LETTER TO THE EDITORS SPATIAL FREQUENCY
FILTERS
(Receiced
IN CAT VISUAL CORTEX’!
21 January
1971)
In an extensive investigation of the properties of comstimulus. If the cell’s preferred width was as narrow as plex and hyper-complex cells in cat visual cortex, the component bars, a larger response to the two-bar which contains a number of interesting results constimulus would be expected because it contains two of cerning response inhibition by additional stimuli, the cell’s preferred stimuli. Cell 79-l (Fig. Sb) appears Glezer. Ivanoff and Tscherbach-(l973) report cells for to show an increased response from one to two bars which the optimal stimulus appears to consist of two and a decrease as more bars are added. Increasing the width of a single bar produces the increase but not the or more bars rather than a single bar. They suggest decreas in response. Thus this cell actually shows a that the results support a model in which cortical receptive fields operate as narrow-band filters performpreferential response for a single bar over a grating. A ing a piece-wise Fourier-analysis of visual images. This number of other cells are reported as showing a deinvestigation is an important extension of previous crease in response as an extra bar is added. This can techniques in the difficult area of hyper-complex cell hardly be described as spatial frequency specificity uninvestigation, and the results, if true, would make a sig- less inhibition is shown for specific frequencies, which nificant bridge between single-cell neurophysiology it was not. This leaves the extensive investigation of cell 89- 1. A and the extensive literature on human psychophysics using periodic luminance gratings (see for example glance at Fig. 4 does not give a convincing impression Campbell and Robson, 1965; Blakemore, Muncey and of marked preference for any aspect of the stimulus Ridley. 1973). configuration used. (It should be remembered that by I shall argue that the results of Glezer rt al. do not chance alone comparisons between 50 results should give convincing support to a model in which the optiproduce roughly twelve comparisons that would differ mal stimulus for cortical cell is a grating rather than sufficiently to appear significant at P = DO1 on an a line. and even if the arguments can be disputed, it is uncorrected t-test.) However, even taking the results a marked distortion of the data to describe the results at face value, it is not clear what stimulus dimenin rigorous mathematical terms. As a psychophysicist_ sions control the magnitude of the response. The I am not competent to assess the neurophysiological authors have abstracted the variable of number of bars techniques, so my comments will be restricted to a for presentation in Fig. 5a, and it does seem that both stimulus-response analysis on the assumption that the for this and other bar widths. response increases with nemophysiology is sound. number of bars by a total of 150 per cent. But the imIn the section concerning spatial frequency analysis pulse counts for the single-bar stimuli show ‘that the authors describe full results from one “typical” simply increasing the bar width of a single bar up to complex cell and supporting data from approximately the maximum width of the grating gives an increase in nine other cells. While it would be prolix to consider response of 100 per cent, which may not be signifiall aspects of these results, it appears that many major cantly less than the increase for multiple bars (see results on which the authors base their conclusions are Table I). subject to alternative explanations for which proper Nevertheless, Fig. 4 does give the impression of controls are not described. For example, the best evi- some spatial frequency specificity in showing a general dence for an optimal response to a grating seems to be preference for four or five bars over three or less. If this in cell 109-J (Figs. Sb and 22). It does respond conwere a question of narrow-band tuning of the cell to vincingly more to movement of three bars than to one a certain spatial frequency, one would expect that bar of the same total width. and it shows several re- stimuli of approximately a certain spatial frequency sponse peaks when traversed by a single bar. However, would consistently be optimal for the cell. Table 1 the peaks seem so variable for different bar widths that shows the impulse counts for most stimuli-arranged in it is not clear whether they are repeatable or are just order of spatial period (reciprocal of spatial frequency). statistical fluctuations. It is not reported whether the Single bars are tabulated separately as they have no cell showed narrow-band spatial-frequency tuning. dominant spatial frequency. It is clear from this table In cell 105-2 (Fig. 7) a larger response is obtained for that very few of the multiple bar responses are larger two bars than for a single bar of the same total width. than the optimal single-bar response. The period for But responses are not shown for a single bar of the maximum response (bold) seems to vary unsystematisame width as the component bars of the two-bar cally with number of bars, and actually shifts the entire 303
Letter to the Editors
.x)J
Table 1. Number of impulses recorded in response to multiple-bar stimuli arranged in order of spatial period of stimulus (from Giezer et ul.. I973)
Sinylc bar
iv = Bar width in degrees of visual angle. s = Bar separation in degrees of visual angle. tr = Xumber of bars in sttmulua i = Number of impulses in response. Maximum response for each value oftz is in bold figures.
iength of the scale (almost a decade of spatial frequency) between the Z and 5 bar stimuli. This is far less tuning than the octave bandwidth that would be expected even from a cell with an excitatory strip and in~i~~t~ry Ranks. I conclude from this that not only does the cell show no evidence of narrow band tuning. but also that it is very doubtful whether spatial frequency can be regarded as the controlling stimulus variable at all. I have been unable to determine what the controlling variable may be, but f suspect that much of the variation beyond overall stimulus size may be random t~u~tuat~o~ in sensitivity. To summarize. the authors’ evidence for spatial frequency specificity is based largely on two ceils. in neither of which were they able to demonstrate narrow-band spatial frequency tuning. Such tuning is a prerequisite for even the crudest sort of Fourier analy sis. which is already known to be possible by means of the classic type of complex cell of Hubel and Weisel ( 1961).which will respond preferentially to gratings of a certa’in spatial frequency with an octave bandwidth. Complex cells are not specialized for spatial frequency as such. since they do not respond preferentially to a multiple-bar stimulus. In conctusion. the search for spatial frequency filters in the visuaf cortex should not ignore the Fact that hyper-complex cells are likely to be connected somewhat irregularly in a minority of cases, SmaIl gaps or crenellations in the fields of a few ceils should not be
regarded as constituting reliable evidence that the cortex contains a bank of spatial frequency filters performing a holographic transform of the stimulus. And while it is true that many fairly regular textures occur in the environment the majority of these are regular in two dimensions (rather than the single dimension of a grating). and would therefore not be optimal stimuli for grating detectors, but would require specialized “speckle detectors” for optimal encoding. C. WILLIA?d
TYLER
REFERENCES
Blakemore C.. Muncey J. P. J. and Ridfey R. M. (1973) Stimulus specificity in the human visual system. I/ision Res. 13, 1913-1932. Campbell F. W. and Robson J. G. (1968) .-\pplication of Fourier analysis to the visibility of gratings. J. Ptlysiuk, Land. 197, 531-366. Glezer V. IX, IvanoKV. A. and Tscherbach T. A. (1975) Investigation of complex and hyper-compler receptive fields of visual cortex oi the cat as spatial frequency fiiters. Vision Res. 13, lSf5-1904. Hub& I3. H. and Weisel T. N. (1961) Receptive fields. binocular interaction and functional architecture in the cat’s visual cortex. J. Physiof., L011fl.160. 106-153.
FILTERS
(Receiced
IN CAT VISUAL CORTEX’!
21 January
1971)
In an extensive investigation of the properties of comstimulus. If the cell’s preferred width was as narrow as plex and hyper-complex cells in cat visual cortex, the component bars, a larger response to the two-bar which contains a number of interesting results constimulus would be expected because it contains two of cerning response inhibition by additional stimuli, the cell’s preferred stimuli. Cell 79-l (Fig. Sb) appears Glezer. Ivanoff and Tscherbach-(l973) report cells for to show an increased response from one to two bars which the optimal stimulus appears to consist of two and a decrease as more bars are added. Increasing the width of a single bar produces the increase but not the or more bars rather than a single bar. They suggest decreas in response. Thus this cell actually shows a that the results support a model in which cortical receptive fields operate as narrow-band filters performpreferential response for a single bar over a grating. A ing a piece-wise Fourier-analysis of visual images. This number of other cells are reported as showing a deinvestigation is an important extension of previous crease in response as an extra bar is added. This can techniques in the difficult area of hyper-complex cell hardly be described as spatial frequency specificity uninvestigation, and the results, if true, would make a sig- less inhibition is shown for specific frequencies, which nificant bridge between single-cell neurophysiology it was not. This leaves the extensive investigation of cell 89- 1. A and the extensive literature on human psychophysics using periodic luminance gratings (see for example glance at Fig. 4 does not give a convincing impression Campbell and Robson, 1965; Blakemore, Muncey and of marked preference for any aspect of the stimulus Ridley. 1973). configuration used. (It should be remembered that by I shall argue that the results of Glezer rt al. do not chance alone comparisons between 50 results should give convincing support to a model in which the optiproduce roughly twelve comparisons that would differ mal stimulus for cortical cell is a grating rather than sufficiently to appear significant at P = DO1 on an a line. and even if the arguments can be disputed, it is uncorrected t-test.) However, even taking the results a marked distortion of the data to describe the results at face value, it is not clear what stimulus dimenin rigorous mathematical terms. As a psychophysicist_ sions control the magnitude of the response. The I am not competent to assess the neurophysiological authors have abstracted the variable of number of bars techniques, so my comments will be restricted to a for presentation in Fig. 5a, and it does seem that both stimulus-response analysis on the assumption that the for this and other bar widths. response increases with nemophysiology is sound. number of bars by a total of 150 per cent. But the imIn the section concerning spatial frequency analysis pulse counts for the single-bar stimuli show ‘that the authors describe full results from one “typical” simply increasing the bar width of a single bar up to complex cell and supporting data from approximately the maximum width of the grating gives an increase in nine other cells. While it would be prolix to consider response of 100 per cent, which may not be signifiall aspects of these results, it appears that many major cantly less than the increase for multiple bars (see results on which the authors base their conclusions are Table I). subject to alternative explanations for which proper Nevertheless, Fig. 4 does give the impression of controls are not described. For example, the best evi- some spatial frequency specificity in showing a general dence for an optimal response to a grating seems to be preference for four or five bars over three or less. If this in cell 109-J (Figs. Sb and 22). It does respond conwere a question of narrow-band tuning of the cell to vincingly more to movement of three bars than to one a certain spatial frequency, one would expect that bar of the same total width. and it shows several re- stimuli of approximately a certain spatial frequency sponse peaks when traversed by a single bar. However, would consistently be optimal for the cell. Table 1 the peaks seem so variable for different bar widths that shows the impulse counts for most stimuli-arranged in it is not clear whether they are repeatable or are just order of spatial period (reciprocal of spatial frequency). statistical fluctuations. It is not reported whether the Single bars are tabulated separately as they have no cell showed narrow-band spatial-frequency tuning. dominant spatial frequency. It is clear from this table In cell 105-2 (Fig. 7) a larger response is obtained for that very few of the multiple bar responses are larger two bars than for a single bar of the same total width. than the optimal single-bar response. The period for But responses are not shown for a single bar of the maximum response (bold) seems to vary unsystematisame width as the component bars of the two-bar cally with number of bars, and actually shifts the entire 303
Letter to the Editors
.x)J
Table 1. Number of impulses recorded in response to multiple-bar stimuli arranged in order of spatial period of stimulus (from Giezer et ul.. I973)
Sinylc bar
iv = Bar width in degrees of visual angle. s = Bar separation in degrees of visual angle. tr = Xumber of bars in sttmulua i = Number of impulses in response. Maximum response for each value oftz is in bold figures.
iength of the scale (almost a decade of spatial frequency) between the Z and 5 bar stimuli. This is far less tuning than the octave bandwidth that would be expected even from a cell with an excitatory strip and in~i~~t~ry Ranks. I conclude from this that not only does the cell show no evidence of narrow band tuning. but also that it is very doubtful whether spatial frequency can be regarded as the controlling stimulus variable at all. I have been unable to determine what the controlling variable may be, but f suspect that much of the variation beyond overall stimulus size may be random t~u~tuat~o~ in sensitivity. To summarize. the authors’ evidence for spatial frequency specificity is based largely on two ceils. in neither of which were they able to demonstrate narrow-band spatial frequency tuning. Such tuning is a prerequisite for even the crudest sort of Fourier analy sis. which is already known to be possible by means of the classic type of complex cell of Hubel and Weisel ( 1961).which will respond preferentially to gratings of a certa’in spatial frequency with an octave bandwidth. Complex cells are not specialized for spatial frequency as such. since they do not respond preferentially to a multiple-bar stimulus. In conctusion. the search for spatial frequency filters in the visuaf cortex should not ignore the Fact that hyper-complex cells are likely to be connected somewhat irregularly in a minority of cases, SmaIl gaps or crenellations in the fields of a few ceils should not be
regarded as constituting reliable evidence that the cortex contains a bank of spatial frequency filters performing a holographic transform of the stimulus. And while it is true that many fairly regular textures occur in the environment the majority of these are regular in two dimensions (rather than the single dimension of a grating). and would therefore not be optimal stimuli for grating detectors, but would require specialized “speckle detectors” for optimal encoding. C. WILLIA?d
TYLER
REFERENCES
Blakemore C.. Muncey J. P. J. and Ridfey R. M. (1973) Stimulus specificity in the human visual system. I/ision Res. 13, 1913-1932. Campbell F. W. and Robson J. G. (1968) .-\pplication of Fourier analysis to the visibility of gratings. J. Ptlysiuk, Land. 197, 531-366. Glezer V. IX, IvanoKV. A. and Tscherbach T. A. (1975) Investigation of complex and hyper-compler receptive fields of visual cortex oi the cat as spatial frequency fiiters. Vision Res. 13, lSf5-1904. Hub& I3. H. and Weisel T. N. (1961) Receptive fields. binocular interaction and functional architecture in the cat’s visual cortex. J. Physiof., L011fl.160. 106-153.
