Evidence for spatially local computations underlying discrimination of periodic patterns in fovea and periphery

Discrimination of spatial phase: The roles of luminance distribution and attention

We can easily discriminate certain phase relations in spatial patterns but not others. Phase perception has been found different in the fovea vs. periphery, and for single patterns vs. textures. Different numbers of mechanisms have been proposed to account for the regularities of phase perception. In this study, I attempt to better understand the mechanisms behind discrimination of spatial phase. In order to reveal the role of luminance cues, I use histogram matching of patterns with different phases. Possible effects of attention were studied using visual search experiments with varied stimulus set size. Simple and compound Gabor patches, broadband lines and edges, and textures composed of those patterns were used as stimuli. The experiments indicate that phase discrimination is mediated by two mechanisms. The first uses luminance differences and operates pre-attentively, in parallel across the visual field. The second compares relative positions of dark and bright segments within an image, and is strictly limited by capacity of attention.

The effect of aging on the spatial frequency selectivity of the human visual system

Changes in the physiological properties of senescent V1 neurons suggest that the mechanisms encoding spatial frequency in primate cortex may become more broadly tuned in old age (Zhang et al., European Journal of Neuroscience, 2008, 28, 201-207). We examined this possibility in two psychophysical experiments that used masking to estimate the bandwidth of spatial frequency-selective mechanisms in younger (age approximately 22years) and older (age approximately 65years) human adults. Contrary to predictions from physiological studies, in both experiments, the spatial frequency selectivity of masking was essentially identical in younger and older subjects.

The effect of aging on the orientational selectivity of the human visual system

Leventhal et al. (Science, 2003, 300(5620), 812-815) reported that orientation selectivity of V1 neurons was significantly reduced in older macaque monkeys, which suggests that mechanisms that encode orientation in humans may become more broadly tuned in old age. We examined this hypothesis in two experiments that used sine-wave masking and notched-noise masking to estimate the bandwidth of orientation-selective mechanisms in younger (age approximately 23 years) and older (age approximately 68 years) human adults. In both experiments, the orientation selectivity of masking was essentially identical in younger and older subjects.

From filters to features: location, orientation, contrast and blur

Consider three main ideas about spatial filtering and feature coding in human spatial vision. (1) Computational theory: the representation of local luminance features--bars and edges--is a crucial step in human vision, forming the basis for many decisions in pattern discrimination. (2) Algorithm: features may be located and characterized in terms of polarity, blur and contrast by comparison of 1st, 2nd and 3rd spatial derivatives taken at a common point. Edges in compound (f + 3f) gratings are seen at or close to peaks of gradient magnitude. More tentatively, bars may be located at peaks of the 2nd derivative or at peaks in the Hilbert transform of the 1st derivative. Peaks of contrast energy do not predict all the features seen. An algorithm for recovering the blur of edges is derived as the square-root of the ratio of 1st to 3rd derivatives at the edge location. This successfully predicts blur matching between Gaussian edges and a variety of other test waveforms, including sine waves. Blur matching is (nearly) contrast invariant, as predicted by this ratio rule. (3) IMPLEMENTATION: experiments on the perception and discrimination of plaids imply that the outputs of tuned filters are combined before feature coding. The adaptive, weighted summation of bandpass filters may serve to synthesize the derivative operators while facilitating the segmentation of overlapping features and preventing the representation from being swamped by noise.

Only two phase mechanisms, ±cosine, in human vision

We evaluated the proposal that there exist detectors of the following four cardinal phases in human vision: +cosine, -cosine, +sine, and -sine. First, we assessed whether there was evidence that these cardinal phases were processed by independent 'labeled lines,' using a discrimination at detection threshold paradigm. Second, we assessed whether suprathreshold phase discrimination was best at phases intermediate between these cardinal values. Third, we tried to replicate previous evidence showing that an absence of facilitation occurs only between cosine pedestals and sine tests (or vice-versa). In all three experimental approaches we found no compelling evidence for four cardinal phase groupings. We did however find evidence for independent detectors for pure increments and decrements (+/-cosine). We suggest that phase discrimination, whether at threshold or suprathreshold, is mediated by mechanisms that encode the relative positions and contrasts of local increments and decrements within the stimulus.

Phase noise and the classification of natural images

We measured the effect of global phase manipulations on a rapid animal categorization task. The Fourier spectra of our images of natural scenes were manipulated by adding zero-mean random phase noise at all spatial frequencies. The phase noise was the independent variable, uniformly and symmetrically distributed between 0 degrees and +/-180 degrees . Subjects were remarkably resistant to phase noise. Even with +/-120 degrees phase noise subjects were still performing at 75% correct. The high resistance of the subjects' animal categorization rate to phase noise suggests that the visual system is highly robust to such random image changes. The proportion of correct answers closely followed the correlation between original and the phase noise-distorted images. Animal detection rate was higher when the same task was performed with contrast reduced versions of the same natural images, at contrasts where the contrast reduction mimicked that resulting from our phase randomization. Since the subjects' categorization rate was better in the contrast experiment, reduction of local contrast alone cannot explain the performance in the phase noise experiment. This result obtained with natural images differs from those obtained for simple sinusoidal stimuli were performance changes due to phase changes are attributed to local contrast changes only. Thus the global phase-change accompanying disruption of image structure such as edges and object boundaries at different spatial scales reduces object classification over and above the performance deficit resulting from reducing contrast. Additional color information improves the categorization performance by 2%.

Image quality assessment based on a degradation model

We model a degraded image as an original image that has been subject to linear frequency distortion and additive noise injection. Since the psychovisual effects of frequency distortion and noise injection are independent, we decouple these two sources of degradation and measure their effect on the human visual system. We develop a distortion measure (DM) of the effect of frequency distortion, and a noise quality measure (NQM) of the effect of additive noise. The NQM, which is based on Peli's (1990) contrast pyramid, takes into account the following: 1) variation in contrast sensitivity with distance, image dimensions, and spatial frequency; 2) variation in the local luminance mean; 3) contrast interaction between spatial frequencies; 4) contrast masking effects. For additive noise, we demonstrate that the nonlinear NQM is a better measure of visual quality than peak signal-to noise ratio (PSNR) and linear quality measures. We compute the DM in three steps. First, we find the frequency distortion in the degraded image. Second, we compute the deviation of this frequency distortion from an allpass response of unity gain (no distortion). Finally, we weight the deviation by a model of the frequency response of the human visual system and integrate over the visible frequencies. We demonstrate how to decouple distortion and additive noise degradation in a practical image restoration system.

Vernier acuity with compound gratings: the whole is equal to the better of its parts

To evaluate the relative importance of local feature and spatial filter models for hyperacuity, vernier thresholds were determined for gratings consisting of a fundamental (Fo) and third harmonic (3F) presented alone, and added together in compound gratings where the relative phase offsets of 3F to Fo was 0, 90, 180 and 270 degrees. Thresholds were determined for a range of spatial frequencies of Fo (0.5-16 c deg-1) for abutting and non-abutting stimuli. Compound grating vernier performance was found to be: (i) invariant with relative phase offset for the abutting and non-abutting conditions; and (ii) predictable from the vernier thresholds for the individual grating components making up the compound stimulus. The results support a view that supra-threshold components in a multi-frequency stimulus act independently and it is the spatial frequency content, not the local feature characteristics, which limit vernier performance.

Detection of temporal structure depends on spatial structure

Observers can more easily detect correlated patterns of temporal contrast modulation within hybrid visual images composed of two components when those components are drawn from the same original picture (Blake, R., & Yang, Y. (1997). Proceedings of the National Academy of Science, 94, 7115-7119). To learn whether spatial phase is a mediating variable, we measured thresholds for detection of contrast modulation over time among component gratings while manipulating spatial phase among those components. In Experiment 1, observers more easily detected correlated contrast modulation when two component gratings were aligned in peaks-subtract phase. Experiment 2 showed that this phase-dependent detectability of synchronized contrast modulation is mediated by the phase-dependent, non-linear interaction among spatial frequency channels. The rigorous evaluation of several a priori reasonable hypotheses indicates that the phase-dependent detectability is not based on local spatial features such as local luminance, contrast or luminance gradient. Taken together, our results indicate that the spatial phase relationship and the temporal correlation of contrast modulation of two component gratings are both important for triggering facilitatory interaction between neural analyzers tuned to those gratings.

Binocular vision enhances phase discrimination by filtering the background

Previous studies have shown that the detectability of a noise-masked target can be enhanced under stereoscopic viewing when the target's interocular disparity differs from that of the noise. This enhanced detectability can be accounted for by a model postulating that the binocular system linearly sums the left-eye and right-eye views of a visual scene. This model also predicts enhanced phase discrimination under specifiable interocular disparities of target and noise. Two experiments were conducted in which subjects were asked to discriminate between two luminance patterns (target and foil) that differed only in phase. The target patterns were constructed by summating two vertical sinusoidal gratings in which the phase difference between the higher and the lower spatial frequency gratings was 45 degrees. The foils contained the same two component frequencies, with a phase difference of -45 degrees. Thus, targets and foils were mirror images of one another. The ability of subjects to discriminate between these stereoscopically viewed mirror-image patterns was investigated under two sets of interocular disparities: those that, according to our model, would unmask one or both spatial frequency components, and those that would leave both components masked by the noise. Phase discrimination was enhanced only when both component frequencies of the target and foil were unmasked. The implications of these findings for template-matching and phase-discrimination models of pattern discrimination are considered.

Detection of chromatic and luminance contrast modulation by the visual system

The data presented in this paper examine the ability of observers to detect a modulation in the contrast of chromatic and luminance gratings as a function of the carrier contrast, duration, and spatial frequency. The nature of the signal underlying this ability is investigated by examining both the paradigm used to make the measurement and the effect of grating masks on performance in the tasks. The results show that observers' ability to discriminate amplitude modulation from an unmodulated carrier is dependent on carrier contrast but only up to approximately 5-8 times carrier-detection threshold. Discrimination is, however, independent of spatial frequency [10-1 cycles per degree (cpd) component-frequency range], carrier color, and, most surprisingly, stimulus duration (1000-30 ms). This set of experiments compliments data from previous papers and assimilates many of the conclusions drawn from this previous data. There is absolutely no evidence for the existence of a distortion product mediating performance under any of the current conditions, and the data seriously question whether the visual system might use such a signal even if it does exist under more extreme conditions than those used here. The evidence suggests that the visual system detects variations in both chromatic and luminance contrast by means of a mechanism operating locally upon the spatial structure of the carrier.

In search of a contrast metric: matching the perceived contrast of Gabor patches at different phases and bandwidths

The definition of contrast in a complex scene is a long-standing problem. The local contrast in an image may be approximated by the contrast of a Gabor patch of varying phase and bandwidth. Observers' perceived (apparent) contrast, as indicated by matching of such patterns, were compared here to the physical contrast calculated by a number of definitions. The 2 c/deg 1-octave Gabor patch stimuli of different phases were presented side by side, separated by 4 deg. During each session the subjects (n = 5) were adapted to the average luminance, and four different contrast levels were randomly interleaved. The subject's task was to indicate which of the two patterns was lower in contrast. Equal apparent contrast was determined by fitting a psychometric function to the data. The results of the matching rejected the hypothesis that either the Michelson formula or the King-Smith and Kulikowski contrast metric (CKK = (Lmax-Lbackground)/Lbackground) was used by the subjects to set the matching. The use of the Nominal contrast (the Michelson contrast of the underlying sinusoid) as an estimate of apparent contrast could not be rejected. In a second experiment the apparent contrast of a 1-octave Gabor patch was matched to the apparent contrast of a 2-octave Gabor patch (of Nominal contrast of 0.1, 0.3, 0.6, 0.8) using the method of adjustment. The results of this experiment disagree with the prediction of the Nominal contrast definition as well. The local band-limited contrast measure (Peli, 1990), when used with the modifications suggested by Lubin (1995) as an estimate of apparent contrast, could not be rejected by the results of either experiment. These results suggest that a computational contrast metric based on multi-scale bandpass filtering is a better estimate of apparent perceived contrast than any of the other metrics tested.

Perceived location of bars and edges in one-dimensional images: computational models and human vision

Observers used a cursor to mark the location and polarity of all the bar and edge features seen in compound (f + 3f) gratings of moderate frequency and contrast. They almost always reported six bars and six edges per cycle of the fundamental frequency (f = 0.4 c/deg, contrast 32%), for all phases of the third harmonic (3f = 1.2 c/deg, contrast 10.7%). This general pattern of features was predicted by the positions of peaks and troughs in the outputs of even and odd filters applied to the stimulus waveform, but not by peaks of "local energy" since there were only two energy peaks per cycle. We considered a family of filters whose amplitude spectrum has slope p on a log-log plot. The best-fitting filter slope was determined for bars (even filter) and edges (odd filter) in conjunction with a classification rule in which all peaks and troughs in the response profile are counted as features. If bars were seen at luminance peaks, and edges seen at gradient peaks (zero-crossings in the second derivative) we should have found p = 0 for bars and p = 1 for edges. In fact, for both bars and edges the best-fitting slope was about p = 0.5. For edges, this is consistent with the use of a smoothed (Gaussian) derivative operator. The filters form a quadrature pair, as in the energy model, but features are not constrained to lie at energy peaks. A compressive transducer preceding the filters improved the goodness-of-fit for predicted edge locations, but did not affect the estimate of filter slopes, nor the goodness-of-fit for bar locations. In an experiment with single blurred edges we confirmed that the perceived location of edges is shifted towards the darker side of the edge in direct proportion to the contrast of the edge. This was well predicted by adding a compressive transducer to the filter model.

Discrimination of compound gratings: spatial-frequency channels or local features?

Models based on spatial-frequency channels and local features provide alternative explanations for suprathreshold pattern discrimination. We compared psychophysical discrimination data with the predictions of the Wilson and Gelb channel model and three local-feature models. The features were peak-valley local contrast, peak-peak local contrast, and luminance gradients. We measured visual sensitivity for discriminating compound gratings (F + 3F or F + 5F, in peaks-add or peaks-subtract phases) whose component contrasts were yoked together so that a contrast increment in one component was accompanied by an equal decrement in the other. The Wilson and Gelb model accounted for the results with peaks-add gratings, but failed to predict those with peaks-subtract gratings. None of the local-feature models explained the results by themselves. Most of the data fell close to an envelope composed of the lowest thresholds of the three feature-detector models, although there were important exceptions. Our findings are consistent with the view that suprathreshold pattern discrimination is mediated by mechanisms responsive to spatially localized features and that more than one type of feature is used.

Phase-reversal discrimination in one and two dimensions: performance is limited by spatial repetition, not spatial frequency content

Lawden [(1983) Vision Research, 23, 1451-1463] used vertical gratings containing two frequencies (F, nF) in phase discrimination (F + nF against F - nF) and compound detection (F + nF against F) experiments, where thresholds were measured by manipulating the contrast of the nF component. When n was varied, Lawden found a phase-plateau of moderate breadth where phase discrimination thresholds were about half of those measured in compound detection. I present the results of similar experiments, using one-dimensional (gratings) and two-dimensional (plaids). In a sine-plaid condition, the 1F grating was split into two 1F plaid components at +/- 45 deg from vertical while the nF component remained a vertical grating. In a square-wave plaid (SqW-plaid) condition the plaid components were square waves. For each of these conditions, the horizontal spatial repetition (SR) of the plaid is given by (F/square root of 2); it is half an octave lower than the spatial frequency (SF) of the oblique components but it is not represented in the stimulus spectrum. By plotting phase discrimination relative to compound detection a phase-plateau was found for all three conditions. When these data were plotted as a function of SF ratio (nF/F) the curves describing the two plaid conditions were found to be leftward translations of that describing the grating condition. However, when the results were plotted as a function of SR ratio (nF/SR), the three functions lay on top of each other. The finding that phase-reversal discrimination is not governed by the Fourier attributes of the stimulus per se, rules out an explanation in terms of a linear, broad-band, phase-sensitive mechanism. Rather, the results imply that information is combined across the set of SF- and orientation-tuned mechanisms before the decision variable. These interactions appear to be governed by the spatial (not Fourier) attributes of the luminance profile of the stimulus. A modified version of Bennett's [(1993) Perception & Psychophysics, 53, 292-304] phase discrimination model is presented as a post-hoc account of the data.

Preattentive equivalence of multicomponent Gabor textures in the central and peripheral visual field

Similarity ratings were obtained to determine the minimum number of Gabor components that would produce a comparison texture that appeared preattentively similar to a 64-component standard texture. All textures were chosen to be both specifiable by a relatively small number of localized spectral components and sufficiently complex to approximate natural textures. The number of component orientations in the set of comparison textures was found to be a particularly important determinant of texture discrimination in that its effect on rated similarity was largely independent of the total number of components making up the texture. Textures were also presented at 0.75 degree and 20 degrees eccentricity, with the latter magnified by a factor of either 2 or 4. The overall similarity rating did not change with either magnification, whereas the critical number of orientations, defined as the number of orientations above which rated similarity was constant, did change for the higher magnification. The latter finding is consistent with the proposition that higher-order discriminations are mediated by higher cortical areas that integrate information across the visual field. Finally, the phase-bandwidth of a set of coherent textures was also varied in order to determine whether more explicit differences in the spatial structure of stimuli might affect rated similarity. In contrast to the results for component orientation, the ratings, obtained at 0.75 degree and 20 degrees, were different even when the phase-bandwidth stimuli were magnified by a factor of 4.

The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity

In this study we investigate the nature of the computations that underlie the encoding of spatial position by the human visual system. Specifically, we explore the relationship between alignment accuracy and retinal eccentricity for stimuli where local luminance, local contrast, and orientation cues do not underlie performance. Spatial scale is especially important for such a comparison because of the well documented spatial inhomogeneity of the human visual field. The results suggest that the relationship between spatial localization and eccentricity is invariant with spatial scale if accuracy and eccentricity are expressed in terms of the stimulus envelope size. We show that the photoreceptor disarray does not determine the limit to performance for this task, the limit is post-receptoral and can be modelled in terms of a positional uncertainty within the early filters located before the response envelope has been extracted. This uncertainty varies with eccentricity in a similar way within each spatial array.

The harmonic bandwidth of phase-reversal discrimination

Previous studies have shown that 180 degrees relative phase shifts in f + 2f gratings are discriminated when the cosine or the sine component of the shift exceeds some criterion (Bennett & Banks, 1987; Field & Nachmias, 1984). The current experiments demonstrate that this result holds for other two-component gratings, provided that the components are within two to three octaves of each other. For frequency differences greater than two to three octaves, phase-reversal discrimination is impossible. A simple model that discriminates phase shifts on the basis of changes in the responses of even- and odd-symmetric spatial filters can account for the results.

Texture segregation based on two-dimensional relative phase differences in composite sine-wave grating patterns

Experiments examined the visual processing of relative phase relations between differently oriented components of a textured pattern. The textures were a super position of three 1.3 c/deg sine-wave gratings rotated 60 deg relative to one another. Global orientation and relative phase were varied. Subjects rated the segregation of pairs of textures presented in a figure/ground configuration at 10 deg retinal eccentricity. Both orientation and phase differences were used in making ratings. It was not simply the difference in relative phase that mattered. The results also depended on the values of the relative two-dimensional (2-D) phases in figure and ground. Mirror-image texture pairs (which may have a large relative phase difference) segregated poorly compared to other pairs with similar phase differences. This suggests that the peripheral visual system does not completely encode 2-D relative phase. Secondary issues include spatial frequency effects, the relevance of figure/ground borders, and better performance in the lower visual field.

The coding of spatial position by the human visual system: effects of spatial scale and contrast

In this study we investigate the nature of the computations that underlie the encoding of spatial position by the human visual system. Specifically, we explore the relationship between alignment accuracy and spatial scale on the one hand, and between alignment accuracy and contrast on the other. We do this for stimuli where local luminance, local contrast, and orientation cues do not underlie performance. The results suggest that spatial localisation is independent of spatial scale and weakly dependent on contrast. We present subsequent models based on the properties of some classes of visual cortical neurones, namely multiplicative noise and contrast energy detection of complex cells, which describe the form of these relationships.

The effects of contrast, spatial scale, and orientation on foveal and peripheral phase discrimination

We examined the effects of contrast, spatial scale, and orientation, on phase discrimination thresholds. In expt I, the ratio of thresholds for 180 deg shifts in F + 2F gratings remained invariant across a wide range of fundamental contrasts. Experiment II demonstrated that random fluctuations in overall pattern contrast did not affect discrimination. Experiment III found that foveal, but not peripheral, thresholds were roughly independent of spatial scale; foveal-peripheral differences in phase sensitivity could not be eliminated by scaling stimulus size. Finally, expt IV found that thresholds for some phase shifts varied significantly with orientation in the periphery; in general, peripheral sensitivity was greatest for radially-oriented gratings. The implications of these findings for models of phase discrimination are discussed.

Contrast in complex images

The physical contrast of simple images such as sinusoidal gratings or a single patch of light on a uniform background is well defined and agrees with the perceived contrast, but this is not so for complex images. Most definitions assign a single contrast value to the whole image, but perceived contrast may vary greatly across the image. Human contrast sensitivity is a function of spatial frequency; therefore the spatial frequency content of an image should be considered in the definition of contrast. In this paper a definition of local band-limited contrast in images is proposed that assigns a contrast value to every point in the image as a function of the spatial frequency band. For each frequency band, the contrast is defined as the ratio of the bandpass-filtered image at the frequency to the low-pass image filtered to an octave below the same frequency (local luminance mean). This definition raises important implications regarding the perception of contrast in complex images and is helpful in understanding the effects of image-processing algorithms on the perceived contrast. A pyramidal image-contrast structure based on this definition is useful in simulating nonlinear, threshold characteristics of spatial vision in both normal observers and the visually impaired.