Keith Langley

Contrast adaptation may enhance contrast discrimination.

Whether contrast adaptation may enhance contrast discrimination is a question that has remained largely unresolved because of conflicting empirical evidence. Greenlee and Heitger (1988), for example, reported that contrast discrimination may be enhanced after contrast adaptation, while Maattanen and Koenderink (1991) did not. This paper aimed to account for the different conclusions reached by these independent researchers by manipulations of key differences that exist between the two studies. It is shown that contrast discrimination may be enhanced after adaptation, but that these effects can vary markedly across subjects and test conditions. Enhancements in contrast discrimination are reported to be significant when adapting and testing at low levels of contrast, but just significant at higher levels of contrast. For high contrast signals; enhancements are shown to be independent of temporal frequency but dependent upon viewing conditions. Under binocular viewing conditions, enhancements in contrast discrimination thresholds are shown to be significantly higher than under monocular viewing conditions. It is suggested that the different conclusions reached by Greenlee and Heitger and by Maattanen and Koenderink may be explained by their respective differences in viewing conditions. The former study used binocular, while the latter study used monocular viewing with an occluding eyepatch.

Stereopsis from contrast envelopes

We report two experiments concerning the site of the principal nonlinearity in second-order stereopsis. The first exploits the asymmetry in perceiving transparency with second-order stimuli found by Langley et al. (1998) (Proceedings of the Royal Society of London B, 265, 1837-1845) i.e. the product of a positive-valued contrast envelope and a mean-zero carrier grating can be seen transparently only when the disparities are consistent with the envelope appearing in front of the carrier. We measured the energy at the envelope frequencies that must be added in order to negate this asymmetry. We report that this amplitude can be predicted from the envelope sidebands and not from the magnitude of compressive pre-cortical nonlinearities measured by other researchers. In the second experiment, contrast threshold elevations were measured for the discrimination of envelope disparities following adaptation to sinusoidal gratings. It is reported that perception of the envelopes depth was affected most when the adapting grating was similar (in orientation and frequency) to the carrier, rather than to the contrast envelope. These results suggest that the principal nonlinearity in second-order stereopsis is cortical, occurring after orientation- and frequency-selective linear filtering.

The stereoscopic anisotropy: individual differences and underlying mechanisms.

Observers are more sensitive to variations in the depth of stereoscopic surfaces in a vertical than in a horizontal direction; however, there are large individual differences in this anisotropy. The authors measured discrimination thresholds for surfaces slanted about a vertical axis or inclined about a horizontal axis for 50 observers. Orientation and spatial frequency discrimination thresholds were also measured. For most observers, thresholds were lower for inclination than for slant and lower for orientation than for spatial frequency. There was a positive correlation between the 2 anisotropies, resulting from positive correlations between (a) orientation and inclination thresholds and (b) spatial frequency and slant thresholds. These results support the notion that surface inclination and slant perception is in part limited by the sensitivity of orientation and spatial frequency mechanisms.

Linear and nonlinear transparencies in binocular vision

When the product of a vertical square–wave grating (contrast envelope) and a horizontal sinusoidal grating (carrier) are viewed binocularly with different disparity cues they can be perceived transparently at different depths. We found, however, that the transparency was asymmetrical; it only occurred when the envelope was perceived to be the overlaying surface. When the same two signals were added, the percept of transparency was symmetrical; either signal could be seen in front of or behind the other at different depths. Differences between these multiplicative and additive signal combinations were examined in two experiments. In one, we measured disparity thresholds for transparency as a function of the spatial frequency of the envelope. In the other, we measured disparity discrimination thresholds. In both experiments the thresholds for the multiplicative condition, unlike the additive condition, showed distinct minima at low envelope frequencies. The different sensitivity curves found for multiplicative and additive signal combinations suggest that different processes mediated the disparity signal. The data are consistent with a two–channel model of binocular matching, with multiple depth cues represented at single retinal locations.

Computational models of coherent and transparent plaid motion.

The perceived motion of two added sinusoidal gratings of similar amplitude and spatial frequency but different orientations is often coherent. However, when either relative grating contrast or frequency are varied, perception may transform to a motion transparency. For plaids, both multiplicative and additive transparent percepts are reported. To explain perception, several computational models of motion transparency are proposed. The most general model considered is, however, a quadratic form with five unknowns. To stabilize the transparent model, additional constraints are introduced so that two velocities may be detected from the motion of plaid patterns. It is shown how this model may be realised by a two-layer (linear) feedforward network and how network learning paradigms may be used to explain some facets of visual perception. To describe the motion of plaid patterns there is an ambiguity because computational models of both coherent and transparent motion may be used to detect image velocity. In view of this competition between models, the issue of model selection is addressed; especially for cases where two or more models fit the image measurements without a residual error. The computational approach that is proposed affords one explanation why perception selects transparency in favour of coherence for plaid patterns by adjustments of relative grating contrast and frequency.

A parametric account of contrast adaptation on contrast perception

The effect of contrast adaptation on perceived contrast is assessed by contrast matching spatially adjacent sinusoidal gratings of similar spatial frequency, but different contrast and orientation. The main empirical question asked is why a high contrast orthogonal adaptor appears to amplify contrast signals through an increase in the slope of the contrast matching function but does not affect the threshold contrast at which a grating is detected. To explain this effect of adaptation, the Naka- Rushton receptor equation is employed as a description of the visual systems contrast response function. It is reported that the effects of adaptation may be described by three isotropic components, namely, signal amplification, division and addition, and one orientation specific component of subtraction. By collating the predictions made by the Naka-Rushton receptor equation with existing psychophysical data, it is shown that the magnitude of the isotropic components of adaptation increase with the contrast of the adapting signal. The orientation specific effect, however, is shown to saturate at relatively low adapting contrast levels. This saturation appears to be inconsistent with the commonly held view that the orientation specific effect represents a functional strategy used by the visual system to combat the problem of neural saturation in response firing rates.

Temporal adaptability and the inverse relationship to sensitivity: a parameter identification model.

Following a prolonged period of visual adaptation to a temporally modulated sinusoidal luminance pattern, the threshold contrast of a similar visual pattern is elevated. The adaptive elevation in threshold contrast is selective for spatial frequency, may saturate at low adaptor contrast, and increases as a function of the spatio-temporal frequency of the adapting signal. A model for signal extraction that is capable of explaining these threshold contrast effects of adaptation is proposed. Contrast adaptation in the model is explained by the identification of the parameters of an environmental model: the autocorrelation function of the visualized signal. The proposed model predicts that the adaptability of threshold contrast is governed by unpredicted signal variations present in the visual signal, and thus represents an internal adjustment by the visual system that takes into account these unpredicted signal variations given the additional possibility for signal corruption by additive noise.

Motion perception and motion estimation by total-least squares.

A computational model of motion perception is proposed. The model, which is gradient-based, adheres to the neural constraint that transmitted signals are positive-valued functions by posing the estimation of image motion as a quadratic programming problem combined with total-least squares: a model that assumes that image signals are contaminated by noise in both the spatial and temporal dimensions. By shrinking motion estimates with a regularizer whose subtractive effect introduces a contrast dependent speed threshold into motion computations, it is shown that the total-least squares model when posed as a quadratic programming problem, is capable of explaining both increases and decreases in perceived speed as these effects were reported by Thompson (1982) to vary as a function of image contrast and temporal frequency. The correlation that exists between the models contrast speed response and results reported from visual psychophysics is consistent with the view that the visual system assumes that image signals may be contaminated by noise in both the spatial and the temporal domain, and that visual motion is influenced by the consequence of these assumptions.

Regularization in a neural model of motion perception

Neurons in sensory systems encode and transmit information about attributes of the environment. Much of the information transmitted by spiking neurons appears to be encoded in the rate at which they fire. This rate necessarily has a positive value. In this paper, the implication of this constraint for models of motion detection is examined. The detection of image motion is represented mathematically as a quadratic programming problem in which variables used to represent image speed are restricted to positive values. This novel representation requires that additional constraints are introduced to stabilize motion computations because quadratic programming problems require a surplus of unknowns to code for image speed. Two further constraints are introduced into the model to take into account possible cases of image degeneracy. They are based upon (i) an a priori preference for small image speeds, and (ii) the assumption that image motion parallel to contours of constant intensity for a one-dimensional signal is zero. The latter assumption is shown to account for perceived biases in speed reported for type I plaid patterns [Castet, E. & Morgan, M. (1996). Apparent speed of type-I symmetrical plaids. Vision Research 36, 223-32]. The model suggests that the visual system uses separate constraints to stabilize motion computations. One set of constraints arises from the nature of the motion detection process itself, while another two constraints take into account possible cases of degeneracy where image contrast is low or near zero and where the image function is one-dimensional and the aperture problem prevails.

A model of motion adaptation and motion after-effects based upon principal component regression.

Abstract. A computational model to help explain effects of adaptation to moving signals is compared with established energy (linear regression) models of motion detection. The proposed model assumes that processed image signals are subject to error in both dimensions of space and time. This assumption constrains models of motion perception to be based upon principal component regression rather than linear regression. It is shown that response suppression of model complex cell neurons that input into the model may account for (1) increases in perceived speed after adaptation to static patterns and testing with slowly moving patterns, (2) significant increases in perceived speed after adaptation to patterns moving at a medium speed and testing at high speed, and (3) decreases in perceived speed in the opponent direction to a quickly moving adapting signal. Neither of predictions (2) or (3) are general features of established accounts of motion detection by visual processes based upon linear regression. Comparisons of the proposed models speed transfer function with existing psychophysical data suggests that the visual system processes motion signals with the tacit assumption that image measurements are subject to error in both space and time.