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Segmentation Informed by Manifold Learning

  • Qilong Zhang
  • Richard Souvenir
  • Robert Pless
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)

Abstract

In many biomedical imaging applications, video sequences are captured with low resolution and low contrast challenging conditions in which to detect, segment, or track features. When image deformations have just a few underlying causes, such as continuously captured cardiac MRI without breath-holds or gating, the captured images lie on a low-dimensional, non-linear manifold. The manifold structure of such image sets can be extracted by automated methods for manifold learning. Furthermore, the manifold structure of these images offers new constraints for tracking and segmentation of relevant image regions. We illustrate how to incorporate these new constraints within a snake-based energy minimization approach, and demonstrate improvements in using snakes to segment a set of cardiac MRI images in challenging conditions.

Keywords

Independent Component Analysis Active Contour Model Manifold Structure Manifold Learn Smoothness Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1, 321–331 (1988)CrossRefGoogle Scholar
  2. 2.
    Cremers, D., Tischhäuser, F., Weickert, J., Schnörr, C.: Diffusion snakes: Introducing statistical shape knowledge into the mumford-shah functional. International Journal of Computer Vision 50, 295–313 (2002)zbMATHCrossRefGoogle Scholar
  3. 3.
    Duncan, J.C., Ayache, N.: Medical image analysis: Progress over two decades and the challenges ahead. IEEE Trans. Pattern Anal. Mach. Intell. 22, 85–106 (2000)CrossRefGoogle Scholar
  4. 4.
    Frangi, A.F., Rueckert, D., Duncan, J.S.: Three-dimensional cardiovascular image analysis. IEEE Trans. Med. Imaging 21, 1005–1010 (2002)CrossRefGoogle Scholar
  5. 5.
    McInerney, T., Terzopoulos, D.: Deformable models in medical images analysis: a survey. Medical Image Analysis 1, 91–108 (1996)CrossRefGoogle Scholar
  6. 6.
    Ueda, N., Mase, K.: Tracking moving contours using energy-minimizing elastic contour models. International Journal of Pattern Recognition and Artificial Intelligence 9, 465–484 (1995)CrossRefGoogle Scholar
  7. 7.
    Geiger, D., Gupta, A., Costa, L.A., Vlontzos, J.: Dynamic programming for detecting, tracking, and matching deformable contours. IEEE Trans. Pattern Anal. Mach. Intell. 17, 294–302 (1995)CrossRefGoogle Scholar
  8. 8.
    Xu, C., Prince, J.L.: Gradient vector flow: A new external force for snakes. In: Proceedings of the Conference on Computer Vision and Pattern Recognition, Washington, DC, USA, p. 66 (1997)Google Scholar
  9. 9.
    Xu, C., Prince, J.L.: Generalized gradient vector flow external forces for active contours. Signal Process 71, 131–139 (1998)zbMATHCrossRefGoogle Scholar
  10. 10.
    Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (1986)Google Scholar
  11. 11.
    Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley and Sons, Chichester (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)CrossRefGoogle Scholar
  13. 13.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  14. 14.
    Weinberger, K.Q., Saul, L.K.: Unsupervised learning of image manifolds by semidefinite programming. Computer Vision and Pattern Recognition (2004)Google Scholar
  15. 15.
    Pless, R., Simon, I.: Embedding images in non-flat spaces. In: Proc. of the International Conference on Imaging Science, Systems, and Technology (2002)Google Scholar
  16. 16.
    Donoho, D.L., Grimes, C.: Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. PNAS 100, 5591–5596 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Brand, M.: Charting a manifold. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems, vol. 15, pp. 961–968. MIT Press, Cambridge (2003)Google Scholar
  18. 18.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. Advances in Neural Information Processing Systems (2002)Google Scholar
  19. 19.
    Lim, I.S., Ciechomski, P.d.H., Sarni, S., Thalmann, D.: Planar arrangement of high-dimensional biomedical data sets by isomap coordinates. In: Proceedings of the 16th IEEE Symposium on Computer-Based Medical Systems, pp. 50–55 (2003)Google Scholar
  20. 20.
    Pless, R.: Differential structure in non-linear image embedding functions. Articulated and Nonrigid Motion (2004)Google Scholar
  21. 21.
    Souvenir, R., Pless, R.: Isomap and non-parametric models of image deformation. In: Proc. IEEE Workshop on Motion and Video Computing, Breckenridge, CO (2005)Google Scholar
  22. 22.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  23. 23.
    Dierckx, P.: Curve and surface fitting with splines. Oxford University Press, Inc., New York (1993)zbMATHGoogle Scholar
  24. 24.
    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)zbMATHCrossRefGoogle Scholar
  25. 25.
    Malpicaa, N., Ledesma-Carbayoa, M., Santosa, A., Prezb, E., Garc-Fernandezb, M., Descob, M.: A coupled active contour model for myocardial tracking in contrast echocardiography. In: Image Understanding and Analysis. Imperial College, London (2004)Google Scholar
  26. 26.
    Zhang, Q., Pless, R.: Segmenting cardiopulmonary images using manifold learning with level sets. In: ICCV workshop on Computer Vision for Biomedical Image Applications: Current Techniques and Future Trends, Beijing, China (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Qilong Zhang
    • 1
  • Richard Souvenir
    • 1
  • Robert Pless
    • 1
  1. 1.Department of Computer Science and EngineeringWashington UniversitySt. LouisUSA

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