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Some evidence against Fourier analysis as a function of the receptive fields in cat's striate cortex
LEXTER TO THE ELMTORS
SOME EVIDENCE AGAINST FOURIER ANALYSIS AS A FUNCTION OF THE RECEPTIVE FIELDS IN CAT’S STRIATE CORTEX (Received
12 Seprember
1979:
in
revisedform 20 January 1980)
To clear up this question we carried out the followSince Hubel and Wiesel (1962) have found the simple and complex receptive fields in cat’s striate cortex the ing experiment. If a neuron sensitive to changes of question of their function in visual processing remainsstimulus o~en~tion really is the Fouler-alter tuned under discussion. In the initial interpretation given by to some spatial frequency then adding to the optimal the authors in cautious words these receptive fields stimulus of the perpendicularly oriented grating must were assumed to be detectors of oriented fines, edges not a&ct the reaction. That was tested The activity of the neurons of field 17 of cat’s visual and other compIex features in the image. At present there appear many works in which the receptive fields cortex was recorded under the condition of chronic are considered as filters of spatial frequencies and the experiment with painiess fixation of the cat’s head in a stereotaxic apparatus (Noda et al., 1970). Two separresponses of such neurons are said to give the amphtudes of harmonics in a series of some orthogonal ate projectors were used to compose visual stimulimoving sinusoidal gratings. Spatial frequencies of the functions. The basic concept of these inv~tigations was sug- gratings were from OS to 5.5 c/deg. They were presented on the spherical (1 m radius) white screen gested by Campbell and Robson (1968). They concluded from the psychophysical experiments that the illuminated homogenously with the background light. Luminance of the bright and dim parts of the gratings human visual system have linearly independent mechanisms tuned to different bands of spatial frequencies. This conclusion is not yet well-supported because any non-linear system under the condition of small input signal behaves as linear one and therefore responds independently to different spatial frequencies of the signal. More essential reasons for the suggestion seem to be found in the experiments on adaptation of the visual system to sinusoidal gratings (Blakemore and Campbell, 1968; Blakemore and Nachmias, 1971). It was revealed in those experiments that the exposition to the bright sinusoidal grating Ied to increase in the threshold contrast of gratings when their spatial frequency came close to those of the adaptation stimulus. The corresponding bandwidth of the adaptation effect was about 2 octaves. The electrophysiological investigation of elements of the visual cortex could give us much stronger evii dence for the su~~tion that they produce Fourieranalysis of the retinal image. The appropriate neuronfilters were found and studied thoroughly (MatTei and Fiorentini, 1973; Gleser et al., 1973, 1976; Tyler, 1978). But these works did not incorporate with the 3 demonstration of linearity of the elements that is to say additivity in the response to the sum of stimuli. Without this additivity the neuron-filters would not maintain their spatial-frequency characteristics under the conditions of natural stimulation when a complex image falls upon each receptive field In that case we could not speak of Fourier-analysis as a main function of those elements of the visual cortex. So it is necessary to look if this response to the sum of stimuli Fig. 1. Histograms of compkx (1 and 2) and simple (3) cells of different spatial frequencies and/or orientation is responses to the movements of the gratings with different the sum of the responses to each stimulus presented spatial frequencks. Movement velocity for 1 and 2, 5 deg/ separately. sec. for 3-2 de@e. The sum of 10 events.
7
1023
Ii
I024
Letter to the Editors
-61 A-B
Fig 2. A. The histogram of the complex cell response to the movement of the optimal grating. B. The histogram of the same cell response to the simultaneous movements of the optimal and the null gratings. A-B. The subtraction of histograms A and B. Frequency, 1c/grad, velocity, 5 deg/sec.
2
-lsec loo 80
I
k
3
lsac
5
% 88 40 30 :: -10 -20 -30 c-
22s A
I
B
A-B
Fig 3. The histograms of responses to the optimal grating on the background of the stable null grating (A) and to the simultaneous movement of both. (Bb I-simple cell in the layer IV, 1.5 c/grad 2 deg/sec; 20 events; 2_4--complex cells, 1.0.5 and 0.5 c/grad. velocities: 5.20 and 5 deg/sec respectively, 20 events; himple cell in layer VI, 0.5 c/grad, 2 deg/sec, 10 events.
1015
Letter to the Editors and background were 4Ocd:m’, 9.5 cd/m2 and 25 cd/m2 respectively. The sizes of the stimuli were 20 x 20’ and the receptive fields were inside this square during all the movements of the gratings. At optimal orientation and velocity the majority of studied neurons showed selectivity to spatial frequencies. Figure 1 demonstrates the responses of three such units to the moving gratings with frequencies: 0.5, 1.0, f.5 c/deg. There were carried out two main experiments. In the first one for each neuron showing frequency selectivity we recorded its response to the optimal stimulus and then the grating with the same spatial frequency but rotated by 90” was projected onto the receptive field. The letter grating gave no response when being presented alone. The recordings of responses to the movements of the two gratings are shown in Fig. 2. This presents the reaction of the neurons to the movement of the two perpendicular gratings (B) and their reaction to the movement of the optimal stimulus (A). In (A-B) we show the difference of the responses (A) and (B). The inhibitory influence of the added grating is obvious. In such experiment the average illumination of the receptive field was changed after projection of the second grating. It could affect the response as a result of changing the neuron’s adaptation level. Therefore we performed another experiment in which both gratings were presented onto the receptive field simultaneously, first the optimal one was moving and then both were moved together, 26 neurons were studied. Figure 3 shows recordings made during one penetration into the cortex. The upper line shows the response of the simple cell apparently from layer IV of cat’s cortex. The next three rows present the responses of the complex cells. The last row shows recordings of the simple cell from layer VI of the cortex. As can be seen from Fig. 3 addition of the other grating significantly reduced the reaction to the main stimulus under the same condition. This property was found in all neurons studied in this experiment. Therefore none of these cells can be the unit of the hypothesized linear system of signal processing because none of them demonstrated additivity in its reaction to the stimuli. Thus. from the response of some simple or complex cell of the visual system the brain cannot calculate the amplitude of the “optimal” (for that cetl) spatial frequency in the picture projected onto the receptive field of the cell though it is highly selective with re-
spect to frequency. Such a calcuiation is impossible because the response of the cell depends greatly on the orthogonal components (and hence the others) of the input signal. That is the reason why we should not say that the pool of such receptive fieId produces the expansion of the retinal image as a series of harmonics (of any kind); at this level of the visual system Fouler-analysis of the image is not carried on. These results in our opinion leave without answer the question of the existence of such “linearly independent mechanisms” of signal processing within other channels of the visual system. Acknowledgements-We would like to express our appreciation to Prof G. Riuolatti for allowing US to perform these experiments in his Iaboratory and to Dr H. A. Buchlel for help with the computer. Institute for Problems of ~n~fmurion transmission Academy of Sciences of the U.S.S.R. Moscow, U.S.S.R.
A. P. PETROV 1. N. P~GAREV G. M. ZENKIS
REFERENCES
Blakemore C. and Campbell F. W. (1969)On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. J. Php siol. 203, 237-260.
Blakcmore C. and Nachmias J. (1971) The orientation selectivity of two visual after-effects. J. Physiol. 213. 157-l 74. Campbell F. W. and Robson J. G. (1968) Application of Fourier analysis to the visibility of gratings. J. Physiol. 197, 551-556. Gleser V. D., Cooperman A. M., Ivanov V. A. and fscherbath T. A. (1973) Investigation of complex and hypercomplex receptive fields of visual cortex of the cat as spatial frequency filters. Vision Res. 13, 1875-1904. GIeser V. D., Cooprman A. M.. Ivanov V.-A. and Tscherbath T. A. (1976) An investigation of spatial frequency characteristics of the complex receptive fields in the visual cortex of the cat. Vision Res. 16, 789-797. Hubel D. G. and Wiesel T. (1962) Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160. 106-154. Maffei L. and Fiorentini A. (1973) The visual cortex as a spatial frequency anatyser. Vision Res. 13, 1235-1267. Noda H., Freeman R. B. Jr., G;es B. and Creutzfeld 0. D. (1970) Neuronal responses in the visual cortex of awake cats to stationary and moving targets. E.~pt Brain Res. 1% 389405. TyIer C. W. (1978) Selectivity for spatial frequency and bar width in cat visual cortex. Vision Res. 18. 121-122.
SOME EVIDENCE AGAINST FOURIER ANALYSIS AS A FUNCTION OF THE RECEPTIVE FIELDS IN CAT’S STRIATE CORTEX (Received
12 Seprember
1979:
in
revisedform 20 January 1980)
To clear up this question we carried out the followSince Hubel and Wiesel (1962) have found the simple and complex receptive fields in cat’s striate cortex the ing experiment. If a neuron sensitive to changes of question of their function in visual processing remainsstimulus o~en~tion really is the Fouler-alter tuned under discussion. In the initial interpretation given by to some spatial frequency then adding to the optimal the authors in cautious words these receptive fields stimulus of the perpendicularly oriented grating must were assumed to be detectors of oriented fines, edges not a&ct the reaction. That was tested The activity of the neurons of field 17 of cat’s visual and other compIex features in the image. At present there appear many works in which the receptive fields cortex was recorded under the condition of chronic are considered as filters of spatial frequencies and the experiment with painiess fixation of the cat’s head in a stereotaxic apparatus (Noda et al., 1970). Two separresponses of such neurons are said to give the amphtudes of harmonics in a series of some orthogonal ate projectors were used to compose visual stimulimoving sinusoidal gratings. Spatial frequencies of the functions. The basic concept of these inv~tigations was sug- gratings were from OS to 5.5 c/deg. They were presented on the spherical (1 m radius) white screen gested by Campbell and Robson (1968). They concluded from the psychophysical experiments that the illuminated homogenously with the background light. Luminance of the bright and dim parts of the gratings human visual system have linearly independent mechanisms tuned to different bands of spatial frequencies. This conclusion is not yet well-supported because any non-linear system under the condition of small input signal behaves as linear one and therefore responds independently to different spatial frequencies of the signal. More essential reasons for the suggestion seem to be found in the experiments on adaptation of the visual system to sinusoidal gratings (Blakemore and Campbell, 1968; Blakemore and Nachmias, 1971). It was revealed in those experiments that the exposition to the bright sinusoidal grating Ied to increase in the threshold contrast of gratings when their spatial frequency came close to those of the adaptation stimulus. The corresponding bandwidth of the adaptation effect was about 2 octaves. The electrophysiological investigation of elements of the visual cortex could give us much stronger evii dence for the su~~tion that they produce Fourieranalysis of the retinal image. The appropriate neuronfilters were found and studied thoroughly (MatTei and Fiorentini, 1973; Gleser et al., 1973, 1976; Tyler, 1978). But these works did not incorporate with the 3 demonstration of linearity of the elements that is to say additivity in the response to the sum of stimuli. Without this additivity the neuron-filters would not maintain their spatial-frequency characteristics under the conditions of natural stimulation when a complex image falls upon each receptive field In that case we could not speak of Fourier-analysis as a main function of those elements of the visual cortex. So it is necessary to look if this response to the sum of stimuli Fig. 1. Histograms of compkx (1 and 2) and simple (3) cells of different spatial frequencies and/or orientation is responses to the movements of the gratings with different the sum of the responses to each stimulus presented spatial frequencks. Movement velocity for 1 and 2, 5 deg/ separately. sec. for 3-2 de@e. The sum of 10 events.
7
1023
Ii
I024
Letter to the Editors
-61 A-B
Fig 2. A. The histogram of the complex cell response to the movement of the optimal grating. B. The histogram of the same cell response to the simultaneous movements of the optimal and the null gratings. A-B. The subtraction of histograms A and B. Frequency, 1c/grad, velocity, 5 deg/sec.
2
-lsec loo 80
I
k
3
lsac
5
% 88 40 30 :: -10 -20 -30 c-
22s A
I
B
A-B
Fig 3. The histograms of responses to the optimal grating on the background of the stable null grating (A) and to the simultaneous movement of both. (Bb I-simple cell in the layer IV, 1.5 c/grad 2 deg/sec; 20 events; 2_4--complex cells, 1.0.5 and 0.5 c/grad. velocities: 5.20 and 5 deg/sec respectively, 20 events; himple cell in layer VI, 0.5 c/grad, 2 deg/sec, 10 events.
1015
Letter to the Editors and background were 4Ocd:m’, 9.5 cd/m2 and 25 cd/m2 respectively. The sizes of the stimuli were 20 x 20’ and the receptive fields were inside this square during all the movements of the gratings. At optimal orientation and velocity the majority of studied neurons showed selectivity to spatial frequencies. Figure 1 demonstrates the responses of three such units to the moving gratings with frequencies: 0.5, 1.0, f.5 c/deg. There were carried out two main experiments. In the first one for each neuron showing frequency selectivity we recorded its response to the optimal stimulus and then the grating with the same spatial frequency but rotated by 90” was projected onto the receptive field. The letter grating gave no response when being presented alone. The recordings of responses to the movements of the two gratings are shown in Fig. 2. This presents the reaction of the neurons to the movement of the two perpendicular gratings (B) and their reaction to the movement of the optimal stimulus (A). In (A-B) we show the difference of the responses (A) and (B). The inhibitory influence of the added grating is obvious. In such experiment the average illumination of the receptive field was changed after projection of the second grating. It could affect the response as a result of changing the neuron’s adaptation level. Therefore we performed another experiment in which both gratings were presented onto the receptive field simultaneously, first the optimal one was moving and then both were moved together, 26 neurons were studied. Figure 3 shows recordings made during one penetration into the cortex. The upper line shows the response of the simple cell apparently from layer IV of cat’s cortex. The next three rows present the responses of the complex cells. The last row shows recordings of the simple cell from layer VI of the cortex. As can be seen from Fig. 3 addition of the other grating significantly reduced the reaction to the main stimulus under the same condition. This property was found in all neurons studied in this experiment. Therefore none of these cells can be the unit of the hypothesized linear system of signal processing because none of them demonstrated additivity in its reaction to the stimuli. Thus. from the response of some simple or complex cell of the visual system the brain cannot calculate the amplitude of the “optimal” (for that cetl) spatial frequency in the picture projected onto the receptive field of the cell though it is highly selective with re-
spect to frequency. Such a calcuiation is impossible because the response of the cell depends greatly on the orthogonal components (and hence the others) of the input signal. That is the reason why we should not say that the pool of such receptive fieId produces the expansion of the retinal image as a series of harmonics (of any kind); at this level of the visual system Fouler-analysis of the image is not carried on. These results in our opinion leave without answer the question of the existence of such “linearly independent mechanisms” of signal processing within other channels of the visual system. Acknowledgements-We would like to express our appreciation to Prof G. Riuolatti for allowing US to perform these experiments in his Iaboratory and to Dr H. A. Buchlel for help with the computer. Institute for Problems of ~n~fmurion transmission Academy of Sciences of the U.S.S.R. Moscow, U.S.S.R.
A. P. PETROV 1. N. P~GAREV G. M. ZENKIS
REFERENCES
Blakemore C. and Campbell F. W. (1969)On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. J. Php siol. 203, 237-260.
Blakcmore C. and Nachmias J. (1971) The orientation selectivity of two visual after-effects. J. Physiol. 213. 157-l 74. Campbell F. W. and Robson J. G. (1968) Application of Fourier analysis to the visibility of gratings. J. Physiol. 197, 551-556. Gleser V. D., Cooperman A. M., Ivanov V. A. and fscherbath T. A. (1973) Investigation of complex and hypercomplex receptive fields of visual cortex of the cat as spatial frequency filters. Vision Res. 13, 1875-1904. GIeser V. D., Cooprman A. M.. Ivanov V.-A. and Tscherbath T. A. (1976) An investigation of spatial frequency characteristics of the complex receptive fields in the visual cortex of the cat. Vision Res. 16, 789-797. Hubel D. G. and Wiesel T. (1962) Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160. 106-154. Maffei L. and Fiorentini A. (1973) The visual cortex as a spatial frequency anatyser. Vision Res. 13, 1235-1267. Noda H., Freeman R. B. Jr., G;es B. and Creutzfeld 0. D. (1970) Neuronal responses in the visual cortex of awake cats to stationary and moving targets. E.~pt Brain Res. 1% 389405. TyIer C. W. (1978) Selectivity for spatial frequency and bar width in cat visual cortex. Vision Res. 18. 121-122.