Separable Time-Causal and Time-Recursive Spatio-Temporal Receptive Fields

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)

Abstract

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hubel, D.H., Wiesel, T.N.: Brain and Visual Perception: The Story of a 25-Year Collaboration. Oxford University Press (2005)Google Scholar
  2. 2.
    DeAngelis, G.C., Ohzawa, I., Freeman, R.D.: Receptive field dynamics in the central visual pathways. Trends in Neuroscience 18, 451–457 (1995)CrossRefGoogle Scholar
  3. 3.
    DeAngelis, G.C., Anzai, A.: A modern view of the classical receptive field: linear and non-linear spatio-temporal processing by V1 neurons. In: Chalupa, L.M., Werner, J.S., (eds.) The Visual Neurosciences, vol. 1, pp. 704–719. MIT Press (2004)Google Scholar
  4. 4.
    Adelson, E., Bergen, J.: Spatiotemporal energy models for the perception of motion. J. Optical Society of America A 2, 284–299 (1985)CrossRefGoogle Scholar
  5. 5.
    Zelnik-Manor, L., Irani, M.: Event-based analysis of video. In: Proc. Computer Vision and Pattern Recognition, Kauai Marriott, Hawaii, pp. II:123–II:130 (2001)Google Scholar
  6. 6.
    Laptev, I., Lindeberg, T.: Local descriptors for spatio-temporal recognition. In: MacLean, W.J. (ed.) SCVMA 2004. LNCS, vol. 3667, pp. 91–103. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  7. 7.
    Jhuang, H., Serre, T., Wolf, L., Poggio, T.: A biologically inspired system for action recognition. In: Int. Conf. on Computer Vision, pp. 1–8 (2007)Google Scholar
  8. 8.
    Shabani, A.H., Clausi, D.A., Zelek, J.S.: Improved spatio-temporal salient feature detection for action recognition. In: British Machine Vision Conf., pp. 1–12 (2011)Google Scholar
  9. 9.
    Fleet, D.J., Langley, K.: Recursive filters for optical flow. IEEE Trans. Pattern Analysis and Machine Intell. 17, 61–67 (1995)CrossRefGoogle Scholar
  10. 10.
    Lindeberg, T., Fagerström, D.: Scale-space with causal time direction. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 229–240. Springer, Heidelberg (1996) CrossRefGoogle Scholar
  11. 11.
    Lindeberg, T.: Generalized Gaussian scale-space axiomatics comprising linear scale-space, affine scale-space and spatio-temporal scale-space. J. of Mathematical Imaging and Vision 40, 36–81 (2011)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Lindeberg, T.: A computational theory of visual receptive fields. Biological Cybernetics 107, 589–635 (2013)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Lindeberg, T.: Scale-space for discrete signals. IEEE Trans. Pattern Analysis and Machine Intell. 12, 234–254 (1990)CrossRefGoogle Scholar
  14. 14.
    Koenderink, J.J.: Scale-time. Biological Cybernetics 58, 159–162 (1988)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Lindeberg, T.: Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction. J. Math. Imaging Vision 3, 349–376 (1993)CrossRefGoogle Scholar
  16. 16.
    Koenderink, J.J.: The structure of images. Biol. Cyb. 50, 363–370 (1984)MATHMathSciNetGoogle Scholar
  17. 17.
    Iijima, T.: Observation theory of two-dimensional visual patterns. Papers of Technical Group on Automata and Automatic Control, IECE, Japan (1962)Google Scholar
  18. 18.
    Florack, L.M.J., ter Haar Romeny, B.M., Koenderink, J.J., Viergever, M.A.: Scale and the differential structure of images. Image Vision Comp. 10, 376–388 (1992)Google Scholar
  19. 19.
    Pauwels, E.J., Fiddelaers, P., Moons, T., van Gool, L.J.: An extended class of scale-invariant and recursive scale-space filters. IEEE Trans. Pattern Analysis and Machine Intell. 17, 691–701 (1995)CrossRefGoogle Scholar
  20. 20.
    Weickert, J., Ishikawa, S., Imiya, A.: On the history of Gaussian scale-space axiomatics. In: Gaussian Scale-Space Theory, pp. 45–59. Springer (1997)Google Scholar
  21. 21.
    Duits, R., Florack, L., de Graaf, J., ter Haar Romeny, B.: On the axioms of scale space theory. J. of Mathematical Imaging and Vision 22, 267–298 (2004)CrossRefGoogle Scholar
  22. 22.
    Fagerström, D.: Spatio-temporal scale-spaces. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 326–337. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  23. 23.
    Koenderink, J.J., van Doorn, A.J.: Receptive field families. Biological Cybernetics 63, 291–298 (1990)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Florack, L.M.J., ter Haar Romeny, B.M., Koenderink, J.J., Viergever, M.A.: Families of tuned scale-space kernels. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 19–23. Springer, Heidelberg (1992) CrossRefGoogle Scholar
  25. 25.
    Tschirsich, M., Kuijper, M.: Notes on discrete Gaussian scale space. J. of Mathematical Imaging and Vision 51, 106–123 (2015)CrossRefMathSciNetGoogle Scholar
  26. 26.
    den Brinker, A.C., Roufs, J.A.J.: Evidence for a generalized Laguerre transform of temporal events by the visual system. Biological Cybernetics 67, 395–402 (1992)CrossRefMATHGoogle Scholar
  27. 27.
    Rivero-Moreno, C.J., Bres, S.: Spatio-temporal primitive extraction using Hermite and Laguerre filters for early vision video indexing. In: Campilho, A.C., Kamel, M.S. (eds.) ICIAR 2004. LNCS, vol. 3211, pp. 825–832. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  28. 28.
    van der Berg, E.S., Reyneke, P.V., de Ridder, C.: Rotational image correlation in the Gauss-Laguerre domain. In: SPIE, vol. 9257, pp. 92570F-1–92570F-17 (2014)Google Scholar
  29. 29.
    Fourtes, M.G.F., Hodgkin, A.L.: Changes in the time scale and sensitivity in the omatadia of limulus. Journal of Physiology 172, 239–263 (1964)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computational Biology, School of Computer Science and CommunicationKTH Royal Institute of TechnologyStockholmSweden

Personalised recommendations