Modeling V1 neuronal responses to orientation disparity H. BRIDGE, 1 B.G. CUMMING, 2 and A.J. PARKER 1 1 University Laboratory of Physiology, Parks Road, Oxford, United Kingdom 2 Laboratory of Sensorimotor Research, NEI, NIH, Bethesda, Maryland (Received February 15, 2001; Accepted October 1, 2001) Abstract The contribution of interocular orientation differences to depth perception, at either the neuronal or the psychophysical level, is unclear. To understand the responses of binocular neurons to orientation disparity, we extended the energy model of Ohzawa et al. (1990) to incorporate binocular differences in receptive-field orientation. The responses of the model to grating stimuli with interocular orientation differences were examined, along with the responses to random dot stereograms (RDS) depicting slanted surfaces. The responses to combinations of stimulus orientations in the two eyes were left–right separable, which means there was no consistent response to the binocular orientation difference. All existing neuronal data concerning orientation disparity can be well described by this type of model (even a version with no disparity selectivity). The disparity sensitive model is nonetheless sensitive to changes in RDS slant, although it requires narrow orientation bandwidth to produce substantial modulation. The disparity-insensitive model shows no selectivity to slant in this stimulus. Several modifications to the model were attempted to improve its selectivity for orientation disparity and 0or slant. A model built by summing several disparity-sensitive models showed left–right inseparable responses, responding maximally to a consistent orientation difference. Despite this property, the selectivity for slant in RDS stimuli was no better than the simple disparity-selective model. The range of models evaluated here demonstrate that interocular orientation differences are neither necessary nor sufficient for signaling slant. In contrast, within the framework of the energy model, positional disparity sensitivity appears to be both necessary and sufficient. Keywords: Orientation disparity, Energy model, Cortical area V1 Introduction When a surface slanted in depth is viewed binocularly, the retinal images of lines on the surface have different orientations in the two eyes. Wheatstone (1838) demonstrated that humans may perceive a line slanted in depth when they are presented with two lines of different orientations in the two eyes. A simple illustration of this is provided in Fig. 1. A table is viewed from above, such that the left eye is aligned with the left edge of the tabletop. The image of that edge on the left retina will therefore be oriented vertically. Due to the separation of the two eyes, the right eye will not be aligned with the left edge of the table. Thus, the image on the right retina will be tilted away from vertical by an angle u: this is the orientation disparity of that edge. One way to calculate slant is by comparing the positional disparities of two or more points along the lines—thereby calcu- lating the gradient of disparity with respect to position in the image. An alternative measure of slant could be derived from the orientation difference between the lines in the two eyes (as de- scribed in Fig. 1). In this scheme the orientation of monocular features is identified separately from their position, so that the calculation of slant from orientation disparities could be indepen- dent of positional disparity (Howard & Rogers, 1995). This re- quires only a single binocular calculation. The geometry of stereo vision guarantees that these two meth- ods yield the same estimate of surface slant, but they represent very different brain mechanisms. If cortical neurons were able to signal monocular stimulus orientation and monocular stimulus position independently, then it would be possible to construct binocular signals related to surface slant from measures of inter- ocular orientation differences (orientation disparities). Blakemore et al. (1972) found a population of neurons in area 17 of the cat that responded maximally when bars of different orientations were presented to the two eyes. It is possible that some of these neurons may be distinct from the population of neurons that can detect positional differences between the two retinal images (Barlow et al., 1967; Nikara et al., 1968). Several psychophysical studies have investigated the possibil- ity that orientation disparities are used in the perception of slant (Mitchison & McKee, 1990; Cagenello & Rogers, 1993). While Mitchison & McKee (1990) concluded that orientation disparities were not used, Cagenello and Rogers (1993) suggested that, based on the anisotropy in perceiving surfaces slanted about a horizontal or a vertical axis, orientation disparities were used for perceiving slant. Moreover, they claim that the neurons described by Blakemore et al. (1972) and Nelson et al. (1977) could be used for extracting Correspondence should be addressed to: H. Bridge, University Labo- ratory of Physiology, Parks Road, Oxford, OX1 3PT, England, UK. E-Mail: holly.bridge@physiol.ox.ac.uk Visual Neuroscience (2001), 18, 879–891. Printed in the USA. Copyright © 2001 Cambridge University Press 0952-5238001 $12.50 DOI: 10.1017.S0952523801186049 879