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A Variational Approach for the Segmentation of the Left Ventricle in Cardiac Image Analysis

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Abstract

In this paper we propose a level set method to segment MR cardiac images. Our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints. The visual information is expressed through a gradient vector flow-based boundary component and a region term that aims at best separating the cardiac contours/regions according to their global intensity properties. In order to deal with misleading visual support, an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance. The resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme, the Additive Operator Splitting. Encouraging experimental results are provided using real data.

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References

  • Adalsteinsson, D. and Sethian, J. 1995. A fast level set method for propagating interfaces. Journal of Computational Physics, 118:269–277.

    Google Scholar 

  • Amadieu, O., Debreuve, E., Barlaud, M., and Aubert, G. 1999. In-ward and outward curve evolution using level set method. In IEEE International Conference on Image Processing, vol. III, pp. 188–192.

    Google Scholar 

  • Blake, A. and Isard, M. 1997. Active Contours. Springer-Verlag: Berlin.

    Google Scholar 

  • Boykov, Y. and Jolly, M.-P. 2000. Interactive organ segmentation using graph cuts. In Medical Imaging Computing and Computer-Assisted Intervention, pp. 276–286.

  • Canny, J. 1986. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8:769–798.

    Google Scholar 

  • Caselles, V., Catte, F., Coll, T., and Dibos, F. 1993. A geometric model for active contours. Numerische Mathematik, 66: 1–31.

    Google Scholar 

  • Caselles, V., Kimmel, R., and Sapiro, G. 1995. Geodesic active contours. In IEEE International Conference in Computer Vision, Boston, USA, pp. 694–699.

  • Chakraborty, A., Staib, H., and Duncan, J. 1994. Deformable boundary finding influenced by region homogeneity. In IEEE Conference on Computer Vision and Pattern Recognition, Los Alamitos, USA, pp. 624–627.

  • Chan, T. and Vese, L. 1999. An active contour model without edges. In International Conference on Scale-Space Theories in Computer Vision, pp. 141–151.

  • Chen, Y., Thiruvenkadam, H., Tagare, H., Huang, F., and Wilson, D. 2001. On the incorporation of shape priors int geometric active contours. In IEEE Workshop On Variational and Level Set Methods, pp. 145–152.

  • Cohen, L. 1991. On active contour models and balloons. CVGIP: Image Understanding, 53:211–218.

    Google Scholar 

  • Cootes, T., Taylor, C., Cooper, C., and Graham, J. 1991. A trainable method of parametric shape description. In British Machine Vision Conference, pp. 54–61.

  • Curwen, R. and Blake, A. 1993. Dynamic contours: Real-time active splines. In Active Vision. A. Blake and A. Yuille (Eds.), The MIT Press, Ch. II, pp. 39–57.

  • Delingette, H., Hebert, M., and Ikeuchi, K. 1992. Shape representation and image segmentation using deformable templates. Image and Vision Computing, 10:132–144.

    Google Scholar 

  • Delingette, H. and Montagnat, J. 2000. Newalgorithms for controling active contours shape and topology. In European Conference on Computer Vision, Dublin, Ireland, pp. 381–395.

  • Deriche, R. 1987. Using Canny's criteria to derive a recursively implemented optimal edge detector. International Journal of Computer Vision, 1:167–187.

    Google Scholar 

  • Deriche, R. and Faugeras, O. 1996. Les EDP en Traitement des Images et Vision par Ordinateur. Traitement du Signal, 13. ftp://ftp-robotvis.inria.fr/pub/html/Papers/deriche-faugeras:96b.ps.gz.

  • Duncan, J. and Ayache, N. 2000. Medical image analysis: progress over two decades and challenges ahead. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22:85–106.

    Google Scholar 

  • Geiger, D., Gupta, A., Costa, L., and Vlontzos, J. 1995. Dynamic programming for detecting, tracking and matching deformable contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17:294–302.

    Google Scholar 

  • Goldenberg, R., Kimmel, R., Rivlin, E., and Rudzsky, M. 1999. Fast geodesic active contours. In International Conference on Scale-Space Theories in Computer Vision, pp. 34–45.

  • Goldenberg, R., Kimmel, R., Rivlin, E., and Rudzsky, M. 2001. Cortex segmentation—A fast variational geometric approach. In IEEE Workshop On Variational and Level Set Methods, pp. 127–135.

  • Gomes, J. and Faugeras, O. 2000. Reconsiling distance functions and level sets. Journal of Visual Communication and Image Representation, 11:209–223.

    Google Scholar 

  • Ivins, J. and Porrill, J. 1995. Constrained active region models for segmenting textures and colours. Image and Vision Computing, 13:431–438.

    Google Scholar 

  • Jolly, M. 2001. Combining edge, region, and shape information to segment the left ventricle in cardiac MR images. In Medical Imaging Computing and Computer-Assisted Intervention, pp. 482–490.

  • Jolly, M., Duta, N., and Funka-Lea, G. 2001. Segmentation of the left ventricle in cardiac MRimages. In IEEE International Conference in Computer Vision, Vancouver, Canada.

  • Kass, M., Witkin, A., and Terzopoulos, D. 1987. Snakes: Active contour models. In IEEE International Conference in Computer Vision, pp. 261–268.

  • Kass, M., Witkin, A., and Terzopoulos, D. 1988. Snakes: Active contour models. International Journal of Computer Vision, 1:321–332.

    Google Scholar 

  • Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., and Yezzi, A. 1995. Gradient flows and geometric active contour models. In IEEE International Conference in Computer Vision, Boston, USA, pp. 810–815.

  • Kimmel, R. 2002. Fast edge integration. In Geometric Level Set Methods in Imaging, Vision and Graphics. S. Osher and N. Paragios (Eds.), Springer Verlag: Berlin, Ch. 4.

    Google Scholar 

  • Leventon, M., Grimson, E., and Faugeras, O. 2000. Statistical shape influence in geodesic active controus. In IEEE Conference on Computer Vision and Pattern Recognition, pp. I:316–322.

    Google Scholar 

  • Lipson, P., Yuille, A., Okeefe, D., Cavanaugh, J., Taaffe, J., and Rosenthal, D. 1990. Deformable templates for feature extraction from medical images. In European Conference on Computer Vision, Antibes, France.

  • Lorigo, L., Faugeras, O., Grimson, W., Keriven, R., and Kikinis, R. 1998. Segmentation of bone in clinical knee MRI using texture-based geodesic active contours. In Medical Imaging Copmuting and Computer-Assisted Intervention.

  • Malladi, R. and Sethian, J. 1998. A real-time algorithm for medical shape recovery. In IEEE International Conference in Computer Vision, Bombay, India, pp. 304–310.

  • Malladi, R., Sethian, J., and Vemuri, B. 1995. Shape modeling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17:158–175.

    Google Scholar 

  • McInerney, T. and Terzopoulos, D. 1996. Deformable models in medical image analysis: A survey. IEEE Transactions on Medical Imaging, 1(2):91–108.

    Google Scholar 

  • McIreney, T. and Terzopoulos, D. 1995. Topologically adaptable snakes. In IEEE International Conference in Computer Vision, Caibridge, USA, pp. 840–845.

  • Metaxas, D. 1996. Physics-Based Deformable Models. Kluwer Academic Publishers: Dordrecht.

    Google Scholar 

  • Osher, S. and Fedkiw, R. 2000. Level set methods. Technical Report CAM-00-08, Mathematics Department, UCLA. ftp://ftp.math.ucla.edu/pub/camreport/cam00-08.ps.gz.

  • Osher, S. and Paragios, N. 2002. Geometric Level Set Methods in Imaging, Vision and Graphics. Springer Verlag: Berlin.

    Google Scholar 

  • Osher, S. and Sethian, J. 1988. Fronts propagating with curvature-dependent speed: Algorithms based on the Hamilton-Jacobi formulation. Journal of Computational Physics, 79:12–49.

    Google Scholar 

  • Paragios, N. 2001. A variational approach for the segmentation of the left ventricle in cardiac images. In IEEE Workshop On Variational and Level Set Methods, Vancouver, Canada, pp. 153–160.

  • Paragios, N. and Deriche, R. 1999. Geodesic active regions for supervised texture segmentation. In IEEE International Conference in Computer Vision, Corfu, Greece, pp. 926–932. Previous: INRIA Research Report, RR 3440, June 1998, http://www.inria.fr/RRRT/RR-3440.html.

  • Paragios, N. and Deriche, R. 2000. Coupled geodesic active regions for image segmentation: A level set approach. In European Conference in Computer Vision, Dublin, Ireland, pp. II:224–240. Previous: INRIA Research Report, RR 3783, October 1999, http://www.inria.fr/RRRT/RR-3783.html.

  • Paragios, N., Mellina-Gottardo, O., and Ramesh, V. 2001. Gradient vector flow fast geodesic active contours. In IEEE International Conference in Computer Vision, Vancouver, Canada, pp. I:67–73.

    Google Scholar 

  • Rousson, M. and Paragios, N. 2002. Shape priors for level set representations. In European Conference on Computer Vision, Copenhangen, Denmark, pp. II:78–93.

    Google Scholar 

  • Samson, C., Blanc-Feraud, L., Aubert, G., and Zerubia, J. 1999. A level set model for image classification. In International Conference on Scale-Space Theories in Computer Vision, pp. 306–317. http://www.inria.fr/RRRT/RR-3662.html.

  • Sapiro, G. 2001. Geometric Partial Differential Equations in Image Processing. Cambridge University Press: Cambridge.

    Google Scholar 

  • Sebastian, T., Tek, H., Wolfe, W., Crisco, J., and Kimia, B. 1998. Segmentation of carpal bones from 3D CT images using skeletally coupled deformable models. In Medical Imaging Computing and Computer-Assisted Intervention, Boston, USA, pp. 1185–1194.

  • Sethian, J. 1996. Level Set Methods. Cambridge University Press: Cambridge.

    Google Scholar 

  • Siddiqi, K., Lauziere, Y.-B., Tannenbaum, A., and Zucker, S. 1997. Area and length minimizing flows for shape segmentation. In IEEE Conference on Computer Vision and Pattern Recognition, Puerto Rico, USA, pp. 621–627.

  • Sifakis, E., Garcia, C., and Tziritas, G. 2002. Bayesian level sets for image segmentation. Journal of Visual Communication and Image Representation, 13:44–64.

    Google Scholar 

  • Staib, L. and Duncan, S. 1992. Boundary finding with parametrically deformable models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14:1061–1075.

    Google Scholar 

  • Terzopoulos, D. and Metaxas, D. 1991. Dynamic 3D models with local and global deformations: Deformable superquadrics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13:703–714.

    Google Scholar 

  • Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable model. Computer Graphics, 21:205–214.

    Google Scholar 

  • Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tucker, D., Fan, A., Grimson, A., and Willsky, A. 2001. Model-based curve evolution technique for image segmentation. In IEEE Conference on Computer Vision and Pattern Recognition, vol. I, pp. 463–468.

    Google Scholar 

  • Tsai, A., Yezzi, A., and Willsky, A. 2000. A curve evolution approach to smoothing and segmentation using the Mumford-shah functional. In IEEE Conference on Computer Vision and Pattern Recognition, pp. I:119–124.

    Google Scholar 

  • Tsitsiklis, J. 1995. Efficient algorithms for globally optimal trajectories. IEEE Transactions on Automatic Control, 40:1528–1538.

    Google Scholar 

  • Vasilevskiy, A. and Siddiqi, K. 2001. Flux maximizing geometric flows. In IEEE International Conference in Computer Vision, Vancouver, Canada.

  • Weickert, J., Haar Romeny, B.M.t., and Viergener, M. 1998. Efficient and reliable scheme for non-linear diffusion and filtering. IEEE Transactions on Image Processing, 7:398–410.

    Google Scholar 

  • Xu, C. and Prince, J. 1997. Gradient vector flow: A new external force for snakes. In IEEE Conference on Computer Vision and Pattern Recognition, Puerto Rico, USA, pp. 66–71.

  • Xu, C. and Prince, L. 1998. Generalized gradient vector flowexternal forces for active contours. Signal Processing: Image Communication, 71:131–139.

    Google Scholar 

  • Yezzi, A. and Soatto, S. 2001. Stereoscopic segmentation. In IEEE International Conference in Computer Vision, Vancouver, Canada, pp. I:56–64.

  • Yezzi, A., Tsai, A., and Willsky, A. 1999. A statistical approach to snakes for bimodal and trimodal imagery. In IEEE International Conference in Computer Vision, Corfu, Greece, pp. 898–903.

  • Yuille, A., Cohen, D., and Hallinan, P. 1989. Feature extrac-tion from faces using deformable templates. In IEEE Conference on Computer Vision and Pattern Recognition, pp. 104–109.

  • Zeng, X., Staib, L., Schukz, R., and Duncan, J. 1998. Volumetric layer segmentation using coupled surfaces propagation. In IEEE Conference on Computer Vision and Pattern Recognition, Santa Barbara, USA, pp. 708–715.

  • Zhu, S. and Yuille, A. 1996. Region competition: Unifying snakes, region growing, and bayes/MDL for multiband image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18:884–900.

    Google Scholar 

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Paragios, N. A Variational Approach for the Segmentation of the Left Ventricle in Cardiac Image Analysis. International Journal of Computer Vision 50, 345–362 (2002). https://doi.org/10.1023/A:1020882509893

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