Hierarchical Properties of Multi-resolution Optical Flow Computation

  • Yusuke Kameda
  • Atsushi Imiya
  • Tomoya Sakai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7584)


Most of the methods to compute optical flows are variational-technique-based methods, which assume that image functions have spatiotemporal continuities and appearance motions are small. In the viewpoint of the discrete errors of spatial- and time-differentials, the appropriate resolution for optical flow depends on both the resolution and the frame rate of images since there is a problem with the accuracy of the discrete approximations of derivatives. Therefore, for low frame-rate images, the appropriate resolution for optical flow should be lower than the resolution of the images. However, many traditional methods estimate optical flow with the same resolution as the images. Therefore, if the resolution of images is too high, down-sampling the images is effective for the variational-technique-based methods. In this paper, we analyze the appropriate resolutions for optical flows estimated by variational optical-flow computations from the viewpoint of the error analysis of optical flows. To analyze the appropriate resolutions, we use hierarchical structures constructed from the multi-resolutions of images. Numerical results show that decreasing image resolutions is effective for computing optical flows by variational optical-flow computations in low frame-rate sequences.


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  1. 1.
    Kameda, Y., Imiya, A.: Classification of Optical Flow by Constraints. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 61–68. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Kameda, Y., Imiya, A., Sakai, T.: Adaptive estimation of Lagrange Multiplier functions of constraint terms for variational computation of optical flow. The Transactions of the Institute of Electronics, Information and Communication Engineers D J95-D, 1644–1653 (2012) (Japanese)Google Scholar
  3. 3.
    Ohnishi, N., Imiya, A.: Featureless robot navigation using optical flow. Connection Science 17, 23–46 (2005)CrossRefGoogle Scholar
  4. 4.
    Klette, R., Kruger, N., Vaudrey, T., Pauwels, K., van Hulle, M., Morales, S., Kandil, F.I., Haeusler, R., Pugeault, N., Rabe, C., Lappe, M.: Performance of Correspondence Algorithms in Vision-Based Driver Assistance Using an Online Image Sequence Database. IEEE Transactions on Vehicular Technology 60, 2012–2026 (2011)CrossRefGoogle Scholar
  5. 5.
    Jagadeesh, V., Karthikeyan, S., Manjunath, B.S.: Spatio-temporal optical flow statistics (STOFS) for activity classification. In: Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing, ICVGIP 2010, pp. 178–182. ACM, New York (2010)CrossRefGoogle Scholar
  6. 6.
    Horn, B.K., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)CrossRefGoogle Scholar
  7. 7.
    Nagel, H.H., Enkelmann, W.: An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences. IEEE Transaction on Pattern Analysis and Machine Intelligence 8, 565–593 (1986)CrossRefGoogle Scholar
  8. 8.
    Weickert, J., Schnörr, C.: A theoretical framework for convex regularizers in PDE-based computation of image motion. International Journal of Computer Vision 45, 245–264 (2001)MATHCrossRefGoogle Scholar
  9. 9.
    Zimmer, H., Bruhn, A., Weickert, J.: Optic Flow in Harmony. International Journal of Computer Vision 93, 368–388 (2011)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Pock, T., Unger, M., Cremers, D., Bischof, H.: Fast and exact solution of Total Variation models on the GPU. In: CVPR Workshop on Visual Computer Vision on GPU’s, pp. 1–8 (2008)Google Scholar
  11. 11.
    Vaudrey, T., Rabe, C., Klette, R., Milburn, J.: Differences between stereo and motion behaviour on synthetic and real-world stereo sequences. In: 2008 23rd International Conference Image and Vision Computing, New Zealand, pp. 1–6. IEEE (2008)Google Scholar
  12. 12.
    Baker, S., Scharstien, D., Lewis, J.P., Roth, S., Black, M.J., Szeliski, R., Scharstein, D.: A Database and Evaluation Methodology for Optical Flow. International Journal of Computer Vision 92, 1–31 (2010)CrossRefGoogle Scholar
  13. 13.
    Barron, J.L., Fleet, D.J., Beauchemin, S.S., Burkitt, T.A.: Performance of optical flow techniques. International Journal of Computer Vision 12, 43–77 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yusuke Kameda
    • 1
  • Atsushi Imiya
    • 2
  • Tomoya Sakai
    • 3
  1. 1.Graduate School of Advanced Integration ScienceChiba UniversityInage-kuJapan
  2. 2.Institute of Media and Information TechnologyChiba UniversityInage-kuJapan
  3. 3.Graduate School of EngineeringNagasaki UniversityNagasakiJapan

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