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The Mean Boundary Curve of Anatomical Objects

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Advanced Concepts for Intelligent Vision Systems (ACIVS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7517))

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Abstract

In this paper, we develop an algorithm to compute the mean shape of a collection of planar curves for the computation of the mean shape of a collection of organs. We first define the relative distortion of a pair of curves using curvatures of curves. Then, we derive the mean of curves as the curve which minimises the total distortion of a collection of shapes.

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References

  1. Hill, D.L.G., et al.: Medical image registration. Phys. Med. Biol. 46, R1–R45 (2001)

    Google Scholar 

  2. Fischer, B., Modersitzki, J.: Ill-posed medicine- an introduction to image registration. Inverse Problem 24, 1–17 (2008)

    Article  MathSciNet  Google Scholar 

  3. Rumpf, M., Wirth, B.: A nonlinear elastic shape averaging approach. SIAM Journal on Imaging Sciences 2, 800–833 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Sebastian, T.B., Klein, P.N., Kimia, B.B.: On aligning curves. IEEE Trans. PAMI 25, 116–125 (2003)

    Article  Google Scholar 

  5. Baeza-Yates, R., Valiente, G.: An image similarity measure based on graph matching. In: Proc. 7th Int. Symp. String Processing and Information Retrieval, pp. 8–38 (2000)

    Google Scholar 

  6. Riesen, K., Bunke, H.: Approximate graph edit distance computation by mean s of bipartite graph matching. Image and Vision Computing 27, 950–959 (2009)

    Article  Google Scholar 

  7. Mémoli, F.: Gromov-Hausdorff distances in Euclidean spaces. In: NORDIA-CVPR (2008)

    Google Scholar 

  8. Arrate, F., Tilak Ratnanather, J., Younes, L.: Diffeomorphic active contours. SIAM J. Imaging Sciences 3, 176–198 (2010)

    Article  MATH  Google Scholar 

  9. Grigorescu, C., Petkov, N.: Distance sets for shape filters and shape recognition. IEEE Trans. IP 12, 1274–1286 (2003)

    MathSciNet  Google Scholar 

  10. Tănase, M., Veltkamp, R.C., Haverkort, H.J.: Multiple Polyline to Polygon Matching. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 60–70. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Arkin, E.M., Chew, L.P., Huttenlocher, D.P., Kedem, K., Mitchell, J.S.B.: An Efficiently Computable Metric for Comparing Polygonal Shapes. IEEE Trans. PAMI 13, 209–216 (1991)

    Article  Google Scholar 

  12. Stegmann, M.B., Gomez, D.D.: A brief introduction to statistical shape analysis, Informatics and Mathematical Modelling, Technical University of Denmark (2002), http://www2.imm.dtu.dk/pubdb/p.php?403

  13. Müller, M.: Information Retrieval for Music and Motion, ch. 4. Springer (2007)

    Google Scholar 

  14. Keogh, E.J., Pazzani, M.J.: Derivative dynamic time warping. In: First SIAM International Conference on Data Mining, SDM 2001 (2001), http://www.cs.ucr.edu/~eamonn/

  15. Srivastava, A., Joshi, S., Mio, W., Liu, X.: Statistical shape analysis: Clustering, learning, and testing. IEEE Trans. PAMI 27, 590–602 (2005)

    Article  Google Scholar 

  16. Sebastian, T.B., Klein, P.N., Kimia, B.B.: On aligning curves. PAMI 25, 116–125 (2003)

    Article  Google Scholar 

  17. Marques, J.S., Abrantes, A.J.: Shape alignment? optimal initial point and pose estimation. Pattern Recognition Letters 18 (1997)

    Google Scholar 

  18. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. IJCV 1, 321–331 (1988)

    Article  Google Scholar 

  19. Sharon, E., Mumford, D.: 2D-shape analysis using conformal mapping. IJCV 70, 55–75 (2006)

    Article  Google Scholar 

  20. Mumford, D., Shah, J.: Boundary detection by minimizing functionals. In: Proc. CVP 1985, pp. 22–26 (1985)

    Google Scholar 

  21. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. on Pure and Applied Math. bXLII, 577–684 (1989)

    Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Morita, K., Imiya, A., Sakai, T., Hontan, H., Masutani, Y. (2012). The Mean Boundary Curve of Anatomical Objects. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P., Zemčík, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2012. Lecture Notes in Computer Science, vol 7517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33140-4_28

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  • DOI: https://doi.org/10.1007/978-3-642-33140-4_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33139-8

  • Online ISBN: 978-3-642-33140-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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