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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F.L. Bookstein, “Size and shape spaces for landmark data in two dimensions”, Statistical Science, Vol. 1, (1986), 181–242.
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.
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.
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.
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.
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.
T.K. Carne, “The geometry of shape spaces, Proc. of the London Math. Soc., vol.3, no.61, (1990), pp.407–432.
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.
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.
I.L. Dryden and K.V. Mardia, “Statistical Shape Analysis”, John Wiley & Son, (1998).
M. Fréchet, “Les courbes aléatoires,” Bull. Inst. Internat. Statist., Vol. 38, pp.499–504, 1961.
Honkela, Timo “Description of Kohonen’s Self-Organizing Map.” http://www.mlab.uiah.fi/timo/som/thesis-som.html
D.G. Kendall, “Stochastic Geometry, chapter Foundation of a theory of random sets”, John Wiley Sons, New York, (1973) 322–376.
D.G. Kendall, “Shape-manifolds, Procrustean metrics, and complex projective spaces”, Bull. London Mathematical Society, (1984), 81–121.
D.G. Kendall, “A survey of the statistical theory of shape”, Statist. Sci., vol.4, no.2, (1989) 87–120.
J.T. Kent and K.V. Mardia, “Shape, procrustes tangent projections and bilateral symmetry”, Biometrika, (2001), 88:469–485.
T. Kohonen, “Self-Organizng Maps”, Springer, (2001).
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).
M. E. Leventon, E. Grimson, and O. Faugeras, “Statistical Shape Influence in Geodesic Active Contours”, Proc. IEEE Conf. CVPR (2000), 316–323.
G. Matheron, “Random Sets and Integral Geometry”, John Wiley & Sons, 1975.
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.
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.
S. Soatto and A. Yezzi, “Deformation: deformining motion, shape average and joint registration and segmentation of images, Computer Vision-ECCV2002.
J. Yang and J.S. Duncan, “3D image segmentation of deformable objects with shape apprearance joint prior models”, MICCAI, (2003), 573–580.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/0-387-29550-X_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-29549-7
Online ISBN: 978-0-387-29550-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)