OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 10 — Oct. 1, 2005
  • pp: 2246–2256

Method of unconfounding orientation and direction tunings in neuronal response to moving bars and gratings

Jun Zhang  »View Author Affiliations

JOSA A, Vol. 22, Issue 10, pp. 2246-2256 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (208 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



When an oriented bar or grating is drifted across the receptive field of a cortical neuron at various orientations, the tuning function reflects both, and thus confounds the orientation (ORI) and the direction-of-motion (DIR) selectivity of the cell. Since ORI (or DIR), by definition, has a period of 180 ( or 360 ) deg cycle , a popular method for separating these two components, due to Wörgötter and Eysel [Biol. Cybern. 57, 349 (1987)] , is to Fourier decompose the neuron’s response along the angular direction and then identify the first and the second harmonic with DIR and ORI, respectively (the SDO method). Zhang [Biol. Cybern. 63, 135 (1990)] pointed out that this interpretation is misconceived—all odd harmonics (not just the first harmonic) reflect the DIR component, whereas all even harmonics (including the second harmonic) contain contributions from both DIR and ORI. Here, a simplified procedure is proposed to accomplish the goal of unconfounding ORI and DIR. We first construct the sum of all odd harmonics of the overall tuning curve, denoted ODDSUM, by calculating the difference in the neuronal response to opposite drifting directions. Then we construct ODDSUM + ODDSUM and identify it with DIR (here denotes the absolute value). Subtracting DIR, that is ODDSUM + ODDSUM , from the overall tuning curve gives ORI. Our method ensures that (i) the reconstructed DIR contains only one, positive peak at the preferred direction and can have power in all harmonics, and (ii) the reconstructed ORI has two peaks separated by 180° and has zero power for all odd harmonics. Using this procedure, we have unconfounded orientation and direction components for a considerable sample of macaque striate cortical cells, and compared the results with those obtained using Wörgötter and Eysel’s SDO method. We found that whereas the estimate of the peak angle of ORI remains largely unaffected, Wörgötter and Eysel’s method considerably overestimated the relative strength of ORI. To conclude, a simple method is provided for appropriately separating the orientation and directional tuning in a neuron’s response that is confounded as a result of the use of drifting oriented stimuli.

© 2005 Optical Society of America

OCIS Codes
(330.4060) Vision, color, and visual optics : Vision modeling
(330.4270) Vision, color, and visual optics : Vision system neurophysiology

ToC Category:
Temporal Processing

Original Manuscript: March 7, 2005
Revised Manuscript: May 31, 2005
Manuscript Accepted: June 1, 2005
Published: October 1, 2005

Jun Zhang, "Method of unconfounding orientation and direction tunings in neuronal response to moving bars and gratings," J. Opt. Soc. Am. A 22, 2246-2256 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Wörgötter, U. T. Eysel, “Quantitative determination of orientational and directional components in the response of visual cortical cells to moving stimuli,” Biol. Cybern. 57, 349–355 (1987). [CrossRef] [PubMed]
  2. F. Wörgötter, T. Muche, E. T. Eysel, “Correlations between directional and orientational tuning of cells in cat striate cortex,” Exp. Brain Res. 83, 665–669 (1991). [CrossRef] [PubMed]
  3. F. Wörgötter, U. T. Eysel, “Topographical aspects of intracortical excitation and inhibition contributing to orientation specificity in area 17 of the cat visual cortex,” Eur. J. Neurosci. 3, 1232–1244 (1991). [CrossRef] [PubMed]
  4. F. Wörgötter, O. Gründel, U. T. Eysel, “Quantification and comparison of cell properties in cat’s striate cortex determined by different types of stimuli,” Eur. J. Neurosci. 2, 928–941 (1990). [CrossRef]
  5. D. O’Carroll, “Feature-detecting neurons in dragonflies,” Nature (London) 362, 541–543 (1993). [CrossRef]
  6. B. Chapman, M. P. Stryker, “Development of orientation selectivity in ferret visual-cortex and effects of deprivation,” J. Neurosci. 13, 5251–5262 (1993). [PubMed]
  7. D. Malonek, R. B.H. Tootell, A. Grinvald, “Optical imaging reveals the functional architecture of neurons processing shape and motion in owl monkey area MT,” Proc. R. Soc. London, Ser. B 258, 109–119 (1994). [CrossRef]
  8. A. Shmuel, A. Grinvald, “Functional organization for direction of motion and its relationship to orientation maps in cat area 18,” J. Neurosci. 16, 6945–6964 (1996). [PubMed]
  9. M. Weliky, L. C. Katz, “Disruption of orientation tuning in visual cortex by artificially correlated neuronal activity,” Nature (London) 386, 680–685 (1997). [CrossRef]
  10. A. Schmidt, J. Engelage, H. J. Bischof, “Single cell responses from the optic tectum of the zebra finch (Taeniopygia guttata castanotis Gould),” J. Comp. Physiol. A 185, 69–79 (1999). [CrossRef]
  11. F. Sengpiel, P. Stawinski, T. Bonhoeffer, “Influence of experience on orientation maps in cat visual cortex,” Nat. Neurosci. 2, 727–732 (1999). [CrossRef] [PubMed]
  12. T. Yousef, T. Bonhoeffer, D.-S. Kim, U. T. Eysel, É. Tóth, Z. F. Kisvárday, “Orientation topography of layer 4 lateral networks revealed by optical imaging in cat visual cortex (area 18),” Eur. J. Neurosci. 11, 4291–4308 (1999). [CrossRef] [PubMed]
  13. J. Sharma, A. Angelucci, M. Sur, “Induction of visual orientation modules in auditory cortex,” Nature (London) 404, 841–847 (2000). [CrossRef]
  14. K. Krug, C. J. Akerman, I. D. Thompson, “Responses of neurons in neonatal cortex and thalamus to patterned visual stimulation through the naturally closed lids,” J. Neurophysiol. 85, 1436–1443 (2001). [PubMed]
  15. A. Schmidt, H. J. Bischof, “Neurons with complex receptive fields in the stratum griseum centrale of the zebra finch (Taeniopygia guttata castanotis Gould) optic tectum” J. Comp. Physiol., A 187, 913–924 (2001). [CrossRef]
  16. C. J. Akerman, D. Smyth, I. D. Thompson, “Visual experience before eye-opening and the development of the retinogeniculate pathway,” Neuron 36, 869–879 (2002). [CrossRef] [PubMed]
  17. F. Sengpiel, F. T. Bonhoeffer, “Orientation specificity of contrast adaptation in visual cortical pinwheel centres and iso-orientation domains,” Eur. J. Neurosci. 15, 876–886 (2002). [CrossRef] [PubMed]
  18. C. Monier, F. Chavane, P. Baudot, L. J. Graham, Y. Frégnac, “Orientation and direction selectivity of synaptic inputs in visual cortical neurons: a diversity of combinations produces spike tuning,” Neuron 37, 663–680 (2003). [CrossRef] [PubMed]
  19. T. H. Schwartz, “Optical imaging of epileptiform events in visual cortex in response to patterned photic stimulation,” Cereb. Cortex 13, 1287–1298 (2003). [CrossRef] [PubMed]
  20. A. G. Leventhal, K. G. Thompson, D. Liu, Y. Zhou, S. J. Ault, “Concomitant sensitivity to orientation, direction, and color of cells in layers 2, 3, and 4 of monkey striate cortex,” J. Neurosci. 15, 1808–1818 (1995). [PubMed]
  21. T. D. Shou, A. G. Leventhal, K. G. Thompson, Y. F. Zhou, “Direction biases of X-type and Y-type retinal ganglion-cells in the cat,” J. Neurophysiol. 73, 1414–1421 (1995). [PubMed]
  22. Y. F. Zhou, A. G. Leventhal, K. G. Thompson, “Visual deprivation does not affect the orientation and direction sensitivity of relay cells in the lateral geniculate nucleus of the cat,” J. Neurosci. 15, 689–698 (1995). [PubMed]
  23. A. G. Leventhal, Y. C. Wang, M. T. Schmolesky, Y. F. Zhou, “Neural correlates of boundary perception,” Visual Neurosci. 15, 1107–1118 (1998). [CrossRef]
  24. A. Shmuel, A. Grinvald, “Coexistence of linear zones and pinwheels within orientation maps in cat visual cortex,” Proc. Natl. Acad. Sci. U.S.A. 97, 5568–5573 (2000). [CrossRef] [PubMed]
  25. E. Batschelet, Circular Statistics in Biology (Academic, 1981).
  26. J. Zhang, “How to unconfound the directional and orientational information in visual neuron’s response,” Biol. Cybern. 63, 135–142 (1990). [CrossRef]
  27. Note that here and below the designation of “first” and “second” harmonics refers to using a fundamental period of 360 deg∕cycle in Fourier analysis. If one were to Fourier decompose, say ORI, using a fundamental period of 180 deg∕cycle, then the second harmonic mentioned above should be renamed the first harmonic (in describing a periodic function with a period of 180 deg∕cycle).
  28. In fact, higher-order harmonics were consistently present even in these authors’ own data; see Ref. [2]. However they were dismissed based on the percentage of total power they contributed. This was misguided, because any single-peaked DIR will have decreasing power in its higher harmonics. In fact, Zhang[26] showed that under quite mild restriction, the strength of the kth harmonic of DIR is proportional to sin(kα)∕k, with α characterizing the bandwidth. So the systematic presence of powers with decreasing strength in higher harmonics cannot be explained away simply as noise; rather it reflects narrow tuning curves of DIR.
  29. Sinusoidal tuning may describe directional selectivity in ganglion cells; the reader is directed to S. G. He et al. , “Distinguishing direction selectivity from orientation selectivity in the rabbit retina,” Visual Neurosci. 15, 439–447 (1998).This is where the vector sum method (and also the SDO analysis) would work well. In estimating the orientation (and by analogy, direction) tuning, the vector sum or SDO method is equivalent to calculating the least-squares fit to a sinusoidal curve, as pointed out by N. V. Swindale, “Orientation tuning curves: empirical description and estimation of parameters,” Biol. Cybern. 78, 45–56 (1998). [CrossRef] [PubMed]
  30. R. L. De Valois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982). [CrossRef] [PubMed]
  31. B. Li, Y. Wang, Y. C. Diao, “Quantification of directional and orientational selectivities of visual neurons to moving stimuli,” Biol. Cybern. 70, 282–290 (1994). [CrossRef]
  32. The reason we do not identify DIR(θ) as [ODDSUM(θ)+∣ODDSUM(θ)∣]∕2 is because all odd harmonics of DIR(θ) are required to be exactly the same as all odd harmonics of R(θ). The reason we do not write DIR(θ) as ODDSUM(θ)+λ∣ODDSUM(θ)∣ for some 0<λ<1 is because we want to completely cancel its negative lobe/peak.
  33. J. Zhang, R. L. De Valois (1998), “Unconfounding orientation and direction tuning in cortical neuron’s response,” Invest. Ophthalmol. Visual Sci. 39, s324 (1998).
  34. R. L. De Valois, N. P. Cottaris, “Inputs to directionally selective simple cells in macaque striate cortex,” Proc. Natl. Acad. Sci. U.S.A. 95, 14488–14493 (1998). [CrossRef] [PubMed]
  35. Note that our analysis applies only to the use of drifting oriented stimuli. When, for instance, cells are driven by flashing oriented stimuli, the use of the circular variance measure in analogy to Eq. (2) to characterize orientation tuning would not be subject to our criticism described here; the reader is directed to Ringach et al. , “Dynamics of orientation tuning in macaque primary visual cortex,” Nature 387, 281–284 (1997) Ringach et al. , “Orientation selectivity in macaque V1: diversity and laminar dependence,” J. Neurol. Sci. 22, 5639–5651 (2002).Also, our analysis will not apply if the stimulus is a drifting random dot pattern because, under certain conditions, the cell’s directional tuning would exhibit a bifurcation of peaks, as shown by Skottun et al. , “On the direction selectivity of cortical neurons to drifting dot patterns,” Visual Neurosci. 11, 885–897 (1994). [CrossRef] [PubMed]
  36. For an approach using a particular parametric form for orientation and direction tuning curves, the reader is directed to Swindale et al. , “The spatial pattern of response magnitude and selectivity for orientation and direction in cat visual cortex,” Cereb. Cortex 13, 225–238 (2003), and the reference by Swindale cited in Ref. [29]. [CrossRef] [PubMed]
  37. F. Wörgötter, U. T. Eysel, “Axial responses in visual cortical cells: Spatial-temporal mechanisms quantified by Fourier components of cortical tuning curves,” Exp. Brain Res. 83, 656–664 (1991). [CrossRef]
  38. If indeed such higher-order tuning mechanism exists, then the correct way of testing it is to assume the quadruple-lobed mechanism Q(θ) to have a period of 90° and hence Fourier decomposable as Q(θ)=q0+q1cos[4(θ−θq)]+q2cos[8(θ−θq)]+⋯. One can then proceed as before and relate (η4,ζ4) to d4, o2, and q1.
  39. This includes, for example, Ref. [9], which reported the weakening of orientation selectivity in the primary visual cortex (V1) of ferrets after chronic electric stimulation of the optic nerve during their early, postnatal visual development.

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