A fundamental problem for any visual system with binocular overlap is the combination of information from the two eyes. Electrophysiology shows that binocular integration of luminance contrast occurs early in visual cortex, but a specific systems architecture has not been established for human vision. Here, we address this by performing binocular summation and monocular, binocular, and dichoptic masking experiments for horizontal 1 cycle per degree test and masking gratings. These data reject three previously published proposals, each of which predict too little binocular summation and insufficient dichoptic facilitation. However, a simple development of one of the rejected models (the twin summation model) and a completely new model (the two-stage model) provide very good fits to the data. Two features common to both models are gently accelerating (almost linear) contrast transduction prior to binocular summation and suppressive ocular interactions that contribute to contrast gain control. With all model parameters fixed, both models correctly predict (1) systematic variation in psychometric slopes, (2) dichoptic contrast matching, and (3) high levels of binocular summation for various levels of binocular pedestal contrast. A review of evidence from elsewhere leads us to favor the two-stage model.

SUMMARY1. The perception of contrast was measured in humans by a technique of subjective contrast-matching, and was compared with contrast sensitivity as defined by threshold measures.2. Contrast-matching between different spatial frequencies was performed correctly (especially at frequencies above 5 c/deg) despite the attenuation by optical and neural factors which cause large differences in contrast thresholds.3. Contrast-matching between single lines of different widths was also veridical, and was not limited by the spatial integration (Ricco's Law) present at threshold. Adaptation to gratings altered the appearance of lines, and this could be best understood in Fourier terms.4. The generality of these results was shown by matching the contrast of pictures which had been filtered so that each contained a one octave band of spatial frequencies.5. Within the limits imposed by threshold and resolution, contrastmatching was largely independent of luminance and position on the retina.6. Six out of eleven astigmatic observers showed considerable suprathreshold compensation for their orientation-specific neural deficit in contrast sensitivity.7. These results define a new property of vision: contrast constancy. It is argued that spatial frequency channels in the visual cortex are organized to compensate for earlier attenuation. This achieves a dramatic 'deblurring' of the image, and optimizes the clarity of vision.

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Human vision can detect spatiotemporal information conveyed by first-order modulations of luminance and by second-order, non-Fourier modulations of image contrast. Models for second-order motion have suggested two filtering stages separated by a rectifying nonlinearity. We explore here the encoding of stationary first-order and second-order gratings, and their interaction. Stimuli consisted of 2-D binary, broad-band, static, visual noise sinusoidally modulated in luminance (LM, first-order) or contrast (CM, second-order). Modulation thresholds were measured in a two-interval forced-choice staircase procedure. Sensitivity curves for LM and CM had similar shape as a function of spatial frequency, and as a function of the size of a circular Gaussian blob of modulation. Weak background gratings present in both intervals produced order-specific facilitation: LM background facilitated LM detection (the dipper function) and CM facilitated CM detection. LM did not facilitate CM, nor vice-versa, neither in-phase nor out-of-phase, and this is strong evidence that LM and CM are detected via separate mechanisms. This conclusion was further supported by an experiment on the detection of LM/CM mixtures. From a general mathematical model and a specific computer simulation we conclude that a single mechanism sensitive to both LM and CM cannot predict the pattern of results for mixtures, while a model containing separate pathways for LM and CM, followed by energy summation, does so successfully and is quantitatively consistent with the finding of order-specific facilitation.