Christian Gout - résumé

D. Apprato, C. Gout, D. Komatitsch, C. Le Guyader, L. Vese, S. Vieira-Testé

Works presented at International Conferences:

C. Le Guyader (speaker), C. Gout, SIAM conference on Image Processing at Salt Lake city 2004, Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods
C. Gout (speaker), C. Le Guyader, L. Vese, MATA 2003 at Cancun, Mexico, 2003: Geodesic active contours under under interpolation conditions.
C. Le Guyader (speaker), D. Apprato, C. Gout, MATA 2003 at Cancun, Mexico, 2003: The Level Set Methods and Image segmentation under interpolation conditions
C. Gout (speaker), D. Apprato, D. Ducassou, E. Laffon, Curves and Surfaces V, Segmentation under interpolation conditions, Saint-Malo, july 2002.
C. Gout (speaker), D. Apprato, SIAM conference on Imaging science, Boston,, Level set method applied to deformable models to segment geophysical images under interpolation conditions, First march 2002.
IEEE 2000 & 2001.
Geophysical imaging: Seminar Harvard at Boston, USA, 1999
Snakes under geometrical constraints: Puerto-Vallarta 1999, Mexico, Talk - Int. Conf.
Denoising & segmentation: Saint-Malo 1999, France, Talk -Int. Conf.

IEEE ICIP 2000 at Vancouver (C Gout, S Vieira Testé: An algorithm for contrast enhancement and segmentation of images , Volume: 2, pp.716 -719, Vancouver, Canada, 2001.)
IEEE Image Analysis and Interpretation at Austin (C Gout, S Vieira Testé: Using deformable models to segment complex structures under geometric constraints, IEEE S. on Image Analysis and Interpretation, pp. 101-105, 2000).
IEEE IGARSS 2000, Honolulu (D Apprato, C Gout, S Vieira Testé: Segmentation of Complex Geophysical 3D Structures, IEEE International Geoscience and Remote Sensing Symposium, vol. 1, pp. 651-653, IEEE Press, Honolulu, 2000.)
CPAM 728, UC Berkeley (D. A, C.G.), 1998
Saint-Malo Proc. (D Apprato, JB Betbeder, C Gout, S Vieira-Testé: A Segmentation method Under Geometric Constraints After Pre-processing, Curves and Surfaces IV, A. Cohen, C. Rabut and L. L. Scumaker eds., pp. 9-18, Vanderbilt University Press, Nashville, 2000).

C. Gout, C. Le Guyader, 2005
Viscosity solution for Geodesic Active Contours under interpolation conditions, submitted
C. Gout, C. Le Guyader, L. Vese, 2005
Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods , Numerical Algorithms 39 (1-3), pp. 155–173, 2005.
C. Le Guyader, D. Apprato, C. Gout, 2005
The Level Set Methods and Image segmentation under interpolation conditions, Numerical Algorithms 39 (1-3), pp. 221–235, 2005.
D. Apprato, D. Ducassou, C. Gout, E. Laffon, C. Le Guyader, 2004
Segmentation of medical image sequence under constraints: application to non-invasive assessment of pulmonary arterial hypertension, Int. J. of Comp. Mathematics 5, pp. 527 - 536, 2004.
Dominique Apprato, Dominique Ducassou, Christian Gout, Eric Laffon and Carole Le Guyader, 2004
Segmentation of Medical Images Sequence for Non Invasive Assessment of Pulmonary Arterial Hypertension, January 2004, CAM Report 04-01, UC Los Angeles.
C. Gout, C. Le Guyader and L. Vese, 2004
Segmentation Under Geometrical Conditions Using Geodesic Active Contours and Interpolation Using Level Set Methods, CAM Report 03-44, 42 pages, UC Los Angeles.
C. Gout, S. Vieira-Testé, 2003
An algorithm for segmentation under interpolation conditions using deformable models, Int. J. of Comp. Math., 80, no. 1, pp. 47-54, 2003.

Level set methods for segmentation under geometrical constraints

Ph. D of Carole Le Guyader (INSA Rouen - advisor C. Gout, 2004): This approach was initiated by the Ph. D thesis of S. Vieira-Testé in 1997 (D. Apprato, see also Gout-Vieira 2000) .
Mots-clés : EDP et Approximation, théorie et applications à l'imagerie mathématique, méthode "level set", équations d'Hamilton Jacobi, contours actifs géodésiques, Fast Marching, Théorème d'Euler-Lagrange, Multiplicateurs de Lagrange, solutions de viscosité, éléments finis de Bogner-Fox-Schmitt, schéma AOS, condition d'entropie, méthode de descente de gradient, formulation variationnelle.
Key words: PDE and approximaion, theory and applications to mathematical imaging, level set method, Hamilton-Jacobi equations, geodesic active contours, Fast MArching, Method, Euler-Lagrange theorem, Lagrange multipliers, viscosity solutions, finite elements of Bogner-Fox-Schmitt, AOS scheme, entropy condition, gradient descent method, variational formulation
We are concerned with the issue of image segmentation under geometrical constraints. This problematics has emerged while analyzing classical methods of edge detection. Indeed, these classical tools (deformable models, geodesic active contours, fast marching, etc...) prove to be fruitless in several scenarios: when image data are missing or of poor quality. In medical imaging for instance, occlusion phenomena can occur: two organs can partly hide each other (e.g of the liver). Besides, two adjacent objects can own homogeneous intrinsic texture so that it is hard to clearly identify the interface beween both items. The classical definition of an edge which is features as the locus of connected points for which the image gradient varies abruptly can no longer be applied. To finish with, in some fields of research and/or for post-processing needs, one can have at one's disposal, in addition to image data, geometrical data to be integrated in the segmentation process. To cope with these hindrances, we propose to design segmentation models that integrate geometrical constraints while satisfying the classical criteria of detection with in particular, the regularity that implies on the contour. Theoretical aspect are studied (viscosity solutions...). Numerical examples are given <click here>.

Ph. D thesis of S. Vieira-Testé (1997) Advisor : D. Apprato	Blue :initial condition; Red : Final result
Orange : initial condition; Yellow : Final result We have here several "triple and quadruple" points.	Orange : initial condition; Yellow : Final result White : Interpolation data


Initial MRI Brain image	Left: Studied zone Right . Obtained result after pre-processing