Introduction

Glass patterns (Glass, 1969; Glass and Perez, 1973) have been used in numerous psychophysical studies to probe form-detecting mechanisms in human observers (Prazdny, 1984; Wilson and Wilkinson, 1998; Dakin, 1997a; Glass and Switkes, 1976; Ross et al., 2000; Prazdny, 1986; Earle, 1985; Dakin and Bex, 2001; Wilson et al., 1997; DeValois and Switkes, 1980). These patterns are created by taking a ``seed'' pattern of randomly placed dots, and then pairing each dot with another according to a particular geometric rule. The example Glass patterns shown on the left side of Figure 3-1 were generated by translating, rotating, and magnifying the ``seed'' pattern and adding the result back to the original field. The percept of global form in each case is clear, but these global percepts arise purely from the local orientation cues given by pairs of dots. In his first description of these patterns, Glass (1969) speculated on the nature of the cortical responses they evoked, and proposed that they would be useful for studying the neural basis of form perception. Closely related random-dot stimuli have been used to successfully probe the neuronal mechanisms underlying global coherent percepts in motion processing (Newsome et al., 1989) and depth perception (Poggio et al., 1985). Glass patterns have not been used extensively in psychophysical experiments in non-human primates. However, it is known that sensitivity to such patterns in the macaque (based on coherence threshold) spans a similar range to that reported in human psychophysical observers (Kiorpes and Movshon, 2002).

Figure 3-1: A, A translational Glass pattern consists of a field of random dots shifted by a distance $r$ in a direction $\theta$ and added to itself. B, A concentric, or rotational, Glass pattern is created by rotating a field of random dots about the center. C, A radial, or expansion, Glass pattern, is obtained by multiplying the radial component of each dot by a constant. The square apertures indicate hypothetical receptive fields of V1 neurons that would contain only a portion of the stimulus. The region within the aperture for the rotational (B) and radial (C) patterns can be approximated by a translational pattern like that in A.

Consideration of the structure of Glass patterns suggests that they are processed in two stages. The first stage must identify local orientation cues in the otherwise random pattern, and the second stage must combine those local signals to extract larger-scale global structures. The local cues for orientation in Glass patterns are individually quite weak, since each dot pair is embedded in a random noisy background. The absence of strong local contours means that the first stage of orientation selective cells in the cortex might provide sparse, irregular signals; a knowledge of these signals is prerequisite to studying their integration by neurons tuned for global form.

In this chapter we report on the responses of neurons in striate cortex (V1), the earliest neurons in the visual pathway with the orientation selectivity needed to begin to parse Glass patterns. V1 receptive fields are quite small compared to the Glass patterns typically used in perceptual experiments, and so would typically contain only a small part of the pattern, as demonstrated by the square apertures in Figure 3-1. A small aperture over any type of extended Glass pattern is approximated well by a translational pattern. We therefore reasoned that a first account of Glass pattern responses in V1 could be obtained by studying translational patterns like the one in the upper panels of Figure 3-1.

We also simulated the response of V1 neurons to such Glass patterns and derived the response of an oriented filter to arbitrary translational Glass patterns. Simulations of rectified, linear spatial receptive fields (Movshon et al., 1978a; DeValois et al., 1982; Movshon et al., 1978b) predict a rather complicated variation in selectivity and responsiveness as a function of dot-pair orientation, separation, and contrast, and they show how receptive field size and aspect ratio can dramatically change selectivity. Recordings of macaque V1 responses to Glass patterns show all the essential features predicted by the model. These results provide a foundation for studying the integration of local signals in downstream visual areas, and also offer an account for some psychophysical observations that appear to depend on this first stage of encoding.