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A noise masking experiment in grating perception at threshold: The implications on binocular summation
RESEARCH
NOTE
A NOISE MASKING EXPERIMENT IN GRATING PERCEPTION AT THRESHOLD: THE IMPLICATIONS ON BINOCULAR SUMMATION* C. BRACCINI,G. GMBARDELLAand G. SI;ETT.\ Ijtituto di Elettrotecnica dell’Universith di Geneva. 16145 Gcnova. (Rrceiced 1 Srpremher 1978; in recisrdform
Abstract-A noise masking
experiment
in Frating
perception
Italy
II Septrmbrr 1979) at threshold
is described.
The contrast
curve has been measured in two different cases. In one case the external noises were identical for the two eyes. In the other case the external noises were only statistically identical, but point-wise different. The sensitivity curve turns out to be significantly higher in the latter case, to an extent which sensitivity
appears to be consistent with the finding that some form of neural integration takes place before grating detection. The implications of the experiments on the models of binocular summation are discussed.
ISTRODUCTION The main aim of this note is to present a new psychophysical technique for investigating the binocular interaction mechanisms in fixed grating perception at threshold (Blake and Fox, 1973; Blake and Levinson, 1977; Campbell and Green, 1965). The technique consists essentially of measuring the binocular contrast sensitivity curves under two different masking conditions: in one case the external masking noises are identical for the two eyes, while in the other case the noises are only statistically identical but point-wise different. By comparing the sensitivity curves in two such cases. and by further comparing them \sith the sensitivity curve in the. absence of external noises, it becomes possible. as we shall see, to evaluate the internal noise (of the visual system) that limits the perception of the gratings at threshold. The technique also allows additional testing of some well known hypotheses and models of binocular interaction. At present our implementation of the above technique is only at a preliminary stage, meaning that our methods need to be improved and the statistics of the experiments must be enlarged. Therefore, the measurements that we have performed so far and those we show below (actually a sample of them) must be considered as only qualitative results, which do, however; represent a successful test of the suggested technique. Our experimental methods and results are given below. together with some comments and indications for further work. METHODSAND
EXPERI.VENTS
Stationary gratings of sinusoidal waveform and vertical orientation have been generated on the screen of * This work has been partially siglio Nazionale delle Ricerche”.
supported
by the “Con-
373
using conventional techniques. an oscilloscope Actually, two different oscilloscopes (phosphors P4 and P31) have been used in two consecutive and complete series of experiments. The average luminance of the screen was 3 cd/m’ in the first series of experiments, and 13 cd.im’ in the second. The useful width of the screen was 8 cm and the distance of the observer from the screen 229 cm, so that the total observation angle was 2’. We have used spatial frequencies between 1 and 20 c deg. The experimental setup was as shown schematically in Fig. 1. The subject looked at the oscilloscope through two half-reflecting screens (“perspex”), one for the left eye and one for the right eye. These screens had a 45’ orientation, as shown in Fig. 1, and allowed. for each eye, superimposing upon the oscilloscope image a noise image coming from the two lateral screens. The masking noise was obtained by means of appropriate slides, which were projected as shown in Fig. I over the two lateral screens. The optical path between the latter and the subject was the same as between the oscilloscope and the subject, so that both images, namely the gratings and noises, were focused. The two projectors were identical and so were the two noise slides, so that it was easy (by exploiting a couple of appropriate reference points) to fuse the two noise images. as required for the case of identical noises. When, vice versa. we wanted to have, for the two eyes, two independent noise images (though statisticatly identical), it was enough to reverse one of the two slides, by exploiting the fact that only a small part of the noise images over the lateral screens were actually used for masking the oscilloscope image. The two noises (“noise images”) in this second case will be referred to as “similar”. In order to vary the noise luminance. a couple of identical light filters could be inserted into the projectors. still preserving the symmetry of the system.
Research
Zore
Oscilloscope (stgnal moge gratings)
\ ‘;
I 1
half - tmsparent
screen I
,” -Fl--
InoIse
magel
-
left
’ !
Experimental set Qditawe
rlaht
schemes
Fig. 1. This experimental setup allows superimposing to the luminous sinusoidal grating formed on the screen of the osci!loscope some optical masking noises, that can be “identical” or simply “similar” for the two eyes. For this purpose two identical noise-slides are used. By projecting them over the tuiO lateral screens, two noise images are created, whose optical distance from the observer is the same as for the signal image. In one case the two noise images are made “identical” and are seen as “fused”. in the other case, by simply rqversing the slide in one of the two projectors, the noise images become point-wise different and independent. while remaining statistically identical (therefore: “similar”).
The average noise luminances used were 0.3, 1.12 and 3.6cd/m2, while the average noise contrast was always 0.18. The noise spectral density (which we measured digitally) turned out to be symmetrical with respect to the orientation of the spatial frequencies, and quite flat as far as the amplitude values were concerned. The cutoff frequency of the noise was close to 2Oc/deg, which was the highest spatial frequency of the gratings used during the experiments. The contrast sensitivity was measured for both monocular and binocular vision, with and without the masking noises. We never used artificial pupils and the monocular tests were performed while the unactive eye was kept closed. The monocular tests were used, in particular, for selecting the subjects with two (almost) equally efficient eyes. Three of our subjects happened to belong to the above category, and the results that we are going to show refer to only one of them. Such results, however. are sufficiently representative of the resutts obtained with the other subjects. The contrast sensitivity curves were obtained by presenting the gratings of different spatial frequencies in a random order and totalling a number of 7 tests for each frequency. Each test took place in the following way:
After choosing a certain spatial frequency, i.e. a grating, the “operator” slowly incremented its contrast C = (I,,,, - L,,)/2t,, (where L stands for luminance) by turning a caIibrated potentiometer, until the “subject” said “stop”, meaning “I see the grating.*’ The corresponding position of the potentiometer was then used for computing, through precomputed tables, the contrast threshold and the inverse of this quantity, which is, by definition, the “contrast sensitivity”, sometimes tailed the “sensitivity” ivithout further specification. Several sensitivity tests were also performed by keeping fixed thi spatial frequency of a grating, and randomly changing its contrast, so that a “psychometric curve” could be built up.
PRELIMINARY
RESULTS
AND
DlSClJSSiOS
A sample of the results of our experiments is shown in Fig. 2, where three sensitivity curves, corresponding to three different experimental situations, have been drawn: without any external noise (S_+,),with similar noises (S,,) and with identical noises (&). The figure shows that for all the examined spatial frequencies one has L
> &” I=-S,”
Research b&an
signal
lummance
3 OCdh’
klem
na6e
lumnance
I 12 cd/m’
SLbject
-
Sensltlvlty
G C
wlthcut
-.-
>)
with
__--
)>
with
SPATIAL
375
Kate
(SW)
nose solar
naises
ldentlcal
FREOUENCIES
(S,”
1
IS,, I
naises
(c/degl
Fig. 2. This figure shows, for one subject, the binocular contrast sensitivity curves in the three cases of “identical” masking noises (S,,), “similar” masking noises (S,,) and no masking noise at all (S,,). For each of the above cases the measures have been effected by randomly changing the spatial frequency of the grating and incrementing its contrast up to the detection point. The sensitivity values are the inverse of the contrast thresholds. The figure clearly shows that the sensitivity is significantly greater in the case of similar noises with respect to the case of identical noises. The extent of their ratio (about 2.8 dB) appears to be consistent with the finding that some form of neural integration takes place between the two channels before any detection process.
as one would expect on the base of what is already known on binocular gratings perception (Blake and Fox, 1973; Blake and Levinson, 1977; Campbell and Green, 1965). In particular, we can say that our experimental results are consistent with the well known and by now sufficiently stated hypothesis that in the perception of gratings co-operation between the two eyes is based on some form of neural integration rather than on a mechanism of “probability summation” (which would imply, in our case, a lower ratio between the experimental values of .S,, and S,,). In the paper of Campbell and Green (1965) a model of such “neural integration” has been explicitly suggested. As shown in Fig. 3, such a model is essentially based on the summation of the outputs from the two monocular channels before any form of gratings detection or discrimination takes place. Each monocular channel is characterized by some internal additive and independent noise. Such a model accounts in particular, and in a rather simple way, for the ,/2 ratio that has been found (Campbell and Green, 1965) between the binocular and the monocular sensitivities at threshold. To this end, it is enough to assume that the final detection mechanism operates on the basis of the signal-to-noise ratio, where the power of the signal (i.e. the gratings) is assumed to be proportional to the square of the contrast. C’. By letting Ni be the power of any one of the internal noises (which are of course
assumed to be independent), we further have that the internal noise power at the input of the detector system is Ni in the monocular case and 2Ni in the binocular case (which easily explains the above mentioned ,/2 ratio between the binocular and monocular sensitivities). Let us now briefly outline how our experimental technique might be used for measuring Ni and further investigating the kind of processing that takes place in the visual system before the blocks of Fig. 3.
lnternulna,se
i 5 ‘T
(rlR 1
right eye signal
+
+
s~%!y~ in=+
+n,l
left eye sqnal
Internal
natse
(n,)
Fig. 3. Crude schema of the interaction between the two monocular channels for sinusoidal gratings perception, according to the suggestion of Campbell and Green (1965). As specified in the text, the two input “signals” should be considered as the result of some earlier processing of the external luminous stimuli.
376
Research Not<
It is generally agreed that such earlier processing essentially consists of some non-linear (i.e. logarithmic) transformation followed by some linear bandpass filtering. This shows (Braccini er (II., 1978) that in the case of our experiments the presence of the external noises is simply equivalent. with respect to the schema of Fig. 3. to adding to the true internal noises niR and niL (right and left) some “equivalent internal noises”, neR and neL. whose power (i.e. the power of any one of them) will be referred to as :VE. If this is the case. we can perform the experiment of measuring the binocular contrast sensitivity curve in three different cases. each corresponding to a different amount of noise power at the input of the detecting system of Fig. 3. The first case. where no external noise is used, corresponds (as already mentioned) to a noise power equal to IN,. The other two cases. where “similar” and “identical” external noises are used, correspond respectively to the noise powers of Z(Ni + N,) and IV, + 3,V,. By assuming that (as implied by the model) the signal-to-noise ratio needed for perception at thresh-
old is always the same. and by measuring the threshold contrast for the three above-mentioned experimental situations. it should be possible to evaluate both .Vi and Ye. This latter quantity might further be used for testing and investigating as already mentioned, the processing stages that precede the blocks of Fig. 3. .~~~no~le~yements-The authors are indebted to Drs Glancarlo Cerofolini and Paolo Pieri for their substantial contribution to the experimental part of this work. REFERENCES
Blake R. and Fox R. (1973) The psychophysical inquiry into binocular summation. Percrpr. Ps.rchophyc. 11, 161-IS5. Blake R. and Levinson E. 11977) Spattal properties of binocular neurones in the human visual system. E.~pi Brain Res. 27, 721-232. Campbell F. W. and Green D. G. (19651 Monocular versus binocular visual acuity. Nnture 208, 191-191. Braccini C., Gambardella G. and Suetta G. (1978) External and internal noises in binocular perception of gratings at threshold. Internal Rem., Istituto di Elettrotecnica. Universita di Genova.
NOTE
A NOISE MASKING EXPERIMENT IN GRATING PERCEPTION AT THRESHOLD: THE IMPLICATIONS ON BINOCULAR SUMMATION* C. BRACCINI,G. GMBARDELLAand G. SI;ETT.\ Ijtituto di Elettrotecnica dell’Universith di Geneva. 16145 Gcnova. (Rrceiced 1 Srpremher 1978; in recisrdform
Abstract-A noise masking
experiment
in Frating
perception
Italy
II Septrmbrr 1979) at threshold
is described.
The contrast
curve has been measured in two different cases. In one case the external noises were identical for the two eyes. In the other case the external noises were only statistically identical, but point-wise different. The sensitivity curve turns out to be significantly higher in the latter case, to an extent which sensitivity
appears to be consistent with the finding that some form of neural integration takes place before grating detection. The implications of the experiments on the models of binocular summation are discussed.
ISTRODUCTION The main aim of this note is to present a new psychophysical technique for investigating the binocular interaction mechanisms in fixed grating perception at threshold (Blake and Fox, 1973; Blake and Levinson, 1977; Campbell and Green, 1965). The technique consists essentially of measuring the binocular contrast sensitivity curves under two different masking conditions: in one case the external masking noises are identical for the two eyes, while in the other case the noises are only statistically identical but point-wise different. By comparing the sensitivity curves in two such cases. and by further comparing them \sith the sensitivity curve in the. absence of external noises, it becomes possible. as we shall see, to evaluate the internal noise (of the visual system) that limits the perception of the gratings at threshold. The technique also allows additional testing of some well known hypotheses and models of binocular interaction. At present our implementation of the above technique is only at a preliminary stage, meaning that our methods need to be improved and the statistics of the experiments must be enlarged. Therefore, the measurements that we have performed so far and those we show below (actually a sample of them) must be considered as only qualitative results, which do, however; represent a successful test of the suggested technique. Our experimental methods and results are given below. together with some comments and indications for further work. METHODSAND
EXPERI.VENTS
Stationary gratings of sinusoidal waveform and vertical orientation have been generated on the screen of * This work has been partially siglio Nazionale delle Ricerche”.
supported
by the “Con-
373
using conventional techniques. an oscilloscope Actually, two different oscilloscopes (phosphors P4 and P31) have been used in two consecutive and complete series of experiments. The average luminance of the screen was 3 cd/m’ in the first series of experiments, and 13 cd.im’ in the second. The useful width of the screen was 8 cm and the distance of the observer from the screen 229 cm, so that the total observation angle was 2’. We have used spatial frequencies between 1 and 20 c deg. The experimental setup was as shown schematically in Fig. 1. The subject looked at the oscilloscope through two half-reflecting screens (“perspex”), one for the left eye and one for the right eye. These screens had a 45’ orientation, as shown in Fig. 1, and allowed. for each eye, superimposing upon the oscilloscope image a noise image coming from the two lateral screens. The masking noise was obtained by means of appropriate slides, which were projected as shown in Fig. I over the two lateral screens. The optical path between the latter and the subject was the same as between the oscilloscope and the subject, so that both images, namely the gratings and noises, were focused. The two projectors were identical and so were the two noise slides, so that it was easy (by exploiting a couple of appropriate reference points) to fuse the two noise images. as required for the case of identical noises. When, vice versa. we wanted to have, for the two eyes, two independent noise images (though statisticatly identical), it was enough to reverse one of the two slides, by exploiting the fact that only a small part of the noise images over the lateral screens were actually used for masking the oscilloscope image. The two noises (“noise images”) in this second case will be referred to as “similar”. In order to vary the noise luminance. a couple of identical light filters could be inserted into the projectors. still preserving the symmetry of the system.
Research
Zore
Oscilloscope (stgnal moge gratings)
\ ‘;
I 1
half - tmsparent
screen I
,” -Fl--
InoIse
magel
-
left
’ !
Experimental set Qditawe
rlaht
schemes
Fig. 1. This experimental setup allows superimposing to the luminous sinusoidal grating formed on the screen of the osci!loscope some optical masking noises, that can be “identical” or simply “similar” for the two eyes. For this purpose two identical noise-slides are used. By projecting them over the tuiO lateral screens, two noise images are created, whose optical distance from the observer is the same as for the signal image. In one case the two noise images are made “identical” and are seen as “fused”. in the other case, by simply rqversing the slide in one of the two projectors, the noise images become point-wise different and independent. while remaining statistically identical (therefore: “similar”).
The average noise luminances used were 0.3, 1.12 and 3.6cd/m2, while the average noise contrast was always 0.18. The noise spectral density (which we measured digitally) turned out to be symmetrical with respect to the orientation of the spatial frequencies, and quite flat as far as the amplitude values were concerned. The cutoff frequency of the noise was close to 2Oc/deg, which was the highest spatial frequency of the gratings used during the experiments. The contrast sensitivity was measured for both monocular and binocular vision, with and without the masking noises. We never used artificial pupils and the monocular tests were performed while the unactive eye was kept closed. The monocular tests were used, in particular, for selecting the subjects with two (almost) equally efficient eyes. Three of our subjects happened to belong to the above category, and the results that we are going to show refer to only one of them. Such results, however. are sufficiently representative of the resutts obtained with the other subjects. The contrast sensitivity curves were obtained by presenting the gratings of different spatial frequencies in a random order and totalling a number of 7 tests for each frequency. Each test took place in the following way:
After choosing a certain spatial frequency, i.e. a grating, the “operator” slowly incremented its contrast C = (I,,,, - L,,)/2t,, (where L stands for luminance) by turning a caIibrated potentiometer, until the “subject” said “stop”, meaning “I see the grating.*’ The corresponding position of the potentiometer was then used for computing, through precomputed tables, the contrast threshold and the inverse of this quantity, which is, by definition, the “contrast sensitivity”, sometimes tailed the “sensitivity” ivithout further specification. Several sensitivity tests were also performed by keeping fixed thi spatial frequency of a grating, and randomly changing its contrast, so that a “psychometric curve” could be built up.
PRELIMINARY
RESULTS
AND
DlSClJSSiOS
A sample of the results of our experiments is shown in Fig. 2, where three sensitivity curves, corresponding to three different experimental situations, have been drawn: without any external noise (S_+,),with similar noises (S,,) and with identical noises (&). The figure shows that for all the examined spatial frequencies one has L
> &” I=-S,”
Research b&an
signal
lummance
3 OCdh’
klem
na6e
lumnance
I 12 cd/m’
SLbject
-
Sensltlvlty
G C
wlthcut
-.-
>)
with
__--
)>
with
SPATIAL
375
Kate
(SW)
nose solar
naises
ldentlcal
FREOUENCIES
(S,”
1
IS,, I
naises
(c/degl
Fig. 2. This figure shows, for one subject, the binocular contrast sensitivity curves in the three cases of “identical” masking noises (S,,), “similar” masking noises (S,,) and no masking noise at all (S,,). For each of the above cases the measures have been effected by randomly changing the spatial frequency of the grating and incrementing its contrast up to the detection point. The sensitivity values are the inverse of the contrast thresholds. The figure clearly shows that the sensitivity is significantly greater in the case of similar noises with respect to the case of identical noises. The extent of their ratio (about 2.8 dB) appears to be consistent with the finding that some form of neural integration takes place between the two channels before any detection process.
as one would expect on the base of what is already known on binocular gratings perception (Blake and Fox, 1973; Blake and Levinson, 1977; Campbell and Green, 1965). In particular, we can say that our experimental results are consistent with the well known and by now sufficiently stated hypothesis that in the perception of gratings co-operation between the two eyes is based on some form of neural integration rather than on a mechanism of “probability summation” (which would imply, in our case, a lower ratio between the experimental values of .S,, and S,,). In the paper of Campbell and Green (1965) a model of such “neural integration” has been explicitly suggested. As shown in Fig. 3, such a model is essentially based on the summation of the outputs from the two monocular channels before any form of gratings detection or discrimination takes place. Each monocular channel is characterized by some internal additive and independent noise. Such a model accounts in particular, and in a rather simple way, for the ,/2 ratio that has been found (Campbell and Green, 1965) between the binocular and the monocular sensitivities at threshold. To this end, it is enough to assume that the final detection mechanism operates on the basis of the signal-to-noise ratio, where the power of the signal (i.e. the gratings) is assumed to be proportional to the square of the contrast. C’. By letting Ni be the power of any one of the internal noises (which are of course
assumed to be independent), we further have that the internal noise power at the input of the detector system is Ni in the monocular case and 2Ni in the binocular case (which easily explains the above mentioned ,/2 ratio between the binocular and monocular sensitivities). Let us now briefly outline how our experimental technique might be used for measuring Ni and further investigating the kind of processing that takes place in the visual system before the blocks of Fig. 3.
lnternulna,se
i 5 ‘T
(rlR 1
right eye signal
+
+
s~%!y~ in=+
+n,l
left eye sqnal
Internal
natse
(n,)
Fig. 3. Crude schema of the interaction between the two monocular channels for sinusoidal gratings perception, according to the suggestion of Campbell and Green (1965). As specified in the text, the two input “signals” should be considered as the result of some earlier processing of the external luminous stimuli.
376
Research Not<
It is generally agreed that such earlier processing essentially consists of some non-linear (i.e. logarithmic) transformation followed by some linear bandpass filtering. This shows (Braccini er (II., 1978) that in the case of our experiments the presence of the external noises is simply equivalent. with respect to the schema of Fig. 3. to adding to the true internal noises niR and niL (right and left) some “equivalent internal noises”, neR and neL. whose power (i.e. the power of any one of them) will be referred to as :VE. If this is the case. we can perform the experiment of measuring the binocular contrast sensitivity curve in three different cases. each corresponding to a different amount of noise power at the input of the detecting system of Fig. 3. The first case. where no external noise is used, corresponds (as already mentioned) to a noise power equal to IN,. The other two cases. where “similar” and “identical” external noises are used, correspond respectively to the noise powers of Z(Ni + N,) and IV, + 3,V,. By assuming that (as implied by the model) the signal-to-noise ratio needed for perception at thresh-
old is always the same. and by measuring the threshold contrast for the three above-mentioned experimental situations. it should be possible to evaluate both .Vi and Ye. This latter quantity might further be used for testing and investigating as already mentioned, the processing stages that precede the blocks of Fig. 3. .~~~no~le~yements-The authors are indebted to Drs Glancarlo Cerofolini and Paolo Pieri for their substantial contribution to the experimental part of this work. REFERENCES
Blake R. and Fox R. (1973) The psychophysical inquiry into binocular summation. Percrpr. Ps.rchophyc. 11, 161-IS5. Blake R. and Levinson E. 11977) Spattal properties of binocular neurones in the human visual system. E.~pi Brain Res. 27, 721-232. Campbell F. W. and Green D. G. (19651 Monocular versus binocular visual acuity. Nnture 208, 191-191. Braccini C., Gambardella G. and Suetta G. (1978) External and internal noises in binocular perception of gratings at threshold. Internal Rem., Istituto di Elettrotecnica. Universita di Genova.