Spatial selectivity of visual mechanisms sensitive to contrast modulation*

V. V. Babenko,a) D. V. Yavna, A. A. Solov’ev, and M. B. Miftakhova

Southern Federal University, Rostov-on-Don

(Submitted February 9, 2011)Opticheskiı̆ Zhurnal 78, 10–16 (December 2011)

This paper is devoted to an investigation of the parameters that specify the spatial adjustment ofvisual mechanisms sensitive to contrast modulation. The bands for tuning to the spatialfrequency, phase, and orientation of the envelope were determined. The masking paradigm wasused to solve this problem. It is found that band-pass tuning applies to all the indicatedparameters. The width of the transmission bands in the problem of detecting contrastmodulation proved to be somewhat wider than for the mechanisms that are sensitive tobrightness modulation. c© 2011 Optical Society of America.

Studies of visual perception have a history that goesback to ancient times. However, the real breakthrough in thisspecialization occurred in the middle of the last century, whennew neurophysiological and psychophysical techniques wereproposed for studying the initial stages of the processing ofvisual information. As a result, the transfer characteristics ofthe human visual system were determined,1 and proofs of itsmultichannel nature were obtained.2 Subsequent study of thespatial selectivity of visual pathways and the determination oftheir structural characteristics3–5 made it possible to advanceto the creation of models of early vision.6,7 As a result,the initial stage of visual processing was represented as aset of parallel linear filters sensitive to brightness gradientsand selective to their localization, orientation, and spatialfrequency. Simple striatal neurons were regarded as suchfilters. Although psychophysical indicators characterize thesimultaneous operation of many parallel paths from the retinato the cortex, these indicators coincided fairly closely with theselectivity parameters of individual striatal neurons.8,9

However, it was subsequently found that far from allvisual problems, even extremely simple ones, can be solvedby means of such a system of filters. Figure 1 showsimages of random-point patterns modulated in brightness (a)and in contrast (b). Our visual system easily detects bothmodulations. However, even though brightness changes canactually be detected by the mechanisms discussed above,contrast changes remain undetected by them. This is becausethe total energy of the stimulus inside the antagonisticsubfields remains unchanged. Such a problem can be solvedonly by spatial unification and comparison of the outputs ofadjacent filters. Many other facts have been obtained that canbe explained only by the operation of spatial grouping. As aresult, the term “second-order filters” has appeared.

According to the concepts that exist today, visualprocessing begins with local linear filtering, as a resultof which the carrier (the attributes of the local elementsof the image) is described. The outputs of these filtersare subjected to nonlinear transformations (half-wave and

* This article is a development of the report “Adjusting second-order visualfilters to the orientation of the envelope,” presented at the conference AppliedOptics–2010.

full-wave rectification) and are combined at the operators ofthe next level. These second-order filters provide a descriptionof the envelopes (the spatial modulations of the attributes).

In order to discriminate the information concerning thecharacteristics of the envelope, the second-order filters mustbe selective to its parameters. It has actually been shown thatthey are sensitive to the orientation of the envelope10 and itsspatial frequency.11

However, the simple statement that they are spatiallyselective is inadequate to create a mathematical model of thesecond-order visual mechanisms. It is necessary to determinethe tuning bands of the filters. This was the goal of ourinvestigation. We studied the tuning characteristics of thesecond-order filters sensitive to contrast modulation. Themasking paradigm was used to solve the formulated problem.

It was necessary in this case to solve a number ofmethodological problems. First, the spectral characteristics ofthe stimulus must not change when the contrast of the carrieris being modulated. Otherwise these changes will already bedetected by the first-order filters. This is why such a customarystimulus as a sinusoidal grating cannot be used as a carrier.If a random-point pattern is used as the carrier, its contrastmodulation does not alter the initial spectrum, since it actuallyincludes all frequencies. However, the action of such a maskon the first-order filters is so great that it is hard to separateout its effect on the second-order filters. The use of filteredband noise as a carrier reduces the action of the mask onthe first-order filters, but the problem of separating out theinfluences remains. It follows from this that patterns are alsonecessary that do not change the initial spectrum when thecontrast is modulated, while it is to the second-filters that theirmasking effect is directed. We have formulated a pattern thatmade it possible to solve the formulated problem.

EXPERIMENTAL TECHNIQUE

Apparatus. The experimental apparatus was based on apersonal computer with a 2.5-GHz Intel Celeron processor,an Intel Graphics Media Accelerator 900 video adapter, anda 17-in. LG Flatron FT 775 monitor. The screen size inpixels was 1024 × 768, the grain size was 0.24 mm, and the

771 J. Opt. Technol. 78 (12), December 2011 1070-9762/2011/120771-06/$15.00 c© 2011 Optical Society of America 771

(a) (b)

FIG. 1. Random-point patterns, brightness modulated (a) and contrast modulated (b).

(a) (b)

FIG. 2. Examples of the textures used here. (a) Test texture, (b) one of the masking textures (orientation of the envelope shifted by 45◦).

frame-scanning frequency was 85 Hz. A regime was used thatprovided 256 shades of grey. The monitor was calibrated bymeans of a luxmeter.

Stimulation. The stimuli were checkerboard texturescomposed of Gabor micropatterns, which are described by

Gλθϕσγ (x, y) = exp((x′2 + γ 2y′2)/2σ 2) cos(2πx′/λ+ ϕ),

where

x′ = x cos θ + y sin θ,

y′ = −x sin θ + y cos θ,

σ = λ√

ln 2/2(2b+ 1)/((2b

− 1)π).

Here σ is the standard deviation of the Gaussian component, λis the wavelength of the cosinusoidal component of the kernel,θ is the orientation of the micropattern, ϕ is the phase shiftof the cosinusoidal component, γ is the “ellipticity” of theGaussian component, and b is the transmission band of thespatial frequency.

The orientation of the elements was vertical in the initialtexture, while the contrast was 0.44. The micropatterns werearranged over the entire monitor screen in checkerboard orderover the centers of the odd cells. The size of the conventional

cells of the checkerboard field was 0.44◦ × 0.44◦. Thefundamental spatial frequency of the carrier (a function of thebrightness variation in the initial texture along the horizontalaxis) was 3.5 cycle/deg.

The test texture was formed by modulating the contrastof the elements of the initial texture. The modulation wascarried out by multiplying the carrier by the envelope (thetwo-dimensional sinusoidal contrast-modulation function; themodulation axis is perpendicular to the orientation of themicropatterns). The amplitude of the envelope smoothlydecreased toward the edges of the screen as a result ofmultiplying it by a two-dimensional cosinusoidal half-wave.The spatial frequency of the envelope was 0.3 cycle/deg. Theenvelope introduced no substantial changes into the stimulusspectrum: The change of the total spectrum at the maximummodulation amplitude did not exceed 5%, and the centralfrequency did not change. The contrast-modulation amplitude(the range of contrast variation in the texture from the initialto the maximum and minimum values) in the test texture wasvariable and varied from 0 to 1.5 dB with a step of 0.1 dB.

The mask was formed by displacing the micropatternsfrom the odd into the even cells of a conventional checker-board field. Such an initial mask matched the test texture in allparameters (the threshold values obtained when this mask was

772 J. Opt. Technol. 78 (12), December 2011 Babenko et al. 772

0.90

0.80

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0.90

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0.50

MMB

AMthr, dB AMthr, dB

AMthr, dB

–2 –1 0 1 2 –2 –1 0 1 2

–2 –1 0 1 2

0.90

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0.70

0.60

SAA

SSA

MMB

(a)

(c)

(b)

(d)

Δf, octaves

–2 –1 0 1 2

Δf, octaves

Δf, octaves

Δf, octaves

YaDV

YaDV

FIG. 3. Threshold amplitude of the contrast modulation vs the discrepancy of the test and the mask with respect to spatial frequency of the envelope for threesubjects (a, b, and c). The horizontal axis shows the shift of the variable mask parameter relative to the test, and the vertical axis shows the threshold modulationamplitude. In the graphs that reflect the individual results, the vertical lines show the confidence intervals. (d) Superposition of the results; the dotted curve showsthe values used to determine the tuning band.

used are denoted on the horizontal axis by the number 0 in thegraphs of Figs. 3–5).

Depending on the problem of the experiment, the spatialfrequency, the phase, or the orientation of the modulationwas varied in the initial mask. In experiment 1, the spatialfrequency of the mask was increased and decreased by 2octaves with a step of 1 octave. In experiment 2, the phaseof the mask was displaced relative to the test with a step of0.25π to the maximum possible shift of 1π . In experiment3, the orientation of the axis of the modulation function waschanged from horizontal to vertical with a step of 22.5◦. Thecontrast-modulation amplitude was maximal (1.5 dB) in all themasks. Examples of the textures used here are shown in Fig. 2.The background luminance of the screen was maintained at alevel of 135 cd/m2.

Procedure. The subjects were located 130 cm from themonitor screen. The angular size of the screen in this casewas 14◦×10.5◦. The procedure of two-alternative compulsorychoice was used to determine the threshold amplitude of thecontrast modulation. First the test texture and then the maskingtexture was presented in each of two time windows, separatedby an interval of 750 ms. The test lasted 200 ms, and themask also lasted 200 ms. The test texture was modulated inone of these windows, and it was not modulated in the other.The phase of the envelope in each presentation was randomlyshifted by −0.25π , 0, and +0.25π in parallel in the test andin the mask. By pressing the corresponding key, the subjectreported in which of the time windows the test texture wasmodified.

Each of the three experiments included five tests,corresponding to the number of masks. The tests were

sequenced in random order. The results of at least 20 sampleswere averaged for each subject with each test. The results ofthe first three or four trials were discarded in this case.

The subjects. Three subjects aged from 20 to 30 years,with normal eyesight or corrected to unity, took part in theexperiments. All the subjects were informed concerning theprocedure of the tests to be carried out, were convinced of thesafety of the experiments for health, and gave their consentto participate in the studies. The studies followed ethicalstandards.

EXPERIMENTAL RESULTS AND DISCUSSION

Selectivity for the spatial frequency of the envelope

Figure 3 shows the dependences that reflect the variationof the threshold amplitude modulation AMthr as the spatialfrequency of the test stimulus diverges by 1f from themasking stimulus. The greatest masking is provided by themask that coincides with the test texture in spatial frequency.Increasing or decreasing the frequency of the envelope in themask (with the test frequency constant) results in a pronounceddecrease of the masking effect. A significant decrease ofthe threshold is observed statistically when the frequenciesdiverge by even 2 octaves.

All the subjects thus had band tuning of their visual mech-anisms to the spatial frequency of the contrast modulation. Thecharacteristics of the resulting curves are extremely complex,and this is illustrated by superimposing them (when the valuesthat reflect the minimum masking are superimposed—with areduction of the frequency of the mask by 2 octaves).

The standard procedure for determining the transmissionband of the filter at the middle of the difference between

773 J. Opt. Technol. 78 (12), December 2011 Babenko et al. 773

1.00

1.10

1.00

0.90

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0.500 0

00

0.25 0.25

0.250.25

0.5 0.5

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0.750.75

1 1

11

Δϕ, π

SAA

MMB

AMthr, dBYaDV

y = –0.16x + 1.0

y = –0.16x + 0.8

y = –0.16x + 0.6

(a)

(c)

(b)

(d)

FIG. 4. Threshold amplitude modulation of the contrast vs discrepancy of the test and the mask with respect to the phase of the envelope (a, b, and c). (d)Superposition of the results; the formulas describe the trend lines.

0

0 0

022.5

22.5 22.5

22.545

45 45

4567.5

67.5 67.5

67.590

90 90

90

0.90

1.10

1.00

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0.70 0.70

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0.50 0.50

0.40 0.40

MMB

SAA

AMthr, dB

Δθ, deg

YaDV(a)

(c) (d)

(b)

FIG. 5. Threshold amplitude modulation of the contrast vs discrepancy of the test and the mask with respect to the orientation of the envelope (a, b, and c). (d)Superposition of the results.

the minimum and maximum threshold values allowed us toestablish that the second-order filters’ tuning band to thespatial frequency is about 1.5 octave: 0.6–0.7 octave onthe side of decreased spatial frequency and 0.7–0.8 octaveon the side where it increases. These results indicate that

the selectivity of the second-order filters to the spatialfrequency of contrast modulation is fairly narrow. However,it is somewhat wider than the analogous values obtained forsecond-order filters that are selective to the spatial frequencyof brightness modulation.

774 J. Opt. Technol. 78 (12), December 2011 Babenko et al. 774

At the same time, it is noteworthy that the threshold valuesas the frequency of the mask increases by 2 octaves are higherthan the symmetric values. This can be associated with theeffects of inhibiting interaction between second-order filtersconstructed at close-lying modulation frequencies. Moreprecisely, one can be dealing with unidirectional inhibitionfrom filters selective to a higher spatial frequency of contrastmodulation.

Selectivity to the phase of the envelope

Shifting the phase of the envelope in the masking stimulusrelative to the envelope in the test texture reduces themodulation-detection threshold. The reduction continues untilthe test and the mask are out of phase by 1.0π . These resultsare shown in Fig. 4. The decrease of the threshold is reliablyobserved by subject MMB even when the relative phase shift1ϕ is 0.5π , while subject YaDV observes it at 0.75π , andSAA at 1.0π . This can indicate that the subjects have differentsensitivities to the phase shifts of the contrast modulation.

However, if we construct the trend lines for eachdependence, it turns out that these linear functions have thesame slope (see the equations in the graphs). The threshold inthis case decreased by half for all the subjects as the phasediverged by 0.5π . This shows that the transmission band inphase is about ±0.5π on the average for the second-orderfilters.

A change of the phase characteristics of periodic stimuliis often regarded as synonymous with a change of localization.In this case, selectivity to phase appears as an integralcharacteristic of the mechanism being studied, since a decisionconcerning the displacement of the simulation is made bythe system on the basis of an analysis of the responses ofa multitude of operators. The phase shift in our experimentswas not accompanied by a displacement of the mask relativeto the test. This made it possible, first, to estimate just thephase sensitivity of the mechanism and, second, to obtainconfirmation of the linearity of the second-order filters, whichis indicated in a number of models of this mechanism (see, forexample, Ref. 12).

Selectivity to the orientation of the envelope

As far as selectivity to the orientation of the envelope isconcerned, we obtained ambiguous results (Fig. 5). Two of thesubjects demonstrate very pronounced selectivity, while thethird demonstrated none.

The presence of selectivity to orientation of the contrastgradient can be evidence that the filters being studiedhave elongated receptive fields, constructed according to theopponent principle. The absence of selectivity, conversely,most likely indicates concentric organization of their receptivefields. Can it be assumed that different rules for combiningfirst-order filters are active in different subjects? This looksunlikely.

Another explanation seems more logical. To all appear-ances, the level of spatial grouping of visual informationthat we studied is not the last. The assumptions of Ref. 13already addressed this possibility. In one of our papers, wealso showed that it is expedient to combine the outputs of

second-order filters constructed with different orientations ofthe envelope.14 It is this operation that makes it possible togive a complete description of a discriminated object. Thishypothesis makes it possible to look at the results of YaDVdifferently. The absence of selectivity to orientation can bebecause the result is affected by the next stage of processing, atwhich the orientation-selective filters are combined. However,it is not possible at this stage of the work to determine whythis operation has a different effect on the results of differentsubjects.

If one starts from the assumption that the second-orderfilters are actually selective to orientation, but that this isnot always detected experimentally (possibly because ofmethodology), the question of the transmission band of thesefilters remains crucial.

Let us consider the results of the two subjects whodemonstrate such selectivity. Superposing them by bringingthe minimum threshold values into coincidence makes itpossible to determine the transmission band. It approximatelyequals ±22.5◦.

CONCLUSION

As a result of this study, it was established thatsecond-order visual mechanisms that are sensitive to contrastmodulation are selective to the spatial frequency, phase, andorientation of the envelope. This confirms the multichannelnature of the stage of spatial grouping of local visualinformation. The characteristics of the spatial tuning of thesefilters have also been determined. Their transmission bandsturned out to be somewhat wider than the analogous bands forfirst-order filters. These results are a necessary link in creatinga mathematical model of second-order visual mechanisms.

a)Email: babenko@sfedu.ru

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