OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 13 — Dec. 2, 2009

The relationship between optimal and biologically plausible decoding of stimulus velocity in the retina

Edmund C. Lalor, Yashar Ahmadian, and Liam Paninski  »View Author Affiliations

JOSA A, Vol. 26, Issue 11, pp. B25-B42 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (520 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A major open problem in systems neuroscience is to understand the relationship between behavior and the detailed spiking properties of neural populations. We assess how faithfully velocity information can be decoded from a population of spiking model retinal neurons whose spatiotemporal receptive fields and ensemble spike train dynamics are closely matched to real data. We describe how to compute the optimal Bayesian estimate of image velocity given the population spike train response and show that, in the case of global translation of an image with known intensity profile, on average the spike train ensemble signals speed with a fractional standard deviation of about 2% across a specific set of stimulus conditions. We further show how to compute the Bayesian velocity estimate in the case where we only have some a priori information about the (naturalistic) spatial correlation structure of the image but do not know the image explicitly. As expected, the performance of the Bayesian decoder is shown to be less accurate with decreasing prior image information. There turns out to be a close mathematical connection between a biologically plausible “motion energy” method for decoding the velocity and the Bayesian decoder in the case that the image is not known. Simulations using the motion energy method and the Bayesian decoder with unknown image reveal that they result in fractional standard deviations of 10% and 6%, respectively, across the same set of stimulus conditions. Estimation performance is rather insensitive to the details of the precise receptive field location, correlated activity between cells, and spike timing.

© 2009 Optical Society of America

OCIS Codes
(330.4060) Vision, color, and visual optics : Vision modeling
(330.4150) Vision, color, and visual optics : Motion detection

Original Manuscript: January 30, 2009
Revised Manuscript: June 14, 2009
Manuscript Accepted: July 23, 2009
Published: September 11, 2009

Virtual Issues
Vol. 4, Iss. 13 Virtual Journal for Biomedical Optics

Edmund C. Lalor, Yashar Ahmadian, and Liam Paninski, "The relationship between optimal and biologically plausible decoding of stimulus velocity in the retina," J. Opt. Soc. Am. A 26, B25-B42 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Meister, L. Lagnado, and D. Baylor, “Concerted signaling by retinal ganglion cells,” Science 270, 1207-1210 (1995). [CrossRef] [PubMed]
  2. S. Nirenberg, S. Carcieri, A. Jacobs, and P. Latham, “Retinal ganglion cells act largely as independent encoders,” Nature 411, 698-701 (2002). [CrossRef]
  3. E. Chichilnisky and R. Kalmar, “Functional asymmetries in ON and OFF ganglion cells of primate retina,” J. Neurosci. 22, 2737-2747 (2002). [PubMed]
  4. E. Frechette, A. Sher, M. Grivich, D. Petrusca, A. Litke, and E. Chichilnisky, “Fidelity of the ensemble code for visual motion in the primate retina,” J. Neurophysiol. 94, 119-135 (2005). [CrossRef]
  5. E. Schneidman, M. Berry, R. Segev, and W. Bialek, “Weak pairwise correlations imply strongly correlated network states in a neural population,” Nature 440, 1007-1012 (2006). [CrossRef] [PubMed]
  6. J. Shlens, G. Field, J. Gauthier, M. Grivich, D. Petrusca, A. Sher, A. Litke, and E. Chichilnisky, “The structure of multi-neuron firing patterns in primate retina,” J. Neurosci. 26, 8254-8266 (2006). [CrossRef] [PubMed]
  7. J. Pillow, J. Shlens, L. Paninski, A. Sher, A. Litke, E. Chichilnisky, and E. Simoncelli, “Spatio-temporal correlations and visual signalling in a complete neuronal population,” Nature 454, 995-999 (2008). [CrossRef] [PubMed]
  8. E. S. Frechette, M. I. Grivich, R. S. Kalmar, A. M. Litke, D. Petrusca, A. Sher, and E. J. Chichilnisky, “Retinal motion signals and limits on speed discrimination,” J. Vision 4, 570 (2004). [CrossRef]
  9. A. Litke, N. Bezayiff, E. Chichilnisky, W. Cunningham, W. Dabrowski, A. Grillo, M. Grivich, P. Grybos, P. Hottowy, S. Kachiguine, R. Kalmar, K. Mathieson, D. Petrusca, M. Rahman, and A. Sher, “What does the eye tell the brain?: Development of a system for the large-scale recording of retinal output activity,” IEEE Trans. Nucl. Sci. 51, 1434-1440 (2004). [CrossRef]
  10. R. Segev, J. Goodhouse, J. Puchalla, and M. Berry, “Recording spikes from a large fraction of the ganglion cells in a retinal patch,” Nat. Neurosci. 7, 1154-1161 (2004). [CrossRef] [PubMed]
  11. D.Knill and W.Richards, eds., Perception as Bayesian Inference (Cambridge Univ. Press, 1996).
  12. E. P. Simoncelli, “Distributed analysis and representation of visual motion,” Ph.D. thesis (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1993). Also available as MIT Media Laboratory Vision and Modeling Technical Report #209.
  13. D. Ascher and N. Grzywacz, “A Bayesian model for the measurement of visual velocity,” Vision Res. 40, 3427-3434 (2000). [CrossRef] [PubMed]
  14. Y. Weiss, E. Simoncelli, and E. Adelson, “Motion illusions as optimal percepts,” Nat. Neurosci. 5, 598-604 (2002). [CrossRef] [PubMed]
  15. E. P. Simoncelli, “Local analysis of visual motion,” in The Visual Neurosciences, L.M.Chalupa and J.S.Werner, eds. (MIT Press, 2003), Chap. 109, pp. 1616-1623.
  16. A. Stocker and E. Simoncelli, “Noise characteristics and prior expectations in human visual speed perception,” Nat. Neurosci. 9, 578-585 (2006). [CrossRef] [PubMed]
  17. A. E. Welchman, J. M. Lam, and H. H. Bulthoff, “Bayesian motion estimation accounts for a surprising bias in 3D vision,” Proc. Natl. Acad. Sci. U.S.A. 105, 12087-12092 (2008). [CrossRef] [PubMed]
  18. F. Hurlimann, D. Kiper, and M. Carandini, “Testing the Bayesian model of perceived speed,” Vision Res. 42, 2253-2257 (2002). [CrossRef] [PubMed]
  19. P. Thompson, K. Brooks, and S. Hammett, “Speed can go up as well as down at low contrast: Implications for models of motion perception,” Vision Res. 46, 782-786 (2005). [CrossRef] [PubMed]
  20. A. Thiel, M. Greschner, C. Eurich, J. Ammermüller, and J. Kretzberg, “Contribution of individual retinal ganglion cell responses to velocity and acceleration encoding,” J. Neurophysiol. 98, 2285-2296 (2007). [CrossRef] [PubMed]
  21. J. Kretzberg, I. Winzenborg, and A. Thiel, “Bayesian analysis of the encoding of constant and changing stimulus velocities by retinal ganglion cells,” presented at Frontiers in Neuroinformatics 2008, Stockholm, September 7-9, 2008.
  22. D. Brillinger, “Maximum likelihood analysis of spike trains of interacting nerve cells,” Biol. Cybern. 59, 189-200 (1988). [CrossRef] [PubMed]
  23. P. McCullagh and J. Nelder, Generalized Linear Models (Chapman & Hall, 1989).
  24. L. Paninski, “Maximum likelihood estimation of cascade point-process neural encoding models,” Network Comput. Neural Syst. 15, 243-262 (2004). [CrossRef]
  25. W. Truccolo, U. Eden, M. Fellows, J. Donoghue, and E. Brown, “A point process frame-work for relating neural spiking activity to spiking history, neural ensemble and extrinsic covariate effects,” J. Neurophysiol. 93, 1074-1089 (2005). [CrossRef]
  26. L. Paninski, J. Pillow, and J. Lewi, “Statistical models for neural encoding, decoding, and optimal stimulus design,” in Computational Neuroscience: Progress in Brain Research, P.Cisek, T.Drew, and J.Kalaska, eds. (Elsevier, 2007).
  27. D. Snyder and M. Miller, Random Point Processes in Time and Space (Springer-Verlag, 1991). [CrossRef]
  28. D. Field, “Relations between the statistics of natural images and the response profiles of cortical cells,” J. Opt. Soc. Am. A 4, 2379-2394 (1987). [CrossRef] [PubMed]
  29. D. H. Brainard, D. R. Williams, and H. Hofer, “Trichromatic reconstruction from the interleaved cone mosaic: Bayesian model and the color appearance of small spots,” J. Vision 8, 1-23 (2008). [CrossRef]
  30. R. Kass and A. Raftery, “Bayes factors,” J. Am. Stat. Assoc. 90, 773-795 (1995). [CrossRef]
  31. E. Brown, L. Frank, D. Tang, M. Quirk, and M. Wilson, “A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells,” J. Neurosci. 18, 7411-7425 (1998). [PubMed]
  32. W. Bialek and A. Zee, “Coding and computation with neural spike trains,” J. Stat. Phys. 59, 103-115 (1990). [CrossRef]
  33. S. Koyama and S. Shinomoto, “Empirical Bayes interpretations of random point events,” J. Phys. A 38, 531-537 (2005). [CrossRef]
  34. J. Pillow, Y. Ahmadian, and L. Paninski, “Model-based decoding, information estimation, and change-point detection in multi-neuron spike trains,” submitted to Neural Comput. [PubMed]
  35. Y. Ahmadian, J. Pillow, and L. Paninski, “Efficient Markov chain Monte Carlo methods for decoding neural spike trains,” submitted to Neural Comput. [PubMed]
  36. E. Adelson and J. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284-99 (1985). [CrossRef] [PubMed]
  37. E. Chichilnisky and R. Kalmar, “Temporal resolution of ensemble visual motion signals in primate retina,” J. Neurosci. 23, 6681-6689 (2003). [PubMed]
  38. W. Bialek (Princeton University, bbrinker@princeton.edu) and R. de Ruyter van Steveninck (Indiana University, deruyter@indiana.edu) (personal communication, 2003).
  39. V. Perry and A. Cowey, “The ganglion cell and cone distributions in the monkey's retina: implications for central magnification factors,” Vision Res. 25, 1795-1810 (1985). [CrossRef] [PubMed]
  40. S. Ullman, The Interpretation of Visual Motion (MIT Press, 1979).
  41. P. Thompson, “Perceived rate of movement depends on contrast,” Vision Res. 22, 377-380 (1982). [CrossRef] [PubMed]
  42. L. Stone and P. Thompson, “Human speed perception is contrast dependent,” Vision Res. 32, 1535-1549 (1992). [CrossRef] [PubMed]
  43. D. C. Bradley and M. S. Goyal, “Velocity computation in the primate visual system,” Nat. Rev. Neurosci. 9, 686-695 (2008). [CrossRef]
  44. M. Potters and W. Bialek, “Statistical mechanics and visual signal processing,” J. Phys. I France 4, 1755-1775 (1994). [CrossRef]
  45. S. McKee, G. Silvermann, and K. Nakayama, “Precise velocity discrimination despite random variations in temporal frequency and contrast,” Vision Res. 26, 609-619 (1986). [CrossRef] [PubMed]
  46. M. Blakemore and R. Snowden, “The effect of contrast upon perceived speed: a general phenomenon?” Perception 28, 33-48 (1999). [CrossRef]
  47. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C (Cambridge Univ. Press, 1992).
  48. N. Shephard and M. Pitt, “Likelihood analysis of non-Gaussian measurement time series,” Biometrika 84, 653-667 (1997). [CrossRef]
  49. R. Davis and G. Rodriguez-Yam, “Estimation for state-space models: an approximate likelihood approach,” Stat. Sin. 15, 381-406 (2005).
  50. L. Paninski, Y. Ahmadian, D. Ferreira, S. Koyama, K. Rahnama, M. Vidne, J. Vogelstein, and W. Wu, “A new look at state-space models for neural data,” J. Comput. Neurosci. (to be published). Epub ahead of print, doi 10.1007/s10827-009-0179-x.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited