Discussion

Glass pattern are part of a more general class of dot stimuli that includes the random-dot kinematogram (RDK) and random-dot stereogram (RDS). The RDS (Julesz, 1971) consists of a pair of images of a uniform texture of dots (randomly generated). Although no form is apparent in this pair, when they are fused binocularly they produce a perception of depth. The RDK is similar, yet offset in time rather than depth. Here, the perception of motion arises from the presentation of successive frames of random texture, which alone cause no perception of form. Both of these types of stimuli, like Glass patterns, are able to produce perceptual effects despite their lack of a continuous contour or moving object. These stimuli have proven useful in psychophysical and physiological experiments, as they can be effective in arguing against the need for an explicit pairing of elements to perceive structure in a stimulus. This is one of the reasons that Glass patterns are an attractive stimulus for the study of form vision.

Both simple and complex cells in V1 typically gave weak but reliable orientation selective responses to dynamic, translational Glass patterns. Neuronal selectivity qualitatively matched our predictions from receptive field models based on oriented, linear filters. Orientation selectivity was generally best when the separation of the dots was about one quarter to one half the optimal spatial period of the receptive field. For larger dot separations ( $r\approx\lambda$), our model predicted and we observed more complicated forms of orientation selectivity in which response peaks 90$^\circ$ from the optimum were sometimes evident and overall selectivity was reduced. Simulations presented in Chapter 4 reveal that this behavior should depend on the selectivity of the neuron, being most prominent for neurons with the narrowest orientation and spatial frequency tuning. We found no strong evidence that tuning to Glass patterns extending beyond the CRF was significantly modulated beyond our expectation (based on suppression to gratings of the same size).

If the local structure of Glass patterns is in fact detected initially by V1 cells and then pooled in downstream areas, limitations imposed in V1 might be reflected in psychophysical data. Two types of data indicate that this is the case. Psychophysical measurements in humans (Wilson and Wilkinson, 1998; Wilson et al., 1997; Ross et al., 2000; Alliston et al., 1999) and macaque monkeys (McCollum et al., 2000) show the optimal dot separation for detection of form in Glass patterns is between 0.1$^\circ$ and 0.2$^\circ$. Recall that our data and simulations show that the best orientation selectivity for a neuron occurred when dot separation was $0.25-0.5$ of the spatial period of the optimal spatial frequency. The range of optimal $r$ values observed behaviorally corresponds to channels or neurons with optimal spatial frequencies between 2.5 and 5 c/deg. This is the range in which both human and monkey observers have their highest contrast sensitivity (Campbell and Robson, 1968; DeValois et al., 1974), and the most common range for the optimal spatial frequencies of macaque cortical neurons representing the central 5$^\circ$ of the visual field (DeValois et al., 1982). Our V1 neuronal population would thus provide the most accurate information about local orientation of the elements of Glass patterns that have dot separations in precisely the range that is optimal for behavior.

An ideal observer model might prove useful in making this connection more concrete. We would need to estimate the noise in the Glass pattern responses and the ability of the observer to efficiently sample these responses to produce a decision. This approach has proved useful in exploring the relationship between neural responses in macaque area MT and psychophysical performance on motion discrimination tasks (Shadlen et al., 1996). Deneve et al. (1999) has suggested that cortical areas may act as ideal observers of the responses of neurons in areas that project to them. This approach might be useful in modeling the behavior of higher cortical areas in response to Glass patterns, based on our data in V1.

A second psychophysical finding that has been related to the responses of V1 cells is the relative ineffectiveness of Glass patterns in which the two dots in a pair are of opposite contrast. Glass and Switkes (1976) and Prazdny (1986) have reported that the correct structure cannot be perceived in opposite-polarity Glass patterns. In particular, Glass and Switkes (1976) reported that opposite-polarity concentric patterns appeared ``spiral-like''. Kovács and Julesz (1992) extended this observation, showing that opposite-polarity Glass patterns elicit reversed perceptions compared to same-polarity patterns (i.e., the perceived orientation is orthogonal to that of the dot pair). These percepts, counterintuitive at the time, were used as evidence to conclude that opposite-polarity Glass patterns did not activate V1 cells. It was suggested that this is consistent with V1 simple cells receiving either on or off inputs, but not both (Tolhurst and Thompson, 1975; Hubel and Wiesel, 1962). However, we have established here that opposite-polarity Glass patterns drive V1 cells (simple and complex) in a manner that can account for the psychophysical results. Furthermore, it is likely that V1 cells receive both on and off inputs in a push-pull fashion (see Ferster and Miller (2000) for review). Our data and simulations both show that neuronal orientation selectivity is reduced for opposite polarity Glass patterns. V1 neurons would therefore provide a less precise signal about dot-pair orientations with opposite-polarity than with same-polarity dots, which would considerably degrade the ability of downstream neurons to extract global form from opposite-polarity dot patterns.

Other aspects of Glass pattern perception do not have obvious correlates in our V1 data. DeValois and Switkes (1980) reported that adapting to a translational Glass pattern caused a reduction in sensitivity to gratings aligned orthogonal, but not parallel, to the dot pair orientation. This curious result does not correspond to any simple expected outcome based on the orientation and spatial frequency selectivity of our V1 neurons. In particular, we would expect maximal adaptation for patterns that were parallel, not orthogonal, to the orientation in the adapting pattern. DeValois and Switkes suggested that the effects they observed might be due to a lack of response by cells in V1 caused by inhibitory interactions among neurons with similar preference. Since our V1 cells respond reliably to translational Glass patterns aligned parallel to a preferred grating stimulus, we conclude that the interactions they propose do not occur at the level of V1.

The links between psychophysical studies of Glass pattern perception and V1 receptive field structure help us to understand the limits of the first stage of form perception, but they cannot provide specific information about downstream stages of analysis that integrate information in Glass patterns to provide signals about global form. Yet, some recent psychophysical and physiological studies do provide clues about this second stage. Wilson and his colleagues have shown that human observers are more sensitive to concentric Glass patterns than to other types (Wilson et al., 1997). However, individual V1 receptive fields are not large enough to give selective responses to concentric over translational structure. The particular salience of the concentric Glass pattern must be due to the action of second-stage mechanisms that selectively pool certain inputs from V1. Neurons in macaque V2 (Hegdé and Van Essen, 2000) and V4 (Gallant et al., 1996,1993) have been reported to be selective for complex shapes including concentric and hyperbolic forms. Neurons such as those may form the neural basis for this second stage, and studying their responses to Glass patterns could yield further insight into the processes by which the visual system converts sparse local orientation signals into salient percepts of global form.