Skip to main content
SpringerLink
Log in

Motion Analysis with the Radon Transform on Log-Polar Images

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

Image projections provide an effective way of describing image contents or estimate particular kinds of motion. However, most (if not all) of previous literature on projections has been done on Cartesian images. In contrast, the work described in this paper is aimed at exploring how projections can be defined on log-polar images and how they perform in estimating motion. In the proposed algorithm, a set of projection signals is computed in two consecutive frames. Then, 1D affine motion between each pair of corresponding projection signals is estimated. Finally, 2D image affine motion is derived from the set of estimated 1D motion parameters, using a 2D-1D motion mapping model (MMM). A reduced, 5-parameter, affine motion model can be estimated with this MMM. The algorithm is implemented in both, log-polar and Cartesian images. Synthetic motion is used for a careful analysis of the strengths and weaknesses of the algorithm. The comparison of the results with log-polar and Cartesian images reveal that the limitations of the approach are due to the MMM, rather than to the inherent difficulties and distortions introduced by the space-variant nature of log-polar images. Another significant finding is that Cartesian images require much more pixels than log-polar images to get comparable estimation performance.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahrns, I., Neumann, H.: A view-based approach for real-time fixation using log-polar mapping. In: Freksa, C. (ed.) Proc. in Artificial Intelligence, pp. 89–96, June 1998

  2. Barnes, N., Sandini, G.: Direction control for an active docking behavior based on the rotational component of log-polar optic flow. In: Tsai, W.-H., Lee, H.-J. (eds.) European Conf. on Computer Vision, vol. 2, pp. 167–181. Dublin, Ireland, June 2000

  3. Bazin, P.-L., Vézien, J.-M.: Integration of geometric elements, euclidean relations, and motion curves for parametric shape and motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 27(12), 1960–1976 (2005)

    Article  Google Scholar 

  4. Bernardino, A., Santos-Victor, J.: Visual behaviors for binocular tracking. Robot. Auton. Syst. 25, 137–146 (1998)

    Article  Google Scholar 

  5. Bernardino, A., Santos-Victor, J., Sandini, G.: Foveated active tracking with redundant 2D motion parameters. Robot. Auton. Syst. 39(3–4), 205–221 (2002)

    Article  Google Scholar 

  6. Bolduc, M., Levine, M.D.: A review of biologically motivated space-variant data reduction models for robotic vision. Comput. Vis. Image Underst. (CVIU) 69(2), 170–184 (1998)

    Article  Google Scholar 

  7. Capurro, C., Panerai, F., Sandini, G.: Dynamic vergence using log-polar images. Int. J. Comput. Vis. 24(1), 79–94 (1997)

    Article  Google Scholar 

  8. Daniilidis, K., Krüger, V.: Optical flow computation in the log-polar plane. In: Hlaváč, V., Šára, R. (eds.) Int. Conf. on Computer Analysis of Images and Patterns (CAIP), pp. 65–72. Springer, Berlin (1995)

    Google Scholar 

  9. Dias, J., Araujo, H., Paredes, C., Batista, J.: Optical normal flow estimation on log-polar images. A solution for real-time binocular vision. Real-Time Imaging 3(3), 213–228 (1997)

    Article  Google Scholar 

  10. Fermüller, C., Aloimonos, Y.: Qualitative egomotion. Int. J. Comput. Vis. 15, 7–29 (1995)

    Article  Google Scholar 

  11. Hager, G.D., Belhumeur, P.N.: Efficient region tracking with parametric models of geometry and illumination. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 20(10), 1025–1039 (1998)

    Article  Google Scholar 

  12. Harris, J., Stocker, H.: Handbook of Mathematics and Computation Science. Springer, New York (1998)

    Google Scholar 

  13. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  14. Huang, Y., Palaniappan, K., Zhuang, X., Cavanaugh, J.E.: Optic flow field segmentation and motion estimation using a robust genetic partitioning algorithm. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 17(12), 1177–1190 (1995)

    Article  Google Scholar 

  15. Kadyrov, A., Petrou, M.: Affine parameter estimation from the Trace transform. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 28(10), 1631–1645 (2006)

    Article  Google Scholar 

  16. Kang, S., Lee, S.-W.: Real-time tracking of multiple objects in space-variant vision based on magnocellular visual pathway. Pattern Recognit. 35(10), 2031–2040 (2002)

    Article  MATH  Google Scholar 

  17. Kim, Y.-H., Martínez, A.M., Kak, A.C.: Robust motion estimation under varying illumination. Image Vis. Comput. (IVC) 23(4), 365–375 (2005)

    Article  Google Scholar 

  18. Krüger, V.: Optical flow estimation in the complex logarithmic plane. Master’s thesis, University of Kiel, Germany (1995)

  19. Manzotti, R., Gasteratos, A., Metta, G., Sandini, G.: Disparity estimation on log-polar images and vergence control. Comput. Vis. Image Underst. (CVIU) 83, 97–117 (2001)

    Article  MATH  Google Scholar 

  20. Milanfar, P.: A model of the effect of image motion in the Radon transform domain. IEEE Trans. Image Process. 8(9), 1276–1281 (1999)

    Article  MathSciNet  Google Scholar 

  21. Montoliu, R., Pla, F.: Accurate image registration by combinig feature-based matching and GLS-based motion estimation. In: International Conference on Computer Vision Theory and Applications, pp. 386–389, March 2007

  22. Okajima, N., Nitta, H., Mitsuhashi, W.: Motion estimation and target tracking in the log-polar geometry. In: 17th Sensor Symposium. Kawasaki, Japan, May 2000

  23. Oshiro, N., Maru, N., Nishikawa, A., Miyazaki, F.: Binocular tracking using log polar mapping. In: IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, vol. 2, pp. 791–798. Osaka, Japan, November 1996

  24. Robinson, D., Milanfar, P.: Efficiency and accuracy tradeoffs in using projections for motion estimation. In: 35th Asilomar Conference on Signals, Systems, and Computers, pp. 545–550, November 2001

  25. Robinson, D., Milanfar, P.: Fast local and global projection-based methods for affine motion estimation. J. Math. Imaging Vis. 18(1), 35–54 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  26. Sandini, G., Metta, G.: Retina-like sensors: motivations, technology and applications. In: Barth, F.G., Humphrey, J.A., Secomb, T.W. (eds.) Sensors and Sensing in Biology and Engineering. Springer, New York (2003)

    Google Scholar 

  27. Schwartz, E.L.: Spatial mapping in the primate sensory projection: Analytic structure and relevance to perception. Biol. Cybern. 25, 181–194 (1977)

    Article  Google Scholar 

  28. Shin, C.W., Inokuchi, S., Kim, K.I.: Retina-like visual sensor for fast tracking and navigation robots. Mach. Vis. Appl. 10, 1–8 (1997)

    Article  Google Scholar 

  29. Silva, C., Santos-Victor, J.: Egomotion estimation using log-polar images. In: Int. Conf. on Computer Vision. Bombay, India, January 1998

  30. Stiller, C., Konrad, J.: Estimating motion in image sequences: A tutorial on modeling and computation of 2D motion. IEEE Signal Process. Mag. 16(4), 70–91 (1999)

    Article  Google Scholar 

  31. Swain, M., Stricker, M.: Promising directions in active vision. Int. J. Comput. Vis. 11(2), 109–126 (1993)

    Article  Google Scholar 

  32. Tistarelli, M., Sandini, G.: On the advantages of polar and log-polar mapping for direct estimation of time-to-impact from optical flow. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 15, 401–410 (1993)

    Article  Google Scholar 

  33. Traver, V.J., Pla, F.: Motion estimation and figure-ground segmentation in log-polar images. In: Int. Conf. on Pattern Recognition (ICPR), pp. 166–169. Québec, Canada, August 2002

  34. Traver, V.J., Pla, F.: Radon-like transforms in log-polar images for affine motion estimation. In: Portuguese Conf. on Pattern Recognition. Aveiro, Portugal, June 2002

  35. Tunley, H., Young, D.: First order optic flow from log-polar sampled images. In: Eklundh, J.-O. (ed.) European Conf. on Computer Vision. LNCS, vol. 800, pp. 132–137. Springer, New York (1994)

    Google Scholar 

  36. Venkatachalapathy, K., Krishnamoorthy, R., Viswanath, K.: A new adaptive search strategy for fast block based motion estimation algorithms. J. Vis. Commun. Image Represent. 15(2), 203–213 (2004)

    Article  Google Scholar 

  37. Wilson, J.C., Hodgson, R.M.: Log-polar mapping applied to pattern representation and recognition. In: Computer Vision and Image Processing, pp. 245–277. Academic Press, New York (1992)

    Google Scholar 

  38. Yeasin, M.: Optical flow in log-mapped image plane: A new approach. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 24(1), 125–131 (2002)

    Article  Google Scholar 

  39. Zokai, S., Wolberg, G.: Image registration using log-polar mappings for recovery of large-scale similarity and projective transformations. IEEE Trans. Image Process. 14(10), 1422–1434 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dep. Llenguatges i Sistemes Informàtics, Universitat Jaume I, Campus Riu Sec, Edifici TI, 12080, Castelló, Spain

    V. Javier Traver & Filiberto Pla

Authors
  1. V. Javier Traver
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Filiberto Pla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Javier Traver.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Traver, V.J., Pla, F. Motion Analysis with the Radon Transform on Log-Polar Images. J Math Imaging Vis 30, 147–165 (2008). https://doi.org/10.1007/s10851-007-0046-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-007-0046-1

Keywords

Search

Navigation