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Statistical Shape Models Using Elastic-String Representations

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Computer Vision – ACCV 2006 (ACCV 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3851))

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Abstract

To develop statistical models for shapes, we utilize an elastic string representation where curves (denoting shapes) can bend and locally stretch (or compress) to optimally match each other, resulting in geodesic paths on shape spaces. We develop statistical models for capturing variability under the elastic-string representation. The basic idea is to project observed shapes onto the tangent spaces at sample means, and use finite-dimensional approximations of these projections to impose probability models. We investigate the use of principal components for dimension reduction, termed tangent PCA or TPCA, and study (i) Gaussian, (ii) mixture of Gaussian, and (iii) non-parametric densities to model the observed shapes. We validate these models using hypothesis testing, statistics of likelihood functions, and random sampling. It is demonstrated that a mixture of Gaussian model on TPCA captures best the observed shapes.

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References

  1. Klassen, E., Srivastava, A., Mio, W., Joshi, S.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Pattern Analysis and Machine Intelligence 26, 372–383 (2004)

    Article  Google Scholar 

  2. Younes, L.: Optimal matching between shapes via elastic deformations. Journal of Image and Vision Computing 17, 381–389 (1999)

    Article  Google Scholar 

  3. Michor, P.W., Mumford, D.: Riemannian geometries on spaces of plane curves. Journal of the European Mathematical Society (2005) (to appear)

    Google Scholar 

  4. Srivastava, A., Joshi, S., Mio, W., Liu, X.: Statistical shape analysis: Clustering, learning and testing. IEEE Transactions on Pattern Analysis and Machine Intelligence 27, 590–602 (2005)

    Article  Google Scholar 

  5. Mio, W., Srivastava, A.: Elastic string models for representation and analysis of planar shapes. In: Proc. of IEEE Computer Vision and Pattern Recognition (2004)

    Google Scholar 

  6. Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. John Wiley & Son, Chichester (1998)

    MATH  Google Scholar 

  7. Le, H.L., Kendall, D.G.: The Riemannian structure of Euclidean shape spaces: a novel environment for statistics. Annals of Statistics 21, 1225–1271 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Karcher, H.: Riemann center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics 30, 509–541 (1977)

    Article  MATH  MathSciNet  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Srivastava, A., Jain, A., Joshi, S., Kaziska, D. (2006). Statistical Shape Models Using Elastic-String Representations. In: Narayanan, P.J., Nayar, S.K., Shum, HY. (eds) Computer Vision – ACCV 2006. ACCV 2006. Lecture Notes in Computer Science, vol 3851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11612032_62

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  • DOI: https://doi.org/10.1007/11612032_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31219-2

  • Online ISBN: 978-3-540-32433-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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