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The Color Monogenic Signal: Application to Color Edge Detection and Color Optical Flow

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Abstract

The aim of this paper is to define an extension of the analytic signal for a color image. We generalize the construction of the so-called monogenic signal to mappings with values in the vectorial part of the Clifford algebra ℝ5,0. Solving a Dirac equation in this context leads to a multiscale signal (relatively to the Poisson scale-space) which contains both structure and color information. The color monogenic signal can be used in a wide range of applications. Two examples are detailed: the first one concerns a multiscale geometric segmentation with respect to a given color; the second one is devoted to the extraction of the optical flow from moving objects of a given color.

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References

  1. Bracewell, R.N.: Two-Dimensional Imaging. Prentice Hall Signal Processing Series. Prentice Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  2. Bruhn, A., Weickert, J.: Lukas/Kanade meets Horn/Schunk: combining local and global optic flow. Int. J. Comput. Vis. 62(3), 211–231 (2005)

    Google Scholar 

  3. Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–714 (1986)

    Article  Google Scholar 

  4. Cumani, A.: Edge detection in multispectral images. Graph. Models Image Proc. 53(1), 40–51 (1991)

    Article  MATH  Google Scholar 

  5. Demarcq, G., Mascarilla, L., Courtellemont, P.: A metric and multiscale color segmentation using the color monogenic signal. In: Lecture Notes in Computer Sciences, vol. 5702, pp. 906–913. (2009)

    Google Scholar 

  6. Demarcq, G., Mascarilla, L., Courtellemont, P.: The color monogenic signal: a new framework for color image processing. Application to color optical flow. In: IEEE Proc. Int. Conf. on Image Processing (ICIP) (2009)

    Google Scholar 

  7. Di Zenzo, S.: A note on the gradient of a multi-image. Comput. Vis. Graph. Image Process. 33(1), 116–125 (1986)

    Article  Google Scholar 

  8. Ebling, J., Scheuermann, G.: Clifford Fourier transform on vector fields. IEEE Trans. Vis. Comput. Graph. 11(4), 469–479 (2005)

    Article  Google Scholar 

  9. Felsberg, M., Sommer, G.: The monogenic signal. IEEE Trans. Signal Process. 49(12), 3136–3144 (2001)

    Article  MathSciNet  Google Scholar 

  10. Felsberg, M., Sommer, G.: The monogenic scale-space: a unifying approach to phase-based image processing in scale-space. J. Math. Imaging Vis. 21, 5–26 (2004)

    Article  MathSciNet  Google Scholar 

  11. Felsberg, M.: Low-level image processing with the structure multivector. Ph.D. thesis, Christian-Albrechts University, Kiel (2002)

  12. Gevers, T.: Color Feature Detection: An Overview. CRC Press, Boca Raton (2006)

    Google Scholar 

  13. Gilbert, J.E., Murray, M.A.M.: Clifford Algebras and Dirac Operators in Harmonic Analysis. Cambridge University Press, Cambridge (1991)

    Book  MATH  Google Scholar 

  14. Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus. Dordrecht, Reidel (1984)

    MATH  Google Scholar 

  15. Horn, B., Schunk, B.: Determining optical flow. Artif. Intell. 17, 185–203 (1981)

    Article  Google Scholar 

  16. Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proc. Seventh International Joint Conference on Artificial Intelligence, pp. 674–679. Vancouver, Canada (1981)

    Google Scholar 

  17. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the Int. Conf. on Computer Vision, vol. 2, pp. 416–423. (2001)

    Google Scholar 

  18. Monga, O., Deriche, R., Malandain, G., Cocquerez, J.: Recursive filtering and edge closing: Two primary tools for 3D edge detection. In: Lecture Notes in Computer Sciences, Computer Vision, ECCV 90, vol. 427, pp. 56–65. (1990)

    Chapter  Google Scholar 

  19. Sapiro, G.: Color snakes. Comput. Vis. Image Underst. 68(2), 407–416 (1997)

    Article  MathSciNet  Google Scholar 

  20. Sommer, G.: Geometric Computing with Clifford Algebras: Theorical Foundations and Applications in Computer Vision and Robotics. Springer, Berlin (2001)

    Google Scholar 

  21. Tschumperlé, D.: Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE’s. Int. J. Comput. Vis. 68(1), 65–82 (2006)

    Article  Google Scholar 

  22. Sumengen, B., Manjunath, B.S.: Multi-scale edge detection and image segmentation. In: European Signal Processing Conference (EUSIPCO) (2005)

    Google Scholar 

  23. Ville, J.: Théorie et applications de la notion de signal analytique. Cables Transm. 2A, 61–74 (1948)

    Google Scholar 

  24. Wietzke, L., Sommer, G., Fleiscmann, O.: The geometry of 2d image signals. In: IEEE Proceedings CVPR 2009, pp. 1690–1697. (2009)

    Google Scholar 

  25. Zang, D., Wietzke, L., Schmaltz, C., Sommer, G.: Dense optical flow estimation from the monogenic curvature tensor. In: Proc. Scale-Space and Variational Methods, vol. 4485, pp. 239–250. (2007)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Laboratoire Mathématiques, Images, Applications (MIA), Université de La Rochelle, Avenue Michel Crépeau, 17042, La Rochelle Cedex, France

    Guillaume Demarcq, Laurent Mascarilla, Michel Berthier & Pierre Courtellemont

Authors
  1. Guillaume Demarcq
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  2. Laurent Mascarilla
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  3. Michel Berthier
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  4. Pierre Courtellemont
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Correspondence to Guillaume Demarcq.

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Demarcq, G., Mascarilla, L., Berthier, M. et al. The Color Monogenic Signal: Application to Color Edge Detection and Color Optical Flow. J Math Imaging Vis 40, 269–284 (2011). https://doi.org/10.1007/s10851-011-0262-6

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  • DOI: https://doi.org/10.1007/s10851-011-0262-6

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