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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-Teste, 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 pulmona...

We present a deformable model technique for geophysical image analysis. Deformable model approaches have been developed extensively in the literature, including prior applications to geophysical or medical image interpretation. In this paper we propose a method to segment a geophysical image under interpolation conditions (well data). The originality of this segmentation method is that it considers the deformable model as a set of articulated curves, which corresponds to the interfaces between different regions. Moreover, the interpolation conditions permit some geometric constraints to be made on the model. The theoretical aspect of the method is given in the case of a three dimensional image. Numerical results are given.

Curve and surface fitting using spline functions from rapidly varying data is a difficult problem. In the bivariate case and without information about the location of the large variations, the usual approximation methods lead to instability phenomenae or undesirable oscillations that can locally and even globally hinder the approximation. So, we propose a new method which uses scale transformations. The originality of the method consists in a pre-processing and a post-processing of the data. Instead of trying to find directly an approximant, we first apply a scale transformation to the z-values of the function. In the particular case of the approximation of surfaces, the originality of the method consists in removing the variations of the unknown function using a scale transformation in pre-processing. And so, the pre-processed data do not have great variations. So, we could use a usual approximant which will not create oscillations. We apply another scale transformation to map the approximant values back...