Singular Perturbations For Heart Image Segmentation Tracking

J. Pousin

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 1, page 183-194
  • ISSN: 0973-5348

Abstract

top
In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.

How to cite

top

Pousin, J.. "Singular Perturbations For Heart Image Segmentation Tracking." Mathematical Modelling of Natural Phenomena 4.1 (2009): 183-194. <http://eudml.org/doc/222389>.

@article{Pousin2009,
abstract = { In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.},
author = {Pousin, J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {images segmentation; linear elasticity; singular perturbations techniques; singular perturbations techniques},
language = {eng},
month = {1},
number = {1},
pages = {183-194},
publisher = {EDP Sciences},
title = {Singular Perturbations For Heart Image Segmentation Tracking},
url = {http://eudml.org/doc/222389},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Pousin, J.
TI - Singular Perturbations For Heart Image Segmentation Tracking
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/1//
PB - EDP Sciences
VL - 4
IS - 1
SP - 183
EP - 194
AB - In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.
LA - eng
KW - images segmentation; linear elasticity; singular perturbations techniques; singular perturbations techniques
UR - http://eudml.org/doc/222389
ER -

References

top
  1. H. Brézis. Analyse fonctionnelle. Masson, Paris 1985.  Zbl0511.46001
  2. C, Xu, J. L. Prince. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing, 7 1998, 359-369.  Zbl0973.94003
  3. P.G. Ciarlet. Mathematical elasticity. North-Holland 1993.  
  4. J. Cousty, L. Najman, M. Couprie, S. Clément-Guinaudeau, T. Goissen, J. Garot. Automated, accurate and fast segmentation of 4D cardiac MR images. Functional Imaging and Modeling of the Heart (FIMH), LNCS, Springer, (2007), No. 4466, 474-483.  
  5. B. Faugeras, J. Pousin. Variational asymptotic derivation of an elastic model arising from the problem of 3D automatic segmentation of cardiac images. Analysis and Applications, 2 (2004), No. 4, 1–33.  Zbl1172.74318
  6. F. Krasucki, S. Lenci. Yield design of bonded joints. Eur. J. Mech. A Solids, 19 (2000), No. 4, 649–667.  Zbl0968.74046
  7. J. Necas. Les méthodes directes en théorie des équations elliptiques. Masson, Paris, 1967.  
  8. O.A. Oleinik, A.S. Shamaev, G.A. Yosifian. Mathematical problems in elasticity and homogenization. Studies in Mathematics and its applications, Noth-Holland 1992.  Zbl0768.73003
  9. Q.C. Pham, F. Vincent, P. Clarysse, P. Croisille, I.E. Magnin. A FEM-based deformable model for the 3D segmentation and tracking of the heart in cardiac MRI., Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis, ISPA (2001), 250-254.  
  10. M. Picq J. Pousin, Y. Rouchdy, A linear 3D elastic segmentation model for vector fields. Application to the heart segmentation in MRI. Journal Of Mathematical Imaging and Vision, 27 (2007), No. 3, 241–255.  
  11. P. Pebay, T. Baker, J. Pousin. Dynamic meshing for finite element based segmentation of cardiac imagery. Fifth World Congress on Computational Mechanics, (2002).  
  12. Y. Rouchdy, J. Pousin , J. Schaerer, P. Clarysse. A nonlinear elastic deformable template for soft structure segmentation. Application to heart segmentation in MRI. J. Inverse Problems, 23 (2007), No. 3, 1017–1035.  Zbl1113.92043
  13. L. Tartar. Topics in nonlinear analysis. Publications Mathématiques d'Orsay, 1978.  Zbl0395.00008
  14. J. Simon. Compact Sets in the Space Lp(O, T; B). Ann. Math. Pura Appl., (IV) Vol. CXLVI (1987), 65-96.  Zbl0629.46031

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.