Spatial frequency interference on grating-induction

Combining 1-D components to extract pattern information: It is about more than component similarity

At least under some conditions, plaid stimuli are processed by combining information first extracted in orientation and scale-selective channels. The rules that govern this combination across channels are only partially understood. Although the available data suggests that only components having similar spatial frequency and contrast are combined, the extent to which this holds has not been firmly established. To address this question, we measured, in human subjects, the short-latency reflexive vergence eye movements induced by stereo plaids in which spatial frequency and contrast of the components are independently varied. We found that, although similarity in component spatial frequency and contrast matter, they interact in a nonseparable way. One way in which this relationship might arise is if the internal estimate of contrast is not a faithful representation of stimulus contrast but is instead spatial frequency–dependent (with higher spatial frequencies being boosted). We propose that such weighting might have been put in place by a mechanism that, in an effort of achieve contrast constancy and/or coding efficiency, regulates the gain of detectors in early visual cortex to equalize their long-term average response to natural images.

The Oriented Difference of Gaussians (ODOG) model of brightness perception: Overview and executable Mathematica notebooks

The Oriented Difference of Gaussians (ODOG) model of brightness (perceived intensity) by Blakeslee and McCourt (Vision Research 39:4361-4377, 1999), which is based on linear spatial filtering by oriented receptive fields followed by contrast normalization, has proven highly successful in parsimoniously predicting the perceived intensity (brightness) of regions in complex visual stimuli such as White's effect, which had been believed to defy filter-based explanations. Unlike competing explanations such as anchoring theory, filling-in, edge-integration, or layer decomposition, the spatial filtering approach embodied by the ODOG model readily accounts for the often overlooked but ubiquitous gradient structure of induction which, while most striking in grating induction, also occurs within the test fields of classical simultaneous brightness contrast and the White stimulus. Also, because the ODOG model does not require defined regions of interest, it is generalizable to any stimulus, including natural images. The ODOG model has motivated other researchers to develop modified versions (LODOG and FLODOG), and has served as an important counterweight and proof of concept to constrain high-level theories which rely on less well understood or justified mechanisms such as unconscious inference, transparency, perceptual grouping, and layer decomposition. Here we provide a brief but comprehensive description of the ODOG model as it has been implemented since 1999, as well as working Mathematica (Wolfram, Inc.) notebooks which users can employ to generate ODOG model predictions for their own stimuli.

How attention enhances spatial resolution: Evidence from selective adaptation to spatial frequency

In this study, we investigated how spatial resolution and covert attention affect performance in a texture segmentation task in which performance peaks at midperiphery and drops at peripheral and central retinal locations. The central impairment is called the central performance drop (CPD; Kehrer, 1989). It has been established that attending to the target location improves performance in the periphery where resolution is too low for the task, but impairs it at central locations where resolution is too high. This is called the central attention impairment (CAI; Yeshurun & Carrasco, 1998, 2000). We employed a cuing procedure in conjunction with selective adaptation to explore (1) whether the CPD is due to the inhibition of low spatial frequency responses by high spatial frequency responses in central locations, and (2) whether the CAI is due to attention's shifting sensitivity to higher spatial frequencies. We found that adaptation to low spatial frequencies does not change performance in this texture segmentation task. However, adaptation to high spatial frequencies diminishes the CPD and eliminates the CAI. These results indicate that the CPD is primarily due to the dominance of high spatial frequency responses and that covert attention enhances spatial resolution by shifting sensitivity to higher spatial frequencies.

Human ocular following initiated by competing image motions: evidence for a winner-take-all mechanism

The initial ocular following responses (OFRs) elicited by 1/4-wavelength steps applied to the missing fundamental (mf) stimulus are in the backward direction and largely determined by the principal Fourier component, the 3rd harmonic [Sheliga, B. M., Chen, K. J., FitzGibbon, E. J., & Miles, F. A. (2005). Initial ocular following in humans: A response to first-order motion energy. Vision Research, 45, 3307-3321]. When the contrast of the 3rd harmonic was selectively reduced below that of the next most prominent harmonic-the 5th, which moves in the opposite (forward) direction-then the OFR reversed direction and the 3rd harmonic effectively lost all of its influence as the OFR was now largely determined by the 5th harmonic. Restricting the stimulus to just two sine waves (of equal efficacy when of equal contrast and presented singly) with the spatial frequencies of the 3rd and 5th harmonics of the mf stimulus indicated that the critical factor was the ratio of their two contrasts: when of similar contrast both were effective (vector sum/averaging), but when the contrast of one was <1/2 that of the other then the one with the lower contrast became ineffective (winner-take-all). This nonlinear dependence on the contrast ratio was attributed to mutual inhibition and was well described by a weighted-average model with just two free parameters. Further experiments with broadband and dual-grating stimuli indicated that nonlinear interactions occur not only in the neural processing of stimuli moving in opposite directions but also of stimuli that share the same direction and differ only in their spatial frequency and speed. Clearly, broad-band and dual-grating stimuli can uncover significant nonlinearities in visual information processing that are not evident with single sine-wave stimuli.

Comparing the spatial-frequency response of first-order and second-order lateral visual interactions: grating induction and contrast-contrast

The magnitudes of two suprathreshold lateral spatial-interaction effects--grating induction and contrast--contrast--were compared with regard to their dependence upon inducing-grating spatial frequency. Both effects cause the contrast of target stimuli embedded in surrounding patterns to be matched nonveridically. The magnitudes of each effect were measured in a common unit that indexed the degree of nonveridical contrast matching across a large range of target-grating contrasts (+/- 0.80). Grating induction was a low-pass effect with respect to spatial frequency, whereas contrast-contrast was bandpass, peaking at approximately 4.0 cycles deg(-1). The magnitude of grating induction exceeded that of contrast--contrast, both overall and at their optimal frequencies (0.03125 and 4.0 cycles deg(-1), respectively); the two effects are equipotent at an inducing-grating spatial frequency of 1.0 cycle deg(-1). A significant negative correlation between the magnitudes of the two effects suggests a link whereby activation of second-order normalization mechanisms may inhibit first-order mechanisms.

Orientation-selective summing mechanisms revealed in visual search

We investigated properties of the neural mechanisms that mediate detection of complex grating targets in an orientation-based visual search task. Targets and distractors were composed of small patches of compound sinusoidal gratings. Components were chosen to differ enough in spatial frequency to stimulate separate and independent mechanisms at the primary cortical layer of processing. The orientations of the components were both vertical in distractor patches. In the uncrossed condition, both components of the target tilted either 3 degrees left or right. In the crossed condition, one component of the target tilted left and the other tilted right. Search was faster and more accurate in the uncrossed condition, ruling out mediation either by V1-like tuned mechanisms or by a higher-level mechanism that signals differences in orientation. Results were consistent with two classes of mid-level summing mechanisms. We argue that mid-level mechanisms such as these may be the neural substrate for conceptual orientation feature maps.

Grating induction: a new explanation for stationary phantom gratings

The magnitude of brightness variations within test fields of grating induction and phantom grating type displays was measured using a pointwise brightness matching paradigm. A range of test field luminances was sampled which encompassed those reported to give rise to both in-phase phantom and counterphase induced gratings. Results from four observers failed to reveal the existence of stationary "in phase" phantom gratings: at all test field luminances the spatial phase of brightness modulations was consistently opposite to that of the inducing grating. At low or high test field luminances, however, test field luminance matches to the bright or dark half-cycles of induced gratings approximate the luminances of the troughs or peaks of the dark or bright half-cycles of the inducing gratings, respectively. Thus, at low test field luminances the dark half-cycle of the inducing grating may appear to continue across the dark test field, and similarly, at high test field luminances the bright half-cycle may appear continuous with the bright test field. Previously misidentified as being "in-phase" with the inducing grating, the appearance of "phantoms" is suggested to arise due to the apparent brightness continuity of these induction-produced half-cycles of the induced grating across the test field.

Contrast-matching analysis of grating induction and suprathreshold contrast perception

The effect that induced gratings [Vision Res. 22, 119 (1982)] exert on the perceived contrast of standard gratings situated within a 0.5 degrees test field was assessed for two observers by a contrast-matching procedure. Five levels of inducing-grating contrast, CI, ranged from 0.0 to 0.75. Functions relating matching contrast, CM, to standard-grating contrast, CS, were obtained at four levels of inducing-grating contrast across a range of standard contrasts, -0.90 < or = CS < or = +0.90, where the sign denotes the spatial phase of the standard relative to the inducing grating. The matching functions possessed three distinct limbs separated by two inflection points; the limb between the inflection points represents a region of high contrast gain. Another measure, canceling contrast, was obtained at the four levels of inducing contrast by variation of CS until the test field appeared spatially homogeneous. Induction magnitude measured in terms of canceling contrast, CC, grew approximately linearly with CI, such that CC = 0.819 (CI). Induction magnitude determined from matching-contrast data obtained for homogeneous test fields (i.e., CM for CS = 0.0) grew as a decelerating function of inducing-grating contrast, such that CM = 0.308(CI]1.8 + 0.096), effectively asymptoting at a contrast of approximately 0.275 for CI > or = 0.50. When the difference between the absolute values of matching and standard contrast, magnitude of CM-magnitude of CS, is plotted against the ratio of standard to inducing-grating contrast, CS/CI, the resulting functions are generally biphasic, revealing regions of both contrast overmatching (i.e., magnitude of CM > magnitude of CS) and contrast undermatching, magnitude of CM < magnitude of CS. A four parameter model is presented that accounts for many features of the raw matching functions and that is mathematically similar to Semmelroth's account of the crispening effect in brightness matching [J. Opt. Soc. Am. 60, 1685 (1970)]. The model describes matching contrast, CM, as the weighted sum of two nonlinear contrast-response functions whose inputs are CS and CS-CI. The results are discussed relative to the crispening effect (the effect of contrast adaptation on perceived contrast) and to similarities and differences in luminance and contrast-domain visual processing.

The effect of edge blur on grating induction magnitude

In order to assess the contribution of high spatial frequency channels (i.e. local, edge-dependent mechanisms) to the grating induction effect, grating induction magnitude was measured as a function of systematic amounts of blurring of the inducing/test field boundary for four test field heights which spanned a two octave range (0.25-2.0 degrees). Measurements were obtained from two subjects using both the cancelling procedure of McCourt [(1982) Vision Research, 22, 119-134] and a contrast matching paradigm. The two measures yielded similar outcomes: consistent with previous results, both matching and cancelling contrast decreased monotonically with increasing test field height. The effect of blurring the edge was to produce a small (eta 2 = 0.6-5.1%), but significant (P < 0.001), increase in grating induction magnitude. A second experiment utilized the contrast matching paradigm to investigate the effect of edge blur at extreme values (i.e. zero blur and maximum blur) on grating induction magnitude across a four octave range of spatial frequency (0.0625-1.0 c/deg). The results of the matching procedure were again consistent with those obtained previously using the cancelling technique: grating induction magnitude decreased monotonically with increasing spatial frequency. The effect of blurring was to produce a modest (eta 2 = 1.0-2.8%), but significant (P < 0.001), elevation in induction magnitude. These results lead to the conclusion that, unlike some other brightness effects, visual spatial filters selectively sensitive to high spatial frequencies, or to the edges which they sharpen, are not essential for the production of the grating induction effect.

Disappearance of grating induction at scotopic luminances

The dependence of grating induction magnitude on retinal illuminance was examined in two subjects. Grating induction magnitude, as determined using the cancellation technique of McCourt, declines monotonically with decreasing retinal illuminance, effectively disappearing at a value of 0.3-0.5 phot td. In a second experiment, sensitivity differences for test lights of 500 and 600 nm were measured as a function of background illuminance in order to gauge the luminance operating range for grating induction with respect to duplex photoreceptor function. Cancelling contrast (and hence grating induction magnitude) fell below detection threshold contrast at retinal illuminances coinciding with the transition from photopic to scotopic visual function. In a third experiment, spatial contrast sensitivity was measured using both spatially extended (10 degrees) and truncated (2 degrees) sinewave gratings at frequencies below 2 c/deg, at three values of retinal illuminance. Illuminance values corresponded to those where grating induction magnitude was, as determined from the first experiment, either maximal, intermediate or negligible. Similar to grating induction, the strength of lateral inhibition, as indexed by the slope of the low-frequency decline in contrast sensitivity, is progressively reduced with decreasing retinal illuminance, particularly for the 2 degree field. There was, however, using the same criteria, evidence of lateral inhibition at a value of retinal illuminance which did not support grating induction. The implications of these results are discussed with respect to classical brightness contrast phenomena, recent neuroanatomical and neurophysiological evidence of segregated parvo- and magnocellular mediated contrast processing systems, and with results from previous studies of the grating induction effect.