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Using the Fisher-Rao Metric to Compute Facial Similarity

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6111))

Abstract

In this paper we show how the Fisher-Rao metric can be used to compute the similarity of fields of surface normals, under the assumption of a von-Mises Fisher (vMF) distribution. We use the similarity measure to analyse differences in facial shape due to gender and expression. Finally, we show the results achieved using BU-3DFEDB and Max Planck datasets.

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References

  1. Bremmer, D., Demaine, E., Erickson, J., Lacono, J., Langerman, S., Morin, P., Toussaint, G.: Output-sensitive algorithms for computing nearest-neighbor decision boundaries (2005)

    Google Scholar 

  2. Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models, their training and application. Computer Vision and Image Understanding 61, 38–59 (1995)

    Article  Google Scholar 

  3. Deuflhard, P.: Newton methods for nonlinear problems. affine invariance and adaptive algoritms (2004)

    Google Scholar 

  4. Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. Wiley Series in Probability and Statistics (1998)

    Google Scholar 

  5. Jurgen, J.: Riemannian Geometry and Geometry Analysis, 5th edn. Springer, Heidelberg (2008), ISBN 978-3540773405

    Google Scholar 

  6. Le, H., Small, C.G.: Multidimensional scaling of simplex shapes. Pattern Recognition 32(9), 1601–1613 (1999)

    Article  Google Scholar 

  7. Mardia, K.V., Jupp, P.E.: Directional Statistics. John Wiley and Sons Ltd., Chichester (2000)

    MATH  Google Scholar 

  8. Maybank, S.J.: Detection of image structures using the fisher information and the rao metric. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2) (2004)

    Google Scholar 

  9. Maybank, S.J.: The fisher-rao metric for projective transformations of the line 63, 191–206 (2005)

    Google Scholar 

  10. Milligan, G.W., Cooper, M.C.: A study of the comparability of external criteria for hierarchical cluster analysis (1986)

    Google Scholar 

  11. Mio, W., Badlyang, D., Liu, X.: A computational approach to fisher information geometry with applications to image analysis. In: Rangarajan, A., Vemuri, B.C., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 18–33. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Pennec, X.: Probabilities and statistics of riemannian manifolds: A geometric approach. Research Report RR-5093, INRIA (2004)

    Google Scholar 

  13. Peter, A., Rangarajan, A.: A new closed-form information metric for shape analysis. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 249–256. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Peter, A., Rangarajan, A.: Shape analysis using the fisher-rao riemannian metric: unifying shape representation and deformation. In: 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, pp. 1164–1167 (2006)

    Google Scholar 

  15. Rand, M.W.: Objective criteria for the evaluation of clustering methods (1971)

    Google Scholar 

  16. Small, C.G.: The Statistical Theory of Shape. Springer, Heidelberg (1996)

    MATH  Google Scholar 

  17. Stephens, M.A.: Use of the von mises distribution to analyse continuous proportions (1982)

    Google Scholar 

  18. Toussaint, G.T.: Geometric proximity graphs for improving nearest neighbor methods in instance-based learning and data mining (2005)

    Google Scholar 

  19. Yeung, K.Y., Ruzzo, L.: Principal component analysis for clustering gene expression data (2001)

    Google Scholar 

  20. Zhang, J., Zhang, X., Krim, H., Walter, G.G.: Object recognition and recognition in shape spaces. Pattern Recognition 36, 1143–1154 (2003)

    Article  Google Scholar 

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Ceolin, S., Hancock, E.R. (2010). Using the Fisher-Rao Metric to Compute Facial Similarity. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2010. Lecture Notes in Computer Science, vol 6111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13772-3_39

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  • DOI: https://doi.org/10.1007/978-3-642-13772-3_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13771-6

  • Online ISBN: 978-3-642-13772-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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