Abstract

In recent literature, particularly interesting stimulus velocity-selective behaviors were found in the response properties of neurons belonging to the primary visual cortex (V1). In this work, 93 simple and complex cell receptive fields were obtained from the recordings of different experiments made on cats (DeAngelis, Blanche, Touryan) with reverse correlation and the spike-triggered covariance methods and then fitted with a three-dimensional Gabor model, so that cells are seen as minimizers of the Heisenberg uncertainty principle over both space and time. Analysis of the model parameters’ cortical distribution suggests that V1 is spatiotemporally organized to maximize the resolution on the stimulus velocity measure.

© 2012 Optical Society of America

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    [CrossRef]

2010

C. Fermuller, H. Ji, and A. Kitaoka, “Illusory motion due to causal time filtering,” Vis. Res. 50, 315–329 (2010).
[CrossRef]

2009

Z. Tan and H. Yao, “The spatiotemporal frequency tuning of LGN receptive field facilitates neural discrimination of natural stimuli,” J. Neurosci. 29, 11409–11416 (2009).
[CrossRef]

2007

S. K. Sasaki and I. Ohzawa, “Internal spatial organization of receptive fields of complex cells in the early visual cortex,” J. Neurophysiol. 98, 1194–1212 (2007).
[CrossRef]

N. Petkov and E. Subramanian, “Motion detection, noise reduction, texture suppression and contour enhancement by spatiotemporal Gabor filters with surround inhibition,” Biolog. Cybern. 97, 423–439 (2007).
[CrossRef]

2005

T. J. Blanche, M. A. Spacek, J. F. Hetke, and N. V. Swindale, “Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording,” J. Neurophysiol. 93, 2987–3000 (2005).
[CrossRef]

C. Weng, C. Yeh, C. R. Stoelzel, and J. M. Alonso, “Receptive field size and response latency are correlated within the cat visual thalamus,” J. Neurophysiol. 93, 3537–3547 (2005).
[CrossRef]

2003

N. J. Priebe, C. R. Casanello, and S. G. Lisberger, “The neural representation of speed in macaque area MT/V5,” J. Neurosci. 23, 5650–5661 (2003).

2002

F. Mechler and D. L. Ringach, “On the classification of simple and complex cells,” Vis. Res. 42, 1017–1033 (2002).
[CrossRef]

D. L. Ringach, M. J. Hawken, and R. Shapley, “Receptive field structure of neurons in monkey primary visual cortex revealed by stimulation with natural image sequences,” J. Vision 2 (2), 1 (2002).
[CrossRef]

J. Touryan, B. Lau, and Y. Dan, “Isolation of relevant visual features from random stimuli for cortical complex cells,” J. Neurosci. 22, 10811–10818 (2002).

2001

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

1999

G. C. DeAngelis, G. M. Ghose, I. Ohzawa, and R. D. Freeman, “Functional micro-organization of primary visual cortex: receptive field analysis of nearby neurons,” J. Neurosci. 19, 4046–4064 (1999).

1996

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity by simple cells in the cat’s visual cortex,” J. Neurophysiol. 75, 1779–1805 (1996).

1995

G. C. DeAngelis, I. Ohzawa, and R. D. Freeman, “Receptive-field dynamics in the central visual pathways,” Trends Neurosci. 18, 451–458 (1995).
[CrossRef]

1993

G. C. De Angelis, I. Ohzawa, and R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cats striate cortex. I. General characteristics and postnatal development,” J. Neurophysiol. 69, 1091–1117 (1993).

1992

J. H. R. Maunsell and J. R. Gibson, “Visual response latencies in striate cortex of the macaque monkey,” J. Neurophysiol. 68, 1332–1344 (1992).

1991

R. C. Reid, R. E. Soodak, and R. M. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

1987

J. P. Jones and L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).

J. P. Jones and L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).

1986

1985

J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. 2, 1160–1169 (1985).
[CrossRef]

E. H. Adelson and J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef]

A. B. Watson and A. J. Ahumada, “Model of human visual-motion sensing,” J. Opt. Soc. Am. A 2, 322–342 (1985).
[CrossRef]

1980

1971

B. G. Cleland, M. W. Dubin, and W. R. Levick, “Sustained and transient neurones in the cat’s retina and lateral geniculate nucleus,” J. Physiol. 217, 473–496 (1971).

1966

D. H. Hubel and T. N. Wiesel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophyisol. 29, 1115–1156 (1966).

1965

D. H. Hubel and T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Physiol. 28, 229–289 (1965).

R. W. Rodieck, “Quantitative analysis of cat retinal ganglion cell response to visual stimuli,” Vis. Res. 5, 583–601 (1965).
[CrossRef]

1946

D. Gabor, “Theory of communication,” J. IEE 93, 429–459 (1946).
[CrossRef]

Adelson, E. H.

Ahumada, A. J.

Alonso, J. M.

C. Weng, C. Yeh, C. R. Stoelzel, and J. M. Alonso, “Receptive field size and response latency are correlated within the cat visual thalamus,” J. Neurophysiol. 93, 3537–3547 (2005).
[CrossRef]

Bergen, J. R.

Blanche, T. J.

T. J. Blanche, M. A. Spacek, J. F. Hetke, and N. V. Swindale, “Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording,” J. Neurophysiol. 93, 2987–3000 (2005).
[CrossRef]

Casanello, C. R.

N. J. Priebe, C. R. Casanello, and S. G. Lisberger, “The neural representation of speed in macaque area MT/V5,” J. Neurosci. 23, 5650–5661 (2003).

Cleland, B. G.

B. G. Cleland, M. W. Dubin, and W. R. Levick, “Sustained and transient neurones in the cat’s retina and lateral geniculate nucleus,” J. Physiol. 217, 473–496 (1971).

Dan, Y.

J. Touryan, B. Lau, and Y. Dan, “Isolation of relevant visual features from random stimuli for cortical complex cells,” J. Neurosci. 22, 10811–10818 (2002).

Daugman, J. G.

J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. 2, 1160–1169 (1985).
[CrossRef]

David, S. V.

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

De Angelis, G. C.

G. C. De Angelis, I. Ohzawa, and R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cats striate cortex. I. General characteristics and postnatal development,” J. Neurophysiol. 69, 1091–1117 (1993).

DeAngelis, G. C.

G. C. DeAngelis, G. M. Ghose, I. Ohzawa, and R. D. Freeman, “Functional micro-organization of primary visual cortex: receptive field analysis of nearby neurons,” J. Neurosci. 19, 4046–4064 (1999).

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity by simple cells in the cat’s visual cortex,” J. Neurophysiol. 75, 1779–1805 (1996).

G. C. DeAngelis, I. Ohzawa, and R. D. Freeman, “Receptive-field dynamics in the central visual pathways,” Trends Neurosci. 18, 451–458 (1995).
[CrossRef]

Dubin, M. W.

B. G. Cleland, M. W. Dubin, and W. R. Levick, “Sustained and transient neurones in the cat’s retina and lateral geniculate nucleus,” J. Physiol. 217, 473–496 (1971).

Farrell, J. E.

Fermuller, C.

C. Fermuller, H. Ji, and A. Kitaoka, “Illusory motion due to causal time filtering,” Vis. Res. 50, 315–329 (2010).
[CrossRef]

Freeman, R. D.

G. C. DeAngelis, G. M. Ghose, I. Ohzawa, and R. D. Freeman, “Functional micro-organization of primary visual cortex: receptive field analysis of nearby neurons,” J. Neurosci. 19, 4046–4064 (1999).

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity by simple cells in the cat’s visual cortex,” J. Neurophysiol. 75, 1779–1805 (1996).

G. C. DeAngelis, I. Ohzawa, and R. D. Freeman, “Receptive-field dynamics in the central visual pathways,” Trends Neurosci. 18, 451–458 (1995).
[CrossRef]

G. C. De Angelis, I. Ohzawa, and R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cats striate cortex. I. General characteristics and postnatal development,” J. Neurophysiol. 69, 1091–1117 (1993).

Gabor, D.

D. Gabor, “Theory of communication,” J. IEE 93, 429–459 (1946).
[CrossRef]

Gallant, J. L.

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

Ghose, G. M.

G. C. DeAngelis, G. M. Ghose, I. Ohzawa, and R. D. Freeman, “Functional micro-organization of primary visual cortex: receptive field analysis of nearby neurons,” J. Neurosci. 19, 4046–4064 (1999).

Gibson, J. R.

J. H. R. Maunsell and J. R. Gibson, “Visual response latencies in striate cortex of the macaque monkey,” J. Neurophysiol. 68, 1332–1344 (1992).

Hawken, M. J.

D. L. Ringach, M. J. Hawken, and R. Shapley, “Receptive field structure of neurons in monkey primary visual cortex revealed by stimulation with natural image sequences,” J. Vision 2 (2), 1 (2002).
[CrossRef]

Hetke, J. F.

T. J. Blanche, M. A. Spacek, J. F. Hetke, and N. V. Swindale, “Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording,” J. Neurophysiol. 93, 2987–3000 (2005).
[CrossRef]

Hsu, A.

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophyisol. 29, 1115–1156 (1966).

D. H. Hubel and T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Physiol. 28, 229–289 (1965).

D. H. Hubel, Eye, Brain, and Vision (Scientific American Library, 1988).

Ji, H.

C. Fermuller, H. Ji, and A. Kitaoka, “Illusory motion due to causal time filtering,” Vis. Res. 50, 315–329 (2010).
[CrossRef]

Jones, J. P.

J. P. Jones and L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).

J. P. Jones and L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).

Kitaoka, A.

C. Fermuller, H. Ji, and A. Kitaoka, “Illusory motion due to causal time filtering,” Vis. Res. 50, 315–329 (2010).
[CrossRef]

Lau, B.

J. Touryan, B. Lau, and Y. Dan, “Isolation of relevant visual features from random stimuli for cortical complex cells,” J. Neurosci. 22, 10811–10818 (2002).

Levick, W. R.

B. G. Cleland, M. W. Dubin, and W. R. Levick, “Sustained and transient neurones in the cat’s retina and lateral geniculate nucleus,” J. Physiol. 217, 473–496 (1971).

Lisberger, S. G.

N. J. Priebe, C. R. Casanello, and S. G. Lisberger, “The neural representation of speed in macaque area MT/V5,” J. Neurosci. 23, 5650–5661 (2003).

Marcelja, S.

Maunsell, J. H. R.

J. H. R. Maunsell and J. R. Gibson, “Visual response latencies in striate cortex of the macaque monkey,” J. Neurophysiol. 68, 1332–1344 (1992).

Mechler, F.

F. Mechler and D. L. Ringach, “On the classification of simple and complex cells,” Vis. Res. 42, 1017–1033 (2002).
[CrossRef]

Ohzawa, I.

S. K. Sasaki and I. Ohzawa, “Internal spatial organization of receptive fields of complex cells in the early visual cortex,” J. Neurophysiol. 98, 1194–1212 (2007).
[CrossRef]

G. C. DeAngelis, G. M. Ghose, I. Ohzawa, and R. D. Freeman, “Functional micro-organization of primary visual cortex: receptive field analysis of nearby neurons,” J. Neurosci. 19, 4046–4064 (1999).

I. Ohzawa, G. C. DeAngelis, and R. D. Freeman, “Encoding of binocular disparity by simple cells in the cat’s visual cortex,” J. Neurophysiol. 75, 1779–1805 (1996).

G. C. DeAngelis, I. Ohzawa, and R. D. Freeman, “Receptive-field dynamics in the central visual pathways,” Trends Neurosci. 18, 451–458 (1995).
[CrossRef]

G. C. De Angelis, I. Ohzawa, and R. D. Freeman, “Spatiotemporal organization of simple-cell receptive fields in the cats striate cortex. I. General characteristics and postnatal development,” J. Neurophysiol. 69, 1091–1117 (1993).

Palmer, L. A.

J. P. Jones and L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).

J. P. Jones and L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).

Petkov, N.

N. Petkov and E. Subramanian, “Motion detection, noise reduction, texture suppression and contour enhancement by spatiotemporal Gabor filters with surround inhibition,” Biolog. Cybern. 97, 423–439 (2007).
[CrossRef]

Priebe, N. J.

N. J. Priebe, C. R. Casanello, and S. G. Lisberger, “The neural representation of speed in macaque area MT/V5,” J. Neurosci. 23, 5650–5661 (2003).

Reid, R. C.

R. C. Reid, R. E. Soodak, and R. M. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

Ringach, D. L.

F. Mechler and D. L. Ringach, “On the classification of simple and complex cells,” Vis. Res. 42, 1017–1033 (2002).
[CrossRef]

D. L. Ringach, M. J. Hawken, and R. Shapley, “Receptive field structure of neurons in monkey primary visual cortex revealed by stimulation with natural image sequences,” J. Vision 2 (2), 1 (2002).
[CrossRef]

Rodieck, R. W.

R. W. Rodieck, “Quantitative analysis of cat retinal ganglion cell response to visual stimuli,” Vis. Res. 5, 583–601 (1965).
[CrossRef]

Sasaki, S. K.

S. K. Sasaki and I. Ohzawa, “Internal spatial organization of receptive fields of complex cells in the early visual cortex,” J. Neurophysiol. 98, 1194–1212 (2007).
[CrossRef]

Shapley, R.

D. L. Ringach, M. J. Hawken, and R. Shapley, “Receptive field structure of neurons in monkey primary visual cortex revealed by stimulation with natural image sequences,” J. Vision 2 (2), 1 (2002).
[CrossRef]

Shapley, R. M.

R. C. Reid, R. E. Soodak, and R. M. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

Singh, N. C.

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

Soodak, R. E.

R. C. Reid, R. E. Soodak, and R. M. Shapley, “Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex,” J. Neurophysiol. 66, 505–529 (1991).

Spacek, M. A.

T. J. Blanche, M. A. Spacek, J. F. Hetke, and N. V. Swindale, “Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording,” J. Neurophysiol. 93, 2987–3000 (2005).
[CrossRef]

Stoelzel, C. R.

C. Weng, C. Yeh, C. R. Stoelzel, and J. M. Alonso, “Receptive field size and response latency are correlated within the cat visual thalamus,” J. Neurophysiol. 93, 3537–3547 (2005).
[CrossRef]

Subramanian, E.

N. Petkov and E. Subramanian, “Motion detection, noise reduction, texture suppression and contour enhancement by spatiotemporal Gabor filters with surround inhibition,” Biolog. Cybern. 97, 423–439 (2007).
[CrossRef]

Swindale, N. V.

T. J. Blanche, M. A. Spacek, J. F. Hetke, and N. V. Swindale, “Polytrodes: high-density silicon electrode arrays for large-scale multiunit recording,” J. Neurophysiol. 93, 2987–3000 (2005).
[CrossRef]

Tan, Z.

Z. Tan and H. Yao, “The spatiotemporal frequency tuning of LGN receptive field facilitates neural discrimination of natural stimuli,” J. Neurosci. 29, 11409–11416 (2009).
[CrossRef]

Theunissen, F. E.

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

Touryan, J.

J. Touryan, B. Lau, and Y. Dan, “Isolation of relevant visual features from random stimuli for cortical complex cells,” J. Neurosci. 22, 10811–10818 (2002).

Vinje, W. E.

F. E. Theunissen, S. V. David, N. C. Singh, A. Hsu, W. E. Vinje, and J. L. Gallant, “Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli,” Network 12, 289–316 (2001).

Watson, A. B.

Weng, C.

C. Weng, C. Yeh, C. R. Stoelzel, and J. M. Alonso, “Receptive field size and response latency are correlated within the cat visual thalamus,” J. Neurophysiol. 93, 3537–3547 (2005).
[CrossRef]

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophyisol. 29, 1115–1156 (1966).

D. H. Hubel and T. N. Wiesel, “Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat,” J. Physiol. 28, 229–289 (1965).

Yao, H.

Z. Tan and H. Yao, “The spatiotemporal frequency tuning of LGN receptive field facilitates neural discrimination of natural stimuli,” J. Neurosci. 29, 11409–11416 (2009).
[CrossRef]

Yeh, C.

C. Weng, C. Yeh, C. R. Stoelzel, and J. M. Alonso, “Receptive field size and response latency are correlated within the cat visual thalamus,” J. Neurophysiol. 93, 3537–3547 (2005).
[CrossRef]

Biolog. Cybern.

N. Petkov and E. Subramanian, “Motion detection, noise reduction, texture suppression and contour enhancement by spatiotemporal Gabor filters with surround inhibition,” Biolog. Cybern. 97, 423–439 (2007).
[CrossRef]

J. IEE

D. Gabor, “Theory of communication,” J. IEE 93, 429–459 (1946).
[CrossRef]

J. Neurophyisol.

D. H. Hubel and T. N. Wiesel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophyisol. 29, 1115–1156 (1966).

J. Neurophysiol.

J. P. Jones and L. A. Palmer, “The two-dimensional spatial structure of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1187–1211 (1987).

J. P. Jones and L. A. Palmer, “An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex,” J. Neurophysiol. 58, 1233–1258 (1987).

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Figures (7)

Fig. 1.
Fig. 1.

In the first row is shown the time course of a simple cell’s RF. In the second row are plotted, for each frame, one-dimensional (1D) profiles obtained by summing RF data along the axis parallel to the cells’ preferred orientation. The middle vertical line in these plots highlights how the RF subregions shift in space through time. This cell is direction selective, and this kind of profile is said to be space–time inseparable. The time interval between each frame is 15 msec.

Fig. 2.
Fig. 2.

Plots showing reconstructed data relative to two RFs, both in the spatiotemporal classical and Fourier domains. Separable profiles can be obtained by the product of two separate real functions defined over space and time (respectively), and they respond to both stimulus movement directions, while inseparable profiles are structurally direction selective. The white lines on the spectral plots mark the horizontal axis relative to the zero temporal frequency. It can be noted that response amplitudes over this line remain consistently low, which is an effect of the late slow dynamics of the RFs.

Fig. 3.
Fig. 3.

(a) In the left plot is the distribution of the SRI of the profiles and subunits belonging to the cells studied: a Gaussian function representing distribution mean and standard deviation is plotted with a dashed line. The right-hand plot illustrates the inverse proportionality governing size versus spatial frequency distribution with a continuous line corresponding to the mean value of their product and dashed lines corresponding to the mean ± 2 SD . (b) The same type of plots show relations between temporal frequency and RF duration.

Fig. 4.
Fig. 4.

(a) Joint spatiotemporal frequency distribution. Complex cell subunits are indicated as black squares, while simple cell profiles are drawn as circles. A dashed line is drawn over a robust linear regression performed over the distribution: it is not intended to fit the data, but just to graphically render the parameters’ correlation. This notation is followed within all the subfigures. (b) Joint spatiotemporal uncertainty distribution. (c) RF sizes versus preferred stimulus velocity. A strong direct proportionality seems to drive these two parameters’ distribution. (d) RF profile duration versus preferred stimulus velocity. A significant negative correlation is found.

Fig. 5.
Fig. 5.

Sensitivity ellipses representing three sample Gabor functions in the spatiotemporal Fourier plane. Uncertainty over the stimulus velocity measure can be defined as the difference between the angular coefficient of the two isovelocity lines tangent to these ellipses.

Fig. 6.
Fig. 6.

A scatter plot of the spatiotemporal sensitivity ellipses associated to the RFs in the dataset. The responses seem to be concentrated at midrange frequency values. However, it is possible to note how their shapes are not randomly distributed: vertically elongated ones clearly prefer higher velocity values.

Fig. 7.
Fig. 7.

Plots showing four different example RFs from the dataset—one for each row. From left to right, original spatiotemporal data, the fitting obtained using our model, and the function relating velocity uncertainty and RF shape. The function shown in the right plot always presents an optimal value of ϵ , where the uncertainty over the stimulus velocity measurement is minimized. Crossed circles are plotted in correspondence to the value relative to the true spatiotemporal shape of the plotted RFs, always placing themselves near to the theoretical minimum value. This is true for all the RFs in the dataset. The fit error defined at the beginning of Section 3 for the RFs in the figure is, from top to bottom, 0, 23, 0, 26, 0, 19, 0, and 37.

Equations (10)

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( Δ x ) ( Δ y ) ( Δ ξ ) ( Δ η ) 1 4 π 2 ,
ǧ ( x , t ) = exp { ( x x 0 ) 2 2 Δ x 2 ( t t 0 ) 2 2 Δ t 2 } × exp { 2 π i [ ξ 0 ( x x 0 ) + ω 0 ( t t 0 ) ] } ,
ϕ = arctan ω 0 ξ 0 .
ǧ s ( x , t ) = C exp [ i ( ξ 0 x + ω 0 t ) ] + ( 1 C ) exp [ i ( ξ 0 x ω 0 t ) ] = exp ( i ξ 0 x ) [ cos ( ω 0 t ) + i ( 1 2 C ) sin ( ω 0 t ) ] ,
SRI = 8 Δ x ξ 0 .
Δ t ω 0 Δ x ξ 0 = v Δ t Δ x 2 3 ,
v 0 = ω 0 ξ 0 .
S A = Δ ξ Δ ω
ϵ = Δ ξ Δ ω .
Δ v = 2 S A 1 ϵ ξ 0 2 + ϵ ω 0 2 S A ξ 0 2 ϵ S A .

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