The role of spatial frequency tuned channels in vergence control

Dense stereo matching over the Panum band

Stereo matching algorithms conventionally match over a range of disparities sufficient to encompass all visible 3D scene points. Human vision, however, works over a narrow band of disparities-Panum's fusional band-whose typical range may be as little as 1/20 of the full range of disparities for visible points. Only points inside the band are fused visually; the remainder of points are seen diplopically. A probabilistic approach is presented for dense stereo matching under the Panum band restriction. It is shown that existing dense stereo algorithms are inadequate in this problem setting and the main problem is segmentation, marking the image into the areas that fall inside the band. An approximation is derived that makes up for missing out-of-band information with a "proxy" based on image autocorrelation. It is shown that the Panum Proxy algorithm achieves accuracy close to what can be obtained when the full disparity band is available, and with gains of between one and two orders of magnitude in computation time. There are also substantial gains in computation space. Panum band processing is also demonstrated in an active stereopsis framework.

The effects of spatial frequency on binocular fusion: from elementary to complex images

Factors limiting binocular fusion were studied using 2-dimensional difference of Gaussian (2D-DOG) stimuli. The proportion of fused stimuli and observer's response time were determined for stimuli that varied in spatial frequency composition between 0.22 and 4.8 cycles per degree. At small disparities, mean fusion response times were short and relatively stable but increased rapidly once the disparity reached a certain critical value. This 2-phase function implies the existence of 2 separate fusional mechanisms: a rapid neurally based fusional process, which operates at small disparities, and a second mechanism involving reflexive vergence movements operating at disparities 2 to 3 times larger. Both mechanisms are highly influenced by spatial frequency, being 4 to 5 times more effective at low spatial frequencies. Additional experiments demonstrated that with compound stimuli, the fusion limit is not determined by the highest spatial frequency components (as had been reported previously) but, rather, can take advantage of the additional fusional range associated with low spatial frequencies. Such cooperation may be obvious only in the case of 2-dimensional stimuli.

Behavioral studies of local stereopsis and disparity vergence in monkeys

Investigations on macaque monkeys have provided much of our knowledge of the neural mechanisms of binocular vision, but there is little psychophysical data on the accuracy of vergence responses or the precision of stereoscopic depth perception in these primates. We have conducted comparative behavioral studies of binocular disparity processing in rhesus monkeys and humans via measurements of prism-induced fixation disparities (disparity vergence) and relative depth discrimination for spatially localized stimuli (local stereopsis). The results of these studies demonstrated a remarkable similarity in both the oculomotor and the sensory aspects of binocular vision in the two species when the stimulus dimensions were specified in visual angles, which were independent of interocular separation. The disparity vergence functions for the two species revealed fusion responses over the same range of prism-induced vergence and comparable vergence errors for stimuli near their fusional limits. Disparity vergence responses were independent of the spatial frequency of the binocular fusion stimulus. Stereothresholds as a function of the spatial frequency of the difference-of-Gaussian stimuli were of the same form, with equivalent stereoacuities, in monkey and human observers. The presence of substantial vergence errors had only a small effect on the precision of stereoscopic depth perception. We conclude that, after compensation for the differences in the lateral separation of their eyes, the operating characteristics of disparity vergence and stereoscopic vision are virtually identical in rhesus monkeys and humans and, consequently, the performance limits for these visual functions must be determined by anatomical and/or neural constraints that are similar in both species.

Computational experiments with a feature based stereo algorithm

Computational models of the human stereo system can provide insight into general information processing constraints that apply to any stereo system, either artificial or biological. In 1977 Marr and Poggio proposed one such computational model, which was characterized as matching certain feature points in difference-of-Gaussian filtered images and using the information obtained by matching coarser resolution representations to restrict the search space for matching finer resolution representations. An implementation of the algorithm and its testing on a range of images was reported in 1980. Since then a number of psychophysical experiments have suggested possible refinements to the model and modifications to the algorithm. As well, recent computational experiments applying the algorithm to a variety of natural images, especially aerial photographs, have led to a number of modifications. In this paper, we present a version of the Marr-Poggio-Grimson algorithm that embodies these modifications, and we illustrate its performance on a series of natural images.

Binocular sensory fusion is limited by spatial resolution

Binocular sensory fusion which was previously thought to have a maximum spatial extent at the fovea of 1 deg is at least 600% larger when stimulated by low spatial frequency (coarse) detail. This upper limit for sensory fusion has a constant phase disparity limit of 90 deg which corresponds to the monocular Rayleigh criterion for spatial resolution of two diffraction patterns. At low spatial frequencies the sensory fusion limit equals the upper disparity limit for stereoscopic depth perception which suggests that a common mechanism underlies these two phenomena.

Vergence eye movements made in response to spatial-frequency-filtered random-dot stereograms

Vergence responses were recorded from practised observers viewing narrow-band spatial-frequency-filtered planar random-dot stereograms. It was found that low spatial frequencies of 1.75-3.5 cycles deg-1 could trigger appropriate vergence responses to larger disparities than could the relatively high spatial frequency of 7.0 cycles deg-1. Nevertheless, appropriate vergence shifts were observed reliably for spatial-frequency/disparity combinations well outside the range predicted by Marr and Poggio's (1979) model of stereo vision. It was also found that for large-disparity/high-spatial-frequency combinations which the subjects could not fuse, the vergence system went into oscillation with the eyes diverging and converging at a frequency of about 1.5 Hz and with an amplitude of about 10-20 min arc. Finally, it was demonstrated that when a prominent monocular cue was superimposed upon a large-disparity/high-spatial-frequency stereogram then a speedy vergence response occurred which resulted in successful fusion. This latter finding supports the hypothesis advanced earlier that monocular cues can facilitate stereopsis by triggering appropriate vergence shifts.