Spatial frequency tuned channels: implications for structure and function from psychophysical and computational studies of stereopsis

The extraction of features and disparities from images by a model based on the neurological organisation of the visual system

A computational simulation of the early stages of mammalian visual processing, from the retina to the primary visual cortex, is described. The simulation uses elements that are organised according to the anatomical connections of the biological visual system. It explores how observed responses of simple cells of the primary visual cortex can be generated by a small number of stages of the types of processing that are observed in the nervous system. Edge features are extracted from single images and disparities between stereoscopic image pairs are detected with good reliability. An important parameter affecting processing was found to be the strength of the surround inhibition between the elements that represent neurones of the primary visual cortex.

Definition and detection of binocular disparity

Stereoacuity experiments tested definitions of binocularly disparate spatial positions by perturbing the binocular correspondence of the two half-images. Dichoptic translations perturbed zero-order retinal positions; expansions perturbed first-order horizontal separations; rotations perturbed first-order orientations; and anisotropic expansions deformed first-order two-dimensional (2D) structure. Each transformation perturbed relative positions in the two half-images by more than 100 arcsec, but stereoacuity thresholds remained about 10 arcsec. Binocular disparity involves second-order 2D differential structure of the monocular half-images, specifying local surface shape. Stereoacuity is much better than nonstereo acuity, suggesting that monocular spatial signals are binocularly correlated.

Is edge information for stereoacuity spatially channeled?

Models of stereopsis generally assume that binocular correspondence is achieved through alignment of luminance edges in the two eyes. Yet the stimulus properties which constitute edge information for stereopsis have not been defined. Three experiments explored the nature of these stimulus properties. The first two experiments tested whether local luminance gradient and the relative phase of spatial components supply information about the position of edges which influences stereosensitivity. In Expt 1, stereothresholds were reduced with increased spatial frequency or contrast of sinusoidal luminance gratings, but no simple relationship between target luminance gradient and stereosensitivity was found. In Expt 2, stereothresholds were equivalent for targets having identical spatial frequency components, but differing in maximum luminance gradient and the relative spatial phase of their components. In addition, stereothresholds were lower for the target having the higher contrast in pairs of unequal-contrast targets having equal maximum luminance gradients. These results suggest that the properties of luminance gradient and relative spatial phase do not influence stereosensitivity independently of spatial frequency and contrast. Experiment 3 directly tested whether stereosensitivity depends on edge information whose disparity is detected independently at different spatial scales. Stereothresholds for IF + 5F compound targets were found to be equivalent to thresholds obtained separately with the more sensitive of the two components. Taken together with a compressive nonlinearity in the relationship between contrast and stereothreshold obtained by others (Halpern and Blake, 1989; Legge and Gu, 1989) and replicated in Expt 1, the results of Expt 3 indicate that, whatever the exact nature of the luminance discontinuity information utilized in disparity detection, it is processed independently at different spatial scales.

The visual assessment of the spatial location of a bright bar

Vernier acuity, three-line interval bisection and line-width discrimination experiments were performed for a target bar stimulus with an asymmetrical orthoaxial contrast profile. This was done in an attempt to identify the nature of the spatial primitives that are involved in the visual coding of spatial location. We conclude that both the zero-crossings and the centroid or extremum of the zero-bounded region of the neural activity distribution that is elicited by the presentation of the target bar, are in principle available to perception. It probably depends on the spatial characteristics of the applied stimulus pattern and the adopted strategy which features are actually used in different localization tasks.

Compound binocular rivalry

Binocular rivalry was examined with random dot patterns consisting of three colours: red, green and grey. The microstructure of the patterns was defined by the individual dots, and the correspondence between the microstructures in the two eyes was manipulated. The macrostructures were defined by the distributions of red, green and grey dots over the displays, so that they consisted of orthogonally striped patterns. The degree of correspondence between the microstructures was varied in Expt 1, together with the spatial frequency of the microstructure. Rivalry periods of the macrostructures were briefer when the microstructures were in correspondence, In Expt 2 the spatial frequencies of the macrostructures were varied. The lower spatial frequency predominated for longer than the higher. The results are discussed in terms of independent pathways for corresponding and rivalry stimulation. In addition a stimulus pairing that produces clear dichoptic colour mixtures is presented.

Positional acuity without monocular cues

The accuracy with which human observers can determine the spatial location of a shape boundary was measured by vernier alignment. The vernier targets were presented as random-dot stereograms, with varying amounts of camouflage in the monocular image. Camouflage decreased vernier acuity, but when the camouflage was broken by stereoscopic disparity, acuity was improved. In the limiting case when the shape boundaries were defined by disparity information alone, vernier thresholds (75% correct, binary forced-choice) were in the region of 40 s visual angle. This is poor acuity in comparison to vernier thresholds with monocular contour, but if the limited resolution acuity for stereopsis is taken into account, cyclopean and monocular positional acuities can be considered quite similar in relation to their respective resolution limits.

The contrast dependence of spatial frequency channel interactions

Interactions between spatial frequency channels were tested in two ways: we measured the discriminability by the visual system between two compound spatial-frequency gratings, of components with spatial frequencies in the ratio 1:3, when the difference between the two gratings was an increase (or decrease) in contrast of both components of the compound grating (contrast discrimination), or when the difference between the two gratings was an increase in contrast of one component and a decrease in contrast of the other component (pattern discrimination). We found that the contrast: pattern discriminability ratio differs significantly from unity in most conditions. Furthermore, this ratio is generally greater when the components of the grating are in peaks-add relative phase than when in peaks-subtract phase. On the other hand, the ratio was close to unity for grating components of spatial frequencies 1 and 9 cycles/deg. These results suggest that the human visual system contains spatial frequency channels with bandwidths of between 1.6 and 3.2 octaves and that these relatively broad channels have peaks-add spatial profiles. The channels appear linear at intermediate contrasts and spatial frequencies, but super-linear at high spatial frequencies and contrasts. Contrast and spatial frequency may be interchangeable for the determination of the linearity of the visual system.

Intensity-response nonlinearities and the theory of edge localization

If an edge having a particular blur profile is exchanged for an edge at the same location but having a different blur profile, apparent movement between the two edges may be seen. The spatial extent of this movement was measured by a cancellation technique. Implications for the theory of edge location are discussed, including the possibility that spatial filtering is preceded by a nonlinear transduction stage.

Binocular adaptation that cannot be measured monocularly

The tilt aftereffect (TAE) is used to demonstrate the existence of a purely binocular process in human vision. A purely binocular process is a process that can be activated only by matched inputs to the two eyes. It is insensitive to monocular stimulation. The TAE can be produced by exposure to a bipartite field with the top tilted to the left of vertical, the bottom to the right. After such adaptation a pair of colinear lines appears bent in the opposite direction. A cyclopean random-dot stereogram can be used as an adapting stimulus. It produces a 2 degree TAE when a cyclopean test stimulus is used and a 1 degree TAE when a binocular but noncyclopean test stimulus is used. If the same noncyclopean pattern is viewed monocularly, no TAE is measurable. The TAE does not transfer from cyclopean adaptation to monocular testing. Apparently, cyclopean stimuli activate a 'purely binocular process' that cannot be activated by either eye alone.

Cooperation between different spatial frequencies in binocular rivalry

In binocular rivalry, stimuli made up of any limited spatial frequency (sf-) range are perceived for a shorter time than patterns consisting of the whole sf-spectrum. This finding indicates a non-linear summation of primarily independent sf-channels in the human visual system.