Richard A. Eagle

Reversed stereo depth and motion direction with anti-correlated stimuli

We used anti-correlated stimuli to compare the correspondence problem in stereo and motion. Subjects performed a two-interval forced-choice disparity/motion direction discrimination task for different displacements. For anti-correlated 1d band-pass noise, we found weak reversed depth and motion. With 2d anti-correlated stimuli, stereo performance was impaired, but the perception of reversed motion was enhanced. We can explain the main features of our data in terms of channels tuned to different spatial frequencies and orientation. We suggest that a key difference between the solution of the correspondence problem by the motion and stereo systems concerns the integration of information at different orientations.

Motion detection is limited by element density not spatial frequency

Two-frame random-element kinematograms were used to study the matching algorithm employed by the visual system to keep track of moving elements. Previous data have shown that the maximum spatial displacement detectable (dmax) for random-dot kinematogram stimuli increases both with increasing dot size and with decreasing centre frequency for spatially band-pass kinematograms. Both of these findings could be explained by either (i) a matching algorithm sensitive to the number of false targets in the display (informational limit) or (ii) spatial-frequency tuned sensors hardwired for detecting displacements of a constant proportion of their preferred frequency (phase-based limit). The present experiment was designed to differentiate between these alternative explanations. The stimuli were band-pass filtered (difference-of-Gaussian) random-dot patterns. The combination of six dot densities and three filter sizes produced 18 experimental conditions and allowed independent control of the spectral content and filtered-element density of the stimuli. When the dot density was high, dmax was larger for the coarse-filtered stimuli, as predicted by both theories. There was also a critical dot density for each filter size, above which dmax was constant but below which dmax rose sharply. This critical density was higher for fine-filtered stimuli such that at the lowest dot density of 0.025%, dmax was constant for all filter sizes. In support of the informational limit model, dmax was found to be directly proportional to the two-dimensional spacing of filtered elements. In contrast, dmax varied from 0.6 to 8.5 cycles of the stimulus peak frequency, suggesting that a phase-based model of motion detection cannot account for the results.

Two-dimensional constraints on three-dimensional structure from motion tasks ☆

Can humans recover metric structure from motion sequences or, as has been claimed by Todd and Bressan [(1990) Perception & Psychophysics, 48, 419-430], are they limited to recovering only relief structure? Two experiments were carried out to investigate this question. In a metric-structure task, the angular thresholds for discriminating two rotating bi-planar structures were approximately 91 deg. By contrast, in a relief-structure task, the angular thresholds for discriminating a planar from a non-planar structure, both undergoing simple rotational motion, were only approximately 11 deg. A computational model is proposed to examine the image motion sensitivity required to perform discriminations of both three-dimensional metric and relief structure from motion. When the experimental data were re-plotted in terms of this two-dimensional sensitivity, the thresholds were found to be the same for both tasks. This finding is related to the models revelation that recovering metric structure from motion is inherently more noise-sensitive than is recovering relief structure from motion. The conclusion is that the differences in angular thresholds reflect the differing nature of the two tasks. There is no evidence that the visual processes themselves are preferentially sensitive to non-metric over metric structure from motion.

The role of perspective effects and accelerations in perceived three-dimensional structure-from-motion.

It has been suggested that perceived three-dimensional (3D) structure-from-motion can be accounted for by a 2-frame orthographic approximation of the flow field. This study investigated the extent to which higher order cues (perspective and acceleration) are used in addition to first-order flow. Participants matched the 3D dihedral angle of a hinged plane (probe) defined by multiple-depth cues to one defined by motion only, for stimulus sizes of 8 and 33 degrees, using perspective and orthographic projection. The results show that perspective effects can be important even for relatively small stimuli (8 degrees) and that accelerations contribute to perceived shape. In all conditions, large biases were found. These are well accounted for by a model in which all relevant flow measurements (first-order, perspective, and acceleration) are used together with estimates of the noise in each. The model has no built-in bias toward particular 3D shapes. Instead, the visual system may act as an optimal estimator of 3D structure-from-motion.

Stereo correspondence in one-dimensional Gabor stimuli.

Previous data [Prince, S.J.D., & Eagle, R.A., (1999). Size-disparity correlation in human binocular depth perception. Proceedings of the Royal Society of London B, 266, 1361-1365] have demonstrated that the upper disparity limit for stereopsis (DMax) is considerably smaller in filtered noise stereograms than in isolated Gabor patches of the same spatial frequency. This discrepancy is not currently understood. Here, the solution of the correspondence problem for bandpass stereograms was further examined. On each trial observers were presented with two one-dimensional Gabor stimuli containing disparities of equal magnitude but opposite sign. Subjects were required to indicate which interval contained the crossed disparity stimulus. It was found that matching behaviour changed as a function of Gabor envelope size. As a function of disparity magnitude, performance cycled between mostly correct and mostly incorrect at large envelope sizes but was always correct at small envelope sizes. At intermediate envelope sizes performance was cyclical at small disparities but always correct at large disparities. The critical envelope size at which performance changed from mostly correct to mostly incorrect at 270 degrees phase disparity was used as a measure of the matching performance as other parameters of the Gabor were varied. Both absolute and relative contrast were shown to influence the perceived sign of matches. Critical envelope size was also found to decrease as a function of spatial frequency, but more slowly than a phase-based limit would predict. These data cannot be predicted by current models of stereopsis, and can be used to constrain future models.

Size-disparity correlation in human binocular depth perception

To use the small horizontal disparities between images projected to the eyes for the recovery of three–dimensional information, our visual system must first identify which feature in one eyes image corresponds with which in the other. The earliest level of disparity processing in primates (V1) contains cells that are spatial–frequency tuned. If such cells have a disparity range that covers only a single period of their mean tuning frequency, there will always be exactly one potential match within this range. Here, this ‘size–disparity’ hypothesis was tested by measuring the contrast sensitivity of stereopsis as a function of disparity for single bandpass–filtered items. It was found that thresholds were low and relatively constant up to disparities an order of magnitude larger than is predicted by this constraint. Furthermore, peak sensitivity was relatively independent of spatial frequency. A control experiment showed that binocular correlation of the carrier is necessary for this task. In a third experiment, the maximum disparity that supports threshold performance was compared for an isolated bandpass item and bandpass–filtered noise. This limit was found to be five times larger for the isolated stimuli. In summary, these findings show that the initial stage of disparity detection is not limited by the size–disparity constraint. For stimuli with multiple false targets, however, processes subsequent to this stage reduce the disparity range over which the correspondence problem can be solved.

Effects of dot density, patch size and contrast on the upper spatial limit for direction discrimination in Random-dot Kinematograms

Two-frame random-dot kinematograms (RDKs) of different dot density, area and contrast were used to study the spatial properties of the human visual motion system. It was found that the maximum spatial displacement at which observers could reliably discriminate the direction of motion (dmax) increased gradually by a factor of up to 6.4 as dot density was decreased from 50 to 0.025% for high Michelson contrast (0.997) stimuli. As stimulus area was reduced from 645 deg2, this trend gradually disappeared so that by a stimulus area of 2.56 deg2, there was no effect of density upon dmax. A further experiment investigated the effects of reducing Michelson contrast from 0.77 to 0.2 on dmax over this same range of dot densities. It was found that at the highest densities, dmax declined as contrast was reduced. Furthermore, for contrasts at and below 0.4, dmax was invariant of density over the range 50-5%. These results can be accounted for by the fact that both reducing contrast, while keeping density fixed, and reducing density, while maintaining a fixed high contrast, reduce the stimulus mean luminance. For all contrasts, decreasing density below 5% led to an increase in dmax. However, the rate of this increase was slower for the lower contrast stimuli. A two-stage model based on bandpass filtering followed by an informationally limited motion detection stage is proposed and shown to provide a good account of these data.

Contrast Masking Reveals Spatial-Frequency Channels in Stereopsis

Yang and Blake (1991 Vision Research 31 1177–1189) investigated depth detection in stereograms containing spatially narrow-band signal and noise energies. The resulting masking functions led them to conclude that stereo vision was subserved by only two channels peaking at 3 and 5 cycles deg−1. Glennerster and Parker (1997 Vision Research 37 2143 – 2152) re-analysed these data, taking into account the relative attenuation of low- and high-frequency noise masks as a consequence of the modulation transfer function (MTF) of the early visual system. They transformed the data using an estimated MTF and found that peak masking was always at the signal frequency across a 2.8 octave range. Here we determine the MTF of the early visual system for individual subjects by measuring contrast thresholds in a 2AFC orientation-discrimination task (horizontal vs vertical) using band-limited stimuli presented in a 7 deg x 7 deg window at 4 deg eccentricity. The filtered stimuli had a bandwidth of 1.5 octaves in frequency and 15° in orientation at half-height. In the subsequent stereo experiment, the same (vertical) filters were used to generate both signal and noise bands. The noise was binocularly uncorrelated and scaled by each subjects MTF. Subjects performed a 2AFC depth-discrimination task (crossed vs uncrossed disparity) to determine threshold signal contrast as a function of signal and mask frequency. The resulting functions showed that peak masking was at the signal frequency over the three octave range tested (0.4–3.2 cycles deg−1). Comparison with simple luminance-masking data from experiments with similar stimuli shows that bandwidths for stereo masking are considerably larger. These data suggest that there are multiple bandpass channels feeding into stereopsis but that their characteristics differ from luminance channels in pattern vision.

What determines the maximum displacement limit for spatially broadband kinematograms

Two experiments are described that are designed to investigate what determines the maximum spatial displacement detectable (dmax) for spatially broadband patterns exposed in a two-frame motion sequence. In experiment 1, dmax was found to be 1.63 times greater for a two-dimensional (2-D) broadband random pattern with a 1/f Fourier amplitude spectrum (equal contrast in each octave) than for a 2-D binary-valued random-dot pattern with a flat spectrum (higher contrast in higher-frequency octaves). In experiment 2, dmax was shown to vary in inverse proportion to the lowest stimulus frequency for random patterns with a one-octave bandwidth and normalized contrast. Furthermore, when these five one-octave patterns were summed together, dmax for this new five-octave pattern was found to be only 1.46 times lower than dmax for the lowest-frequency one-octave pattern presented alone. A model is described in which direction discrimination is based on the nearest-neighbor matching of zero crossings in the output of a single-spatial-filter bandpass in both spatial frequency and orientation. Data from the model show that the difference between dmax for the five-octave and the lowest one-octave patterns can be accounted for by the same filter passing some of the additional higher frequencies in the former pattern. Furthermore, it is argued that all the data can be accounted for by assuming that dmax is determined by the coarsest spatial filter activated by each stimulus. Modeling the results of both experiments suggests that the bandwidth of this filter is ~2.6 octaves and reaches peak sensitivity at ~0.47 c/deg. The model is shown to be capable of accounting for a wide range of other two-frame dmax data.

The role of perspective information in the recovery of 3D structure-from-motion

When investigating the recovery of three-dimensional structure-from-motion (SFM), vision scientists often assume that scaled-orthographic projection, which removes effects due to depth variations across the object, is an adequate approximation to full perspective projection. This is so even though SFM judgements can, in principle, be improved by exploiting perspective projection of scenes on to the retina. In an experiment, pairs of rotating hinged planes (open books) were simulated on a computer monitor, under either perspective or orthographic projection, and human observers were asked to indicate which they perceived had the larger dihedral angle. For small displays (4.6 x 6.0 degrees) discrimination thresholds were found to be similar under the two conditions, but diverged for all larger stimuli. In particular, as stimulus size was increased, performance under orthographic projection declined and by a stimulus size of 32 x 41 degrees performance was at chance for all subjects. In contrast, thresholds decreased under perspective projection as stimulus size was increased. These results show that human observers can use the information gained from perspective projection to recover SFM and that scaled-orthographic projection becomes an unacceptable approximation even at quite modest stimulus sizes. A model of SFM that incorporates measurement errors on the retinal motions accounts for performance under both projection systems, suggesting that this early noise forms the primary limitation on 3D discrimination performance.