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Region Matching with Missing Parts

  • Alessandro Duci
  • Anthony J. Yezzi
  • Sanjoy Mitter
  • Stefano Soatto
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2352)

Abstract

We present a variational approach to the problem of registering planar shapes despite missing parts. Registration is achieved through the evolution of a partial differential equation that simultaneously estimates the shape of the missing region, the underlying “complete shape” and the collection of group elements (Euclidean or affine) corresponding to the registration. Our technique applies both to shapes, for instance represented as characteristic functions (binary images), and to grayscale images, where all intensity levels evolve simultaneously in a partial differential equation. It can therefore be used to perform “region inpainting” and to register collections of images despite occlusions. The novelty of the approach lies on the fact that, rather than estimating the missing region in each image independently, we pose the problem as a joint registration with respect to an underlying “complete shape” from which the complete version of the original data is obtained via a group action.

Keywords

shape variational registration missing part inpainting 
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References

  1. 1.
    R. Azencott, F. Coldefy, and L. Younes. A distance for elastic matching in object recognition. Proc. 13th Intl. Conf. on Patt. Recog, 1:687–691, 1996.CrossRefGoogle Scholar
  2. 2.
    S. Belongie, J. Malik, and J. Puzicha. Matching shapes. In Proc. of the IEEE Intl. Conf. on Computer Vision, 2001.Google Scholar
  3. 3.
    D. Bereziat, I. Herlin, and L. Younes. Motion detection in meteorological images sequences: Two methods and their comparison. In Proc. of the SPIE, 1997.Google Scholar
  4. 4.
    M. Berger and G. Gerig. Deformable area-based template matching with application to low contrast imagery, 1998.Google Scholar
  5. 5.
    M. Burl, T. Leung, and P. Perona. Face localization via shape statistics. In Proc. Intl. Workshop on automatic face and gesture recognition, pages 154–159, Zurich, June 1995. IEEE Computer Soc.Google Scholar
  6. 6.
    T. K. Carne. The geometry of shape spaces. Proc. of the London Math. Soc. (3) 61, 3(61):407–432, 1990.CrossRefMathSciNetGoogle Scholar
  7. 7.
    H. Chui and A. Rangarajan. A new algorithm for non-rigid point matching. In Proc. of the IEEE Intl. Conf. on Comp. Vis. and Patt. Recog., pages 44–51, 2000.Google Scholar
  8. 8.
    M. Fischler and R. Elschlager. The representation and matching of pictorial structures. IEEE Transactions on Computers, 22(1):67–92, 1973.CrossRefGoogle Scholar
  9. 9.
    U. Grenander. General Pattern Theory. Oxford University Press, 1993.Google Scholar
  10. 10.
    U. Grenander and M. I. Miller. Representation of knowledge in complex systems. J. Roy. Statist. Soc. Ser. B, 56:549–603, 1994.zbMATHMathSciNetGoogle Scholar
  11. 11.
    S. H. Kang, T. F. Chan, and S. Soatto. Multiple image inpainting. In Proc. of the 3DPVT, Padova, IT, June 2002.Google Scholar
  12. 12.
    D. G. Kendall. Shape manifolds, procrustean metrics and complex projective spaces. Bull. London Math. Soc., 16, 1984.Google Scholar
  13. 13.
    B. Kimia, A. Tannebaum, and S. Zucker. Shapes, shocks, and deformations i: the components of two-dimensional shape and the reaction-diffusion space. Int’l J. Computer Vision, 15:189–224, 1995.CrossRefGoogle Scholar
  14. 14.
    R. Kimmel and A. Bruckstein. Tracking level sets by level sets: a method for solving the shape from shading problem. Computer Vision, Graphics and Image Understanding, (62)1:47–58, 1995.CrossRefGoogle Scholar
  15. 15.
    R. Kimmel, N. Kiryati, and A. M. Bruckstein. Multivalued distance maps for motion planning on surfaces with moving obstacles. IEEE Trans. Robot. & Autom., 14(3):427–435, 1998.CrossRefGoogle Scholar
  16. 16.
    M. Lades, C. Borbruggen, J. Buhmann, J. Lange, C. von der Malsburg, R. Wurtz, and W. Konen. Distortion invariatn object rcognition in the dynamic link architecture. IEEE Trans. on Computers, 42(3):300–311, 1993.CrossRefGoogle Scholar
  17. 17.
    H. Le and D. G. Kendall. The riemannian structure of euclidean shape spaces: a novel environment for statistics. The Annals of Statistics, 21(3):1225–1271, 1993.zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    R. Malladi, R. Kimmel, D. Adalsteinsson, V. Caselles G. Sapiro, and J. A. Sethian. A geometric approach to segmentation and analysis of 3d medical images. In Proc. Mathematical Methods in Biomedical Image Analysis Workshop, pages 21–22, 1996.Google Scholar
  19. 19.
    R. Malladi, J. A. Sethian, and B. C. Vemuri. Shape modeling with front propagation: A level set approach. IEEE Trans. on Pattern Analysis and Machine Intelligence, 17(2):158–175, 1995.CrossRefGoogle Scholar
  20. 20.
    K. V. Mardia and I. L. Dryden. Shape distributions for landmark data. Adv. appl. prob., 21(4):742–755, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    M. I. Miller and L. Younes. Group action, diffeomorphism and matching: a general framework. In Proc. of SCTV, 1999.Google Scholar
  22. 22.
    C. Nastar, B. Moghaddam, and A. Pentland. Generalized image matching: Statistical learning of physically-based deformations. In Proceedings of the Fourth European Conference on Computer Vision (ECCV’96), Cambridge, UK, April 1996.Google Scholar
  23. 23.
    S. Osher and J. Sethian. Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi equations. J. of Comp. Physics, 79:12–49, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    X. Pennec. Multiple Registration and Mean Rigid Shapes-Application to the 3D case. In I.L. Dryden K.V. Mardia, C.A. Gill, editor, Image Fusion and Shape Variability Techniques (16th Leeds Annual Statistical (LASR) Workshop), pages 178–185, july 1996.Google Scholar
  25. 25.
    Anand Rangarajan, Haili Chui, and Eric Mjolsness. A new distance measure for non-rigid image matching. In Energy Minimization Methods in Computer Vision and Pattern Recognition, pages 237–252, 1999.Google Scholar
  26. 26.
    C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia. A level set model for image classification. In in International Conference on Scale-Space Theories in Computer Vision, pages 306–317, 1999.Google Scholar
  27. 27.
    K. Siddiqi, A. Shokoufandeh, S. Dickinson, and S. Zucker. Shock graphs and shape matching, 1998.Google Scholar
  28. 28.
    P. Thompson and A. W. Toga. A surface-based technique for warping three-dimensional images of the brain. IEEE Trans. Med. Imaging, 15(4):402–417, 1996.CrossRefGoogle Scholar
  29. 29.
    R. C. Veltkamp and M. Hagedoorn. State of the art in shape matching. Technical Report UU-CS-1999-27, University of Utrecht, 1999.Google Scholar
  30. 30.
    A. Yezzi and S. Soatto. Stereoscopic segmentation. In Proc. of the Intl. Conf. on Computer Vision, pages 59–66, 2001.Google Scholar
  31. 31.
    L. Younes. Computable elastic distances between shapes. SIAM J. of Appl. Math., 1998.Google Scholar
  32. 32.
    A. Yuille. Deformable templates for face recognition. J. of Cognitive Neurosci., 3(1):59–70, 1991.CrossRefGoogle Scholar
  33. 33.
    S. Zhu, T. Lee, and A. Yuille. Region competition: Unifying snakes, region growing, energy /bayes/mdl for multi-band image segmentation. In Int. Conf. on Computer Vision, pages 416–423, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alessandro Duci
    • 1
    • 4
  • Anthony J. Yezzi
    • 2
  • Sanjoy Mitter
    • 3
  • Stefano Soatto
    • 4
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Georgia Institute of TechnologyAtlanta
  3. 3.Massachusetts Institute of TechnologyCambridge
  4. 4.University of California at Los AngelesLos Angeles

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