Skip to main content
Log in

Reaction–diffusion algorithm for stereo disparity detection

  • Original Paper
  • Published:
Machine Vision and Applications Aims and scope Submit manuscript

Abstract

The present paper proposes a novel stereo algorithm utilizing multi-sets of reaction–diffusion equations. The problem of detecting a stereo disparity map becomes the segmentation problem, in which the uniqueness assumption and the continuity assumption on disparity distribution are taken into account. A set of reaction–diffusion equations realizes the continuity assumption, while a mutual-inhibition mechanism among the multi-sets realizes the uniqueness one. In addition, each set of equations has a self-inhibition mechanism, which is necessary for the reaction-diffusion equations applied to stereo disparity detection. Performance of the proposed algorithm is evaluated for well-known test stereo images.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. Int. J. Comp. Vis. 47(1/2/3), 7–42 (2002)

    Article  MATH  Google Scholar 

  2. Brown, M.Z., Burschka, D., Hager, G.D.: Advances in computational stereo. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003)

    Article  Google Scholar 

  3. Marr, D., Poggio, T.: Cooperative computation of stereo disparity. Science 194, 283–287 (1976)

    Article  Google Scholar 

  4. Marr, D., Palm, G., Poggio, T.: Analysis of a cooperative stereo algorithm. Biol. Cybern. 28, 223–239 (1978)

    Article  Google Scholar 

  5. Zitnick, C.L., Kanade, T.: A cooperative algorithm for stereo matching and occlusion detection. IEEE Trans. Pattern Anal. Mach. Intell. 22(7), 675–684 (2000)

    Article  Google Scholar 

  6. Marr, D., Hildreth, E.: Theory of edge detection. Proc. R. Soc. Lond. B 207, 187–217 (1980)

    Article  Google Scholar 

  7. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)

    Article  Google Scholar 

  8. Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. Int. J. Comp. Vis. 52(2/3), 189–203 (2003)

    Article  Google Scholar 

  9. Kuhnert, L.: A new optical photochemical memory device in a light-sensitive chemical active medium. Nature 319, 393–394 (1986)

    Article  Google Scholar 

  10. Kuhnert, L., Agladze, K.I., Krinsky, V.I.: Image processing using light-sensitive chemical waves. Nature 337, 244–247 (1989)

    Article  Google Scholar 

  11. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)

    Google Scholar 

  12. FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445–466 (1961)

    Article  Google Scholar 

  13. Nagumo, J., Arimoto, S., Yoshizawa, S.: An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061–2070 (1962)

    Article  Google Scholar 

  14. Asai, T., Costello, B.D.L., Adamatzky, A.: Silicon implementation of a chemical reaction-diffusion processor for computation of Voronoi diagram. Int. J. Bifurcat. Chaos 15(10), 3307–3320 (2005)

    Article  Google Scholar 

  15. Adamatzky, A., Costello, B.D.L., Asai, T.: Reaction-diffusion Computers. Elsevier, Amsterdam (2005)

    Google Scholar 

  16. Nomura, A., Ichikawa, M., Miike, H., Ebihara, M., Mahara, H., Sakurai, T.: Realizing visual functions with the reaction-diffusion mechanism. J. Phys. Soc. Jpn. 72(9), 2385–2395 (2003)

    Article  Google Scholar 

  17. Ebihara, M., Mahara, H., Sakurai, T., Nomura, A., Osa, A., Miike, H.: Segmentation and edge detection of noisy image and low contrast image based on a reaction-diffusion model. (in Japanese) J. Inst. Image Electron. Eng. Jpn. 32(4), 378–385 (2003)

    Google Scholar 

  18. Nomura, A., Ichikawa, M., Miike, H.: Realizing the grouping process with the reaction-diffusion model. (in Japanese) IPSJ Trans. Comp. Vis. Image Media 45(SIG 8/CVIM-9), 26–39 (2004)

    Google Scholar 

  19. Julesz, B.: Binocular depth perception of computer-generated patterns. Bell Syst. Tech. J. 39(5), 1125–1162 (1960)

    Google Scholar 

  20. Turing, A.M.: The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37–72 (1952)

    Article  Google Scholar 

  21. Murray, J.D.: Mathematical biology. Springer, Berlin (1989)

    MATH  Google Scholar 

  22. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C. Cambridge University Press, Cambridge (1988)

    MATH  Google Scholar 

  23. Scharstein, D., Szeliski, R.: Middlebury stereo vision page. http://vision.middlebury.edu/stereo/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Atsushi Nomura.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nomura, A., Ichikawa, M. & Miike, H. Reaction–diffusion algorithm for stereo disparity detection. Machine Vision and Applications 20, 175–187 (2009). https://doi.org/10.1007/s00138-007-0117-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00138-007-0117-8

Keywords

Navigation