Tensor Processing for Texture and Colour Segmentation

  • Rodrigo de Luis-García
  • Rachid Deriche
  • Mikael Rousson
  • Carlos Alberola-López
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3540)

Abstract

In this paper, we propose an original approach for texture and colour segmentation based on the tensor processing of the nonlinear structure tensor. While the tensor structure is a well established tool for image segmentation, its advantages were only partly used because of the vector processing of that information. In this work, we use more appropriate definitions of tensor distance grounded in concepts from information theory and compare their performance on a large number of images. We clearly show that the traditional Frobenius norm-based tensor distance is not the most appropriate one. Symmetrized KL divergence and Riemannian distance intrinsic to the manifold of the symmetric positive definite matrices are tested and compared. Adding to that, the extended structure tensor and the compact structure tensor are two new concepts that we present to incorporate gray or colour information without losing the tensor properties. The performance and the superiority of the Riemannian based approach over some recent studies are demonstrated on a large number of gray-level and colour data sets as well as real images.

Keywords

Colour Image Segmentation Method Geodesic Distance Structure Tensor Texture Segmentation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bigun, J., Grandlund, G.H., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans. on PAMI 13(8), 775–790 (1991)Google Scholar
  2. 2.
    Bigun, J., Grandlund, G.H.: Optimal orientation detection of linear symmetry. In: Proc. 1st IEEE ICCV, London (June 1987)Google Scholar
  3. 3.
    Bovik, A.C., Clark, M., Geisler, W.S.: Multichannel texture analysis using localized spatial filters. IEEE Trans. on PAMI 12(1), 55–73 (1990)Google Scholar
  4. 4.
    Brox, T., Weickert, J.: Nonlinear matrix diffusion for optic flow estimation. In: Van Gool, L. (ed.) DAGM 2002. LNCS, vol. 2449, pp. 446–453. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Brox, T., Rousson, M., Deriche, R., Weickert, J.: Unsupervised segmentation incorporating colour, texture, and motion. INRIA, Research Rep. 4760 (march 2003)Google Scholar
  6. 6.
    Brox, T., Weickert, J., Burgeth, B., Mrázek, P.: Nonlinear structure tensors, Preprint No. 113, Department of Mathematics, Saarland University, Saarbrücken, Germany (October 2004)Google Scholar
  7. 7.
    Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. on IP 10(2), 266–277 (2001); Pattern Recognition 36(9), 1929-1943 (2003)MATHGoogle Scholar
  8. 8.
    Cremers, D., Tischhauser, F., Weickert, J., Schnorr, C.: Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional. International Journal of Computer Vision 50(3), 295–313 (2002)MATHCrossRefGoogle Scholar
  9. 9.
    Dervieux, A., Thomasset, F.: A finite element method for the simulation of Rayleigh-Taylor instability. Lecture Notes in Mathematics 771, 145–159 (1979)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Dervieux, A., Thomasset, F.: Multifluid incompressible flows by a finite element method. International Conference on Numerical Methods in Fluid Dynamics, 158–163 (1980)Google Scholar
  11. 11.
    Feddern, C., Weickert, J., Burgeth, B., Welk, M.: Curvature-driven PDE methods for matrix-valued images., Technical Report No. 104, Department of Mathematics, Saarland University, Saarbrücken, Germany (April 2004)Google Scholar
  12. 12.
    Foerstner, W., Gulch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: Intercomm. Conf. on Fast Proc. of Photogrammetric. Data, Interlaken, June 1987, pp. 281–305 (1987)Google Scholar
  13. 13.
    Lenglet, C., Rousson, M., Deriche, R., Faugeras, O.: Statistics on multivariate normal distributions: A geometric approach and its application to diffusion tensor mri. INRIA, Research Report 5242 (June 2004)Google Scholar
  14. 14.
    Lenglet, C., Rousson, M., Deriche, R., Faugeras, O.: Toward segmentation of 3D probability density fields by surface evolution: Application to diffusion mri. INRIA, Research Rep. 5243 (June 2004)Google Scholar
  15. 15.
    Lenglet, C., Rousson, M., Deriche, R.: Segmentation of 3d probability density fields by surface evolution: Application to diffusion mri. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 18–25. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Leventon, M.E., Faugeras, O., Grimson, W.E.L., Wells Iii, W.M.: Level set based segmentation with intensity and curvature priors. In: Proc. of the IEEE Workshop on MMBIA, Hilton Head, SC, USAs, June 2000, pp. 4–11 (2000)Google Scholar
  17. 17.
    de Luis-Garcia, R., Deriche, R., Lenglet, C., Rousson, M.: Tensor processing for texture and colour segmentation. INRIA, Research. Rep. (In press)Google Scholar
  18. 18.
    Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: A level set approach. IEEE Trans. on PAMI 17(2), 158–175 (1995)Google Scholar
  19. 19.
    Paragios, N., Deriche, R.: Geodesic active regions and level set methods for supervised texture segmentation. The International Journal of Computer Vision 46(3), 223–247 (2002)MATHCrossRefGoogle Scholar
  20. 20.
    Paragios, N., Deriche, R.: Geodesic active regions: A new framework to deal with frame partition problems in computer vision. Journal of Visual Communication and Image Representation 13, 249–268 (2002)CrossRefGoogle Scholar
  21. 21.
    Rousson, M., Brox, T., Deriche, R.: Active unsupervised texture segmentation on a diffusion based feature space. In: Proc. of CVPR, Madison, Wisconsin, USA (June 2003)Google Scholar
  22. 22.
    Rousson, M., Lenglet, C., Deriche, R.: Level set and region based surface propagation for diffusion tensor mri segmentation. In: Proc. of the Computer Vision Approaches to Medical Image Analysis Workshop, Prague (May 2004)Google Scholar
  23. 23.
    Osher, S., Sethian, J.A.: Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulation. Journal of Computational Physics 79, 12–49 (1988)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Wang, Z., Vemuri, B.C.: An affine invariant tensor dissimilarity measure and its applications to tensor-valued image segmentation. In: Proc. of the IEEE CVPR, Washington DC, USA, pp. 228–233 (2004)Google Scholar
  25. 25.
    Wang, Z., Vemuri, B.C.: Tensor field segmentation using region based active contour model. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 304–315. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Rodrigo de Luis-García
    • 1
  • Rachid Deriche
    • 2
  • Mikael Rousson
    • 2
  • Carlos Alberola-López
    • 1
  1. 1.ETSI TelecomunicaciónUniversity of ValladolidValladolidSpain
  2. 2.Projet OdysséeINRIA Sophia-AntipolisFrance

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