Spatial-frequency discrimination and detection: comparison of postadaptation thresholds

We found that inspecting a sine-wave grating elevated threshold for spatial-frequency discrimination as it does for contrast detection, but discrimination threshold was maximally elevated at about twice the adapting frequency, where detection threshold was little affected; and detection threshold was maximally elevated at the adapting frequency, where discrimination threshold was not elevated at all. Orientation tuning was roughly similar for contrast and for discrimination threshold elevations; elevations fell by half at between 7 and 17 deg from the adapting orientation. We compared our findings with the predictions of three models of discrimination: (1) The data are inconsistent with the idea that the most strongly stimulated channels are the most important channels for discrimination. (2) With an additional assumption, the Hirsch-Hylton scaled-lattice model could account for our finding that discrimination threshold elevations are asymmetric. (3) With no additional assumptions, the idea that discrimination is determined by the relative activities of multiple overlapping spatial-frequency channels or size-tuned neurons can account for our finding that discrimination thresholds are asymmetric. We propose a physiologically based discrimination model: Asymmetrically tuned cortical cells feed a ratio-tuned neural mechanism whose properties are formally analogous to those of ratio-tuned neurons that have recently been found in cat visual cortex. The linear relation between firing frequency and contrast can explain why discrimination threshold is substantially independent of contrast.     

Recurrent networks in human visual cortex: psychophysical evidence

To study the neuronal circuitry underlying visual spatial-integration processes, we measured the effect of short and long chains of proximal Gabor-signal (GS) flankers (sigma = lambda = 0.15 degrees) on the contrast-discrimination function of a foveal GS target. We found that the same pattern of lateral masks enhanced target detection with low-contrast pedestals and strongly suppressed the discrimination of a range of intermediate pedestal contrasts (pedestal contrast <30%). Increasing the number of the flankers reversed the suppressive effect. The data suggest that the main influence of the proximal flankers is maintained by activity-dependent interactions and not by linear spatial summation. With an increased number of flankers, we found a nonmonotonic relationship between the discrimination thresholds and the number of flankers, supporting the notion that the discrimination thresholds are mediated by excitatory-inhibitory recurrent networks that manifest the dynamics of large neuronal populations in the neocortex [Proc. Natl. Acad. Sci. USA 94, 10426 (1997)].     

Spatiotemporal filters in the detection of background modulation targets

The background modulation method has been proposed as a useful test of early visual mechanisms [Biol. Cybern. 37, 77 (1980); Biol. Cybern. 47, 173 (1983)]. The task involves measuring detection thresholds for a luminous spot (increment) drifting over a spatially or temporally modulated background. The study explores the nature of the detecting mechanism in terms of spatial and temporal filters for both spatial and temporal background modulations. In both cases we find that thresholds can be explained by spatial contrast cues generated by the moving spot and that their spatiotemporal characteristics suggest detection by magnocellular processes.     

Blur tolerance for luminance and chromatic stimuli

We investigated the blur tolerance of human observers for stimuli modulated along the isoluminant red-green, the isoluminant yellow-blue, and the luminance (black-white) direction in color space. We report the following results: (i) Blur difference thresholds for red-green and luminance stimuli (of equal cone contrast) are very similar and as low as 0.5 min of visual angle; for yellow-blue the lowest blur thresholds are much higher (1.5 min of visual angle). (ii) The smallest blur thresholds are found for slightly blurred square waves (reference blur of 1 arc min) and not for sharp edges. (iii) Blur thresholds for red-green and black-white follow a Weber law for reference (pedestal) blurs greater than the optimum blur. (iv) Using the model proposed by Watt and Morgan [Vision Res. 24, 1387 (1984)] we estimated the internal blur of the visual system for the black-white and the red-green color directions and arrived at the following estimates: 1.2 arc min for black-white stimuli at 10% contrast and 0.9 arc min for red-green stimuli at 10% cone contrast. Blur tolerance for yellow-blue is independent of external blur and cannot be predicted by the model. (v) The contrast dependence of blur sensitivity is similar for red-green and luminance modulations (slopes of -0.15 and -0.16 in log-log coordinates, respectively) and slightly stronger for yellow-blue (slope = -0.75). Blur discrimination thresholds are not predicted by the contrast sensitivity function of the visual system. Our findings are useful for predicting blur tolerance for complex images and provide a spatial frequency cutoff point when Gaussian low-pass filters are used for noise removal in colored images. They are also useful as a baseline for the study of visual disorders such as amblyopia.     

Foveal contour interaction: detection and discrimination

Contour interaction, the detrimental effect of flanking features on the discrimination of optotypes, has been studied mainly close to the visual acuity limit. We were interested to know how these results compare with those for the detection of targets. According to the simplest model of contour interaction, comparable detection effects would be expected. The case for low-level masking would be further strengthened if the form and nature of the dependence on flank separation and flank polarity followed that typically found in studies of lateral spatial masking [Vision Res. 33, 993 (1993)]. Landolt Cs subtending a visual angle of 0.25 degrees, 0.5 degrees, and 1.0 degrees were presented and contrast thresholds for detecting the presence of the Landolt C and discriminating its orientation were measured in five normal subjects as a function of flank separation and flank polarity. The results obtained for the relationship between detection and discrimination depend on the size of the target used. For small letters, discrimination but not detection was significantly affected by flanking bars. For large letters, detection and discrimination were affected to the same extent. However, in this case the effectiveness of opposite-polarity flanks and the finding that facilitation occurred at close, not far, flank separations suggests that the simplest explanation in terms of masking may not be applicable.     

Independence of orientation and size in spatial discriminations

This study of form vision explores the relationships between orientation and spatial frequency in suprathreshold discrimination tasks. Orientation discrimination thresholds for sine-wave gratings were 0.3-0.5 deg, much less than the roughly 10-24-deg orientational bandwidth of channels; spatial-frequency discrimination thresholds were 3-7%, much less than the roughly 1.2-octave spatial-frequency bandwidth of channels. We find that spatial-frequency discrimination between two gratings was as acute when the two gratings were orthogonal as when they were parallel. Orientation discrimination between two gratings was as acute when the two gratings had the same spatial frequencies as when they had different spatial frequencies. Thus orientation and spatial frequency are independent dimensions at the discrimination stage of spatial information processing.     

Effects of high-contrast peripheral patterns on the detection threshold of sinusoidal targets

Detection thresholds of sinusoidal gratings in the simultaneous presence of high-contrast peripheral masking stimuli partially overlapping the test gratings were determined as a function of the separation between the center of the test grating and the peripheral stimulus by a two-alternative forced-choice method. The results showed that the threshold-elevating effect of simultaneously present peripheral masking stimuli depends on how much of the test grating is left unexposed. An additional experiment, in which the detection thresholds in the absence of the peripheral stimulus were determined as a function of the number of cycles of the test grating, enabled us to show that the threshold-elevating effect is somewhat higher than the effect of simply cutting the test grating down in size. The threshold-elevating effects caused by high-contrast peripheral masking stimuli can be explained in terms of a lateral inhibition and a probability summation across space, taking into account the nonuniform sensitivity across the visual field.     

Foveal contrast thresholds exhibit spatial-frequency- and polarity-specific contour interactions

Traditionally, contour interaction has been investigated at the visual acuity limit using a Landolt C and flanking bars, performance being quantified in terms of a percent correct measure. More recently, it has been shown that the properties of the contour interaction are different when larger stimuli are used: Contour interaction is not polarity specific, and spatial frequency tuning for an unflanked C is broader. Here we quantify contour interaction for stimuli 5x larger than the resolution limit in terms of contrast thresholds. We show that polarity of bars has little effect on unfiltered stimuli but does show very different effects on the spatial-frequency-tuning curves for discrimination of the Landolt C. This explains the polarity dependence of crowding at the visual acuity limit and its independence for larger unfiltered targets. Thus the underlying filtering function is composed of more than one mechanism, affected differently depending on the relative polarity of the test and flank contours.     

Luminance spatial scale facilitates stereoscopic depth segmentation

Are differences in luminance spatial frequency between surfaces that overlap in depth useful for surface segmentation? We examined this question, using a novel stimulus termed a dual-surface disparity grating. The dual-surface grating was made from Gabor micropatterns and consisted of two superimposed sinusoidal disparity gratings of identical disparity-modulation spatial frequency and orientation but of opposite spatial phase. Corrugation amplitude thresholds for discrimination of the orientation of the dual-surface grating were obtained as a function of the difference in Gabor (luminance) spatial frequency between the two surfaces. When the Gabor micropatterns on the two surfaces were identical in spatial frequency, thresholds were very high and in some instances impossible to obtain. However, with as little as a 1-octave difference in spatial frequency between the surfaces, thresholds fell sharply to near-asymptotic levels. The fall in thresholds paralleled a change in the appearance of the stimulus from one of irregular depth to stereo transparency. The most parsimonious explanation for this finding is that the introduction of a between-surface luminance spatial-frequency difference reduces the number of spurious cross-surface binocular matches, thus helping to reveal the three-dimensional structure of the stimulus.     

Elevation of Vernier thresholds during image motion depends on target configuration

Previously we showed that thresholds for abutting Vernier targets are unaffected by motion, as long as the targets are processed by the same spatial-frequency channel at each velocity and remain equally detectable [Invest. Ophthalmol. Visual Sci. (Suppl.) 37, S734 (1996)]. In this study we compared Vernier thresholds for stationary and moving abutting and nonabutting targets (gaps = 0, 18, and 36 arc min) for velocities of 0-16 deg/s. The Vernier targets were spatially filtered vertical lines (peak spatial frequency = 3.3 or 6.6 c/deg), presented at contrast levels of two, four, and eight times the detection threshold of each component line. Unlike the results for abutting targets, Vernier thresholds for nonabutting targets worsen with velocity as well as gap size. The results for abutting Vernier targets are consistent with the hypothesis that thresholds are mediated by oriented spatial filters, whose responses increase proportionally with the stimulus contrast. The velocity-dependent thresholds found for nonabutting Vernier targets can be explained on the basis of local-sign comparisons if the comparison process is assumed to include a small amount of temporal noise.     

Color-signal filtering in the Fourier-frequency domain

We have analyzed the Fourier-frequency content of spectral power distributions deriving from three types of illuminants (daylight, incandescent, and fluorescent) and the color signals from both biochrome and nonbiochrome surfaces lit by these illuminants. As far as daylight and the incandescent illuminant are concerned, after filtering the signals through parabolic (low-pass) filters in the Fourier-frequency domain and then reconstructing them, we found that most of the spectral information was contained below 0.016 c/nm. When fluorescent illuminants were involved, we were unable to recover either the original illuminants or color signals to any satisfactory degree. We also used the spectral modulation sensitivity function, which is related to the human visual system's color discrimination thresholds, as a Fourier-frequency filter and obtained consistently less reliable results than with low-pass filtering. We provide comparative results for daylight signals recovered by three different methods. We found reconstructions based on linear models to be the most effective.     

Contour interaction for an easily resolvable stimulus

It is well known that adjacent contours can reduce the visual acuity of single letters. Although this has traditionally been considered only in terms of a neural-based interaction, it has recently been suggested that the information content in the stimulus may account for the interaction. Here we ask the question, "Do similar interference effects occur for the discrimination of low-contrast letters whose size is larger than that corresponding to the resolution limit?" If so, previous acuity-based interaction results may be of more general importance. We show that while there are interference effects of nearby contours, they are of a form different from that observed at the resolution limit. In particular, the contrast polarity of the nearby contour is unimportant, which in turn suggests that a physical explanation is inappropriate. Also, the discrimination of an easily resolvable, unflanked Landolt C target requires information over a much wider spatial-frequency range than its counterpart at the resolution limit.     

Spatiotemporal interpolation and quality of apparent motion.

We investigate the conditions under which stimuli in apparent (sampled) motion are indistinguishable from those in smooth motion and compare this discrimination with the precision achieved by the visual system in interpolating apparent motion. In an initial experiment, observers were required to discriminate smooth from apparent motion, at variable step sizes, contrasts, velocities, and stimulus types (broadband line or bar stimuli and grating patches of different spatial frequency). Thresholds for discriminating smooth from sampled motion were approximately 40 arc min under optimal conditions, corresponding to the diameter of foveal photoreceptors. The tolerated step size between stations increased with velocity, more so for low- than for high-spatial-frequency stimuli. Tolerated step size decreased with presentation duration and with stimulus contrast. A separate experiment examined precision of interpolation. Vernier offsets were produced through temporal delays along the trajectory of an apparent motion, and thresholds for the discrimination of direction of offset were measured as a function of speed of motion and of distance between stations of apparent motion. Perfect interpolation was achieved for distances between stations of approximately 2 arc min. A model based on spatiotemporal filtering at an early stage of processing accounts well for the results of both types of experiments.     

Incoherent pattern detection using a liquid-crystal active lens

Incoherent pattern detection by a simple imaging system using a liquid-crystal active lens is proposed. The imaging system works as a spatial filtering system with a rewritable phase-only filter. We found that, in the incoherent matched filtering system, a conventional phase-only filter has a higher optical efficiency but a lower pattern discrimination than a complex filter. To improve the pattern discrimination ability, we optimized the phase-only filter by using simulated annealing and a genetic algorithm. We designed phase-only filters that have discrimination ability comparable with that in a complex filter. The performance of optimized phase-only filters is experimentally demonstrated.     

Two-laser, large-field hyperspectral microarray scanner for the analysis of multicolor microarrays

We describe the development and operation of a two-laser, large-field hyperspectral scanner for analysis of multicolor genotyping microarrays. In contrast to confocal microarray scanners, in which wavelength selectivity is obtained by positioning band-pass filters in front of a photomultiplier detector, hyperspectral microarray scanners collect the complete visible emission spectrum from the labeled microarrays. Hyperspectral scanning permits discrimination of multiple spectrally overlapping fluorescent labels with minimal use of optical filters, thus offering important advantages over standard filter-based multicolor microarray scanners. The scanner uses two-sided oblique line illumination of microarrays. Two lasers are used for the excitation of dyes in the visible and near-infrared spectral regions. The hyperspectral scanner was evaluated with commercially available two-color calibration slides and with in-house-printed four-color microarrays containing dyes with spectral properties similar to their commercial genotyping array counterparts.     

Spatial-scale contribution to the detection of mirror symmetry in fractal noise.

We investigated how the detection of mirror symmetry depends on the distribution of contrast energy across spatial scales. Stimuli consisted of vertically symmetric noise patterns with fractal power spectra defined by 1/f beta slopes (-2 < or = beta < or = 5). While overall rms contrast remained fixed at 25%, symmetry-detection thresholds were obtained by corrupting the signal with variable amounts of noise with identical spectral characteristics. A first experiment measured thresholds as a function of spectral slope, and performance was found to be substantially facilitated in images with power spectra that characterize natural scenes (1.2 < or = beta < or = 3.2). In a second experiment, symmetry was removed from randomly chosen octave bands and replaced by noise with the same spectral profile. Results revealed that only in images with 1/f2 spectra does performance decrease by constant amounts across all frequency bands. Together, the results imply that symmetry mechanisms extract equal amounts of information from constant-octave frequency bands but lack the ability to whiten stimuli whose spectral slopes differ from those of natural scenes. Results are qualitatively well predicted by a multichannel model that (1) relies on spatial filters with equal-volume point-spread functions and constant-octave frequency bandwidths and (2) restricts the computation of symmetry to spatial regions whose dimensions are proportional to the filters' spatial scale. These findings are also consistent with the notion that mechanisms that mediate the perception of form exploit the ability of early vision to reduce second-order redundancy in natural scenes.     

Spatial-frequency adaptation affects spatial-probability summation

The effects of spatial-frequency adaptation on spatial-probability summation were investigated by two techniques: the measurement of the dependence of cosine grating sensitivity on the number of cycles presented and the determination of the frequency-of-seeing curve for a cosine grating. Both measurements indicate that the contribution of spatial-probability summation to adapted grating thresholds is reduced in comparison with unadapted conditions. This reduction in the effects of spatial-probability summation, together with the decrease in local sensitivity, which depends on the spatial inhomogeneity of the visual system, is sufficient to account for the threshold elevation aftereffect measured when adapting and testing with cosine gratings.     

Contrast statistics for foveated visual systems: fixation selection by minimizing contrast entropy

The human visual system combines a wide field of view with a high-resolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy to be effective, the visual system needs sophisticated central mechanisms that efficiently exploit the varying spatial resolution of the retina. To gain insight into some of the design requirements of these central mechanisms, we have analyzed the effects of variable spatial resolution on local contrast in 300 calibrated natural images. Specifically, for each retinal eccentricity (which produces a certain effective level of blur), and for each value of local contrast observed at that eccentricity, we measured the probability distribution of the local contrast in the unblurred image. These conditional probability distributions can be regarded as posterior probability distributions for the "true" unblurred contrast, given an observed contrast at a given eccentricity. We find that these conditional probability distributions are adequately described by a few simple formulas. To explore how these statistics might be exploited by central perceptual mechanisms, we consider the task of selecting successive fixation points, where the goal on each fixation is to maximize total contrast information gained about the image (i.e., minimize total contrast uncertainty). We derive an entropy minimization algorithm and find that it performs optimally at reducing total contrast uncertainty and that it also works well at reducing the mean squared error between the original image and the image reconstructed from the multiple fixations. Our results show that measurements of local contrast alone could efficiently drive the scan paths of the eye when the goal is to gain as much information about the spatial structure of a scene as possible.     

Dispersion multiplexing with broadband filtering for miniature spectrometers

We replace the traditional grating used in a dispersive spectrometer with a multiplex holographic grating to increase the spectral range sensed by the instrument. The multiplexed grating allows us to measure three different, overlapping spectral bands on a color digital focal plane. The detector's broadband color filters, along with a computational inversion algorithm, let us disambiguate measurements made from the three bands. The overlapping spectral bands allow us to measure a greater spectral bandwidth than a traditional spectrometer with the same sized detector. Additionally, our spectrometer uses a static coded aperture mask in the place of a slit. The aperture mask allows increased light throughput, offsetting the photon loss at the broadband filters. We present our proof-of-concept dispersion multiplexing spectrometer design with experimental measurements to verify its operation.     

Quantitative measures of boundary and contrast enhancement in speckle reduction in ultrasonic B-mode images using spatial bessel filters

The spatial Bessel filters are studied for their ability to reduce ultrasonic speckle and enhance the boundaries of regions of interest (ROI) in medical B-mode images. Using the concept of the heterogeneity index, a new parameter is defined to provide a quantitative measure of the edge visibility. It is hypothesized that this edge visibility parameter will be almost equal to unity if the ROI does not contain a boundary and greater than unity when the ROI contains a boundary. Analyses of 2 computer-synthesized images containing speckle and B-mode images of tissue-mimicking phantoms were carried out. The improvement in contrast and enhancement in edge visibility were estimated. In addition, parametric images containing a map of the edge visibility were created that showed clear boundaries. The quantitative measures strongly support the visual perception of contrast and enhanced edge visibility provided by the spatial Bessel filters. Results demonstrate the potential use of Bessel spatial filters in providing speckle reduction along with the ability to enhance the boundaries of regions of interest in B-mode images.