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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.22.002246


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Abstract

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

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-10-2246


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References

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  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. . 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 showed that under quite mild restriction, the strength of the kth harmonic of DIR is proportional to sin(kalpha)/k, with alpha 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, "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: empiricaldescription and estimation of parameters," Biol. Cybern. 78, 45-56 (1998).
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  32. The reason we do not identify DIR(theta) as [ODDSUM(theta)+∣ODDSUM(theta)∣]/2 is because all odd harmonics of DIR(theta) are required to be exactly the same as all odd harmonics of R(theta). The reason we do not write DIR(theta) as ODDSUM(theta)+lambda∣ODDSUM(theta)∣ for some 0<lambda<1 is because we want to completely cancel its negative lobe/peak.
  33. J. Zhang and R. L. De Valois (1998), "Unconfounding orientation and direction tuning in cortical neuron's response," Invest. Ophthalmol. Visual Sci. 39, s324 (1998).
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  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. to characterize orientation tuning would not be subject to our criticism described here; the reader is directed to Ringach, "Dynamics of orientation tuning in macaque primary visual cortex," Nature 387, 281-284 (1997) and Ringach, "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, "On the direction selectivity of cortical neurons to drifting dot patterns," Visual Neurosci. 11, 885-897 (1994).
  36. For an approach using a particular parametric form for orientation and direction tuning curves, the reader is directed to Swindale, "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. .
  37. F. Wörgötter and 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).
  38. If indeed such higher-order tuning mechanism exists, then the correct way of testing it is to assume the quadruple-lobed mechanism Q(theta) to have a period of 90° and hence Fourier decomposable as Q(theta)=q0+q1cos[4(theta−thetaq)]+q2cos[8(theta−thetaq)]+⋯. One can then proceed as before and relate (eta4,zeta4) to d4, o2, and q1.
  39. This includes, for example, Ref. , 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.

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