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Generating Geometric Models through Self-Organizing Maps

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Multiscale Optimization Methods and Applications

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 82))

Summary

A new algorithm for generating shape models using a Self-Organizing map (SOM) is presented. The aim of the model is to develop an approach for shape representation and classification to detect differences in the shape of anatomical structures. The Self-Organizing map requires specification of the number of clusters in advance, but does not depend upon the choice of an initial contour. This technique has the advantage of generating shape representation of each cluster and classifying given contours simultaneously. To measure the closeness between two contours, the area difference method is used. The Self-Organizing map is combined with the area difference method and is applied to human heart cardiac borders. The experimental results show the effectiveness of the algorithm in generating shape representation and classification of given various human heart cardiac borders.

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References

  1. F.L. Bookstein, “Size and shape spaces for landmark data in two dimensions”, Statistical Science, Vol. 1, (1986), 181–242.

    MATH  Google Scholar 

  2. Y. Chen, H. Tagare, M. S.R. Thiruvenkadam, F. Huang, D. Wilson, A. Geiser, K. Gopinath, and R. Briggs, “Using prior shapes in geometric active contours in a variational framework”, International Journal of Computer Vision, Vol.50,(3), (2002), 315–328.

    Article  Google Scholar 

  3. V. Caselles, F. Catté, T. Coll, and F. Dibos, “A geometric model for active contours in image processing”, Numerische Mathematik, Vol.66, (1993), 1–31.

    Article  MathSciNet  Google Scholar 

  4. Y. Chen, F. Huang, H. Tagare, M. Rao, D. Wilson, and A. Geiser “Using prior shapes and intensity profiles in medical image segmentation”, Proceedings of International Conference on Computer Vision, Nice, France, (2003), 1117–1124.

    Google Scholar 

  5. Y. Chen, F. Huang, D. Wilson, and A. Geiser “Segmentation with shape and intensity priors”, Proceedings, Second International Conference on Image and Graphics, August 2002, Hefei, China, (2003), 378–385.

    Google Scholar 

  6. Y. Chen, W. Guo, F. Huang, D. Wilson, and A. Geiser “Using prior shapes and points in medical image segmentation”, Proceedings of Energy Minimization Methods in Computer Vision and Pattern Recognition, Lisbon, Portugal, July 7–9, (2003), 291–305.

    Google Scholar 

  7. T.K. Carne, “The geometry of shape spaces, Proc. of the London Math. Soc., vol.3, no.61, (1990), pp.407–432.

    MathSciNet  Google Scholar 

  8. T. Cootes, C. Taylor, D. Cooper and J. Graham, “Active shape model-their training and application, Computer Vision and Image Understanding, Vol. 61 (1995), pp. 38–59.

    Article  Google Scholar 

  9. Y. Chen, D. Wilson and F. Huang, “A new procrustes methods for generating geometric models”, Proceedings of World Multiconference on Systems, Cybernetics and Informatics, July 22–25, 2001, Orlando, (2001), 227–232.

    Google Scholar 

  10. I.L. Dryden and K.V. Mardia, “Statistical Shape Analysis”, John Wiley & Son, (1998).

    Google Scholar 

  11. M. Fréchet, “Les courbes aléatoires,” Bull. Inst. Internat. Statist., Vol. 38, pp.499–504, 1961.

    MATH  MathSciNet  Google Scholar 

  12. Honkela, Timo “Description of Kohonen’s Self-Organizing Map.” http://www.mlab.uiah.fi/timo/som/thesis-som.html

    Google Scholar 

  13. D.G. Kendall, “Stochastic Geometry, chapter Foundation of a theory of random sets”, John Wiley Sons, New York, (1973) 322–376.

    Google Scholar 

  14. D.G. Kendall, “Shape-manifolds, Procrustean metrics, and complex projective spaces”, Bull. London Mathematical Society, (1984), 81–121.

    Google Scholar 

  15. D.G. Kendall, “A survey of the statistical theory of shape”, Statist. Sci., vol.4, no.2, (1989) 87–120.

    MATH  MathSciNet  Google Scholar 

  16. J.T. Kent and K.V. Mardia, “Shape, procrustes tangent projections and bilateral symmetry”, Biometrika, (2001), 88:469–485.

    Article  MathSciNet  Google Scholar 

  17. T. Kohonen, “Self-Organizng Maps”, Springer, (2001).

    Google Scholar 

  18. M. E. Leventon, O. Faugeras, E. Crimson, W. Wells. “Level Set Based Segmentation with Intensity and Curvature Priors” Mathematical Methods in Biomedical Image Analysis, (2000).

    Google Scholar 

  19. M. E. Leventon, E. Grimson, and O. Faugeras, “Statistical Shape Influence in Geodesic Active Contours”, Proc. IEEE Conf. CVPR (2000), 316–323.

    Google Scholar 

  20. G. Matheron, “Random Sets and Integral Geometry”, John Wiley & Sons, 1975.

    Google Scholar 

  21. N. Paragios and M. Rousson, “Shape prior for level set representations”, Computer Vision-ECCV2002, the 7th European Conference on Computer Vision, Copenhgen, Demark, May 2002 Proceeding.

    Google Scholar 

  22. N. Paragios, M. Rousson, and V. Ramesh, “Marching distance functions: a shape-to-area variational approach for global-to-local registration”, Computer Vision-ECCV2002, 775–789.

    Google Scholar 

  23. S. Soatto and A. Yezzi, “Deformation: deformining motion, shape average and joint registration and segmentation of images, Computer Vision-ECCV2002.

    Google Scholar 

  24. J. Yang and J.S. Duncan, “3D image segmentation of deformable objects with shape apprearance joint prior models”, MICCAI, (2003), 573–580.

    Google Scholar 

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© 2006 Springer Science+Business Media, Inc.

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An, Jh., Chen, Y., Chang, M.N., Wilson, D., Geiser, E. (2006). Generating Geometric Models through Self-Organizing Maps. In: Hager, W.W., Huang, SJ., Pardalos, P.M., Prokopyev, O.A. (eds) Multiscale Optimization Methods and Applications. Nonconvex Optimization and Its Applications, vol 82. Springer, Boston, MA. https://doi.org/10.1007/0-387-29550-X_10

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