.net