Terminator disparity contributes to stereo matching for eye movements and perception

Abstract

In the context of motion detection, the endings (or terminators) of 1-D features can be detected as 2-D features, affecting the perceived direction of motion of the 1-D features (the barber-pole illusion) and the direction of tracking eye movements. In the realm of binocular disparity processing, an equivalent role for the disparity of terminators has not been established. Here we explore the stereo analogy of the barber-pole stimulus, applying disparity to a 1-D noise stimulus seen through an elongated, zero-disparity, aperture. We found that, in human subjects, these stimuli induce robust short-latency reflexive vergence eye movements, initially in the direction orthogonal to the 1-D features, but shortly thereafter in the direction predicted by the disparity of the terminators. In addition, these same stimuli induce vivid depth percepts, which can only be attributed to the disparity of line terminators. When the 1-D noise patterns are given opposite contrast in the two eyes (anticorrelation), both components of the vergence response reverse sign. Finally, terminators drive vergence even when the aperture is defined by a texture (as opposed to a contrast) boundary. These findings prove that terminators contribute to stereo matching, and constrain the type of neuronal mechanisms that might be responsible for the detection of terminator disparity.

Figure 1.

Visual stimuli. We used 1-D binary random noise line patterns, presented within apertures. Here we show for each experiment a sample of the stimuli presented to the left (left column) and right (right column) eye. A, In the main experiment, the pattern seen by the two eyes had 20′ of disparity (horizontal for the vertical pattern, vertical for the horizontal pattern), whereas the aperture (a parallelogram with the long sides tilted ±45°) had zero disparity. The terminators along the long sides of the aperture (see central inset, where the binocular location of one pattern segment is highlighted) had a disparity vector aligned with the aperture. B, The contrast of the pattern (having 20′ of disparity) is multiplied by a 2-D Gaussian function (zero disparity), tilted ±45°, with a 4:1 ratio for the SDs. In this case, there are no hard line endings, so terminator detectors should be only weakly activated. C, Like in A, but now the aperture has the same disparity as that of the pattern. In this configuration, the disparity of the terminators is the same as the pattern, i.e., it does not have a component parallel to the pattern orientation. D, In this configuration, two noise patterns are presented, one in the center and the other in the periphery. The aperture through which the central pattern is seen is shifted, in the direction parallel to the noise patterns, in the two eyes. When the same central and peripheral noise patterns are shown to the two eyes, along the long edges of the aperture each pattern has terminators that have the same disparity as the aperture. However, when different patterns are shown to the two eyes, only the aperture has disparity. E, Like in A, but now the pattern is anticorrelated across eyes.

Figure 2.

DVRs to correlated noise patterns seen through a zero-disparity oblique aperture. When the noise patterns (with 20′ of disparity) are viewed through an oblique zero-disparity hard aperture (Fig. 1A), the initial DVR is in the direction orthogonal to the pattern, but subsequently a response in the direction parallel to the long edges of the aperture emerges. In the top row we show, for our three subjects, responses when the pattern was vertical (with horizontal disparity). The time course of the horizontal (black) and vertical (gray) components of vergence velocity is shown for both aperture orientations (thick lines for +45°, thin lines for −45°). This is graphically indicated in the legend. Responses induced by a horizontal pattern (with vertical disparity) are shown in the bottom row. The black and gray tick marks indicate the latency of the horizontal and vertical components of the response, respectively (for values, see Table 1).

Figure 3.

DVRs to correlated noise patterns seen through a zero-disparity 2-D Gaussian aperture. Same format and noise patterns as in Figure 2, but the contrast of the patterns is now modulated by a zero-disparity 2-D Gaussian function (Fig. 1B). The early DVR component, driven by the disparity orthogonal to the pattern, is still present, but the late component is either very attenuated (JH) or has disappeared altogether (other subjects). The latency of each component is indicated by the black and gray tick marks, and listed in Table 1.

Figure 4.

DVRs to correlated noise patterns seen through a parallelogram, which itself had disparity. Same format and noise patterns as in Figure 2, but the aperture now has the same disparity as the pattern (Fig. 1C). When the disparity is horizontal (vertical pattern, top row), a purely horizontal, short-latency, DVR is observed, reflecting the absence of off-axis terminator disparity. When the disparity is vertical (horizontal pattern, bottom row), a short-latency vertical DVR component is followed by a delayed horizontal DVR. The sign of this late component is, however, opposite that in Figure 2, indicating that it is not directly related to the orientation of the aperture, but rather to its disparity. The latency of each component is indicated by the black and gray tick marks, and listed in Table 1.

Figure 5.

DVRs to zero-disparity noise patterns seen through a rectangular aperture with disparity. Here, two different noise patterns are presented, one inside and the other outside a rectangular aperture. Both noise patterns either have zero disparity (thick lines) or are uncorrelated across eyes (thin lines). In the top row we show the horizontal vergence responses elicited when the pattern is horizontal, and the aperture is vertical, with horizontal disparity. In the bottom row we plot the vertical vergence response induced with vertical patterns, and a horizontal (with vertical disparity) aperture. In all three subjects, the presence of terminator disparity results in considerably stronger responses. Also, responses to aperture disparity are much stronger for horizontal than for vertical disparity. Latencies of the two responses are indicated by tick marks, and listed in Table 2.

Figure 6.

DVRs to anticorrelated noise patterns seen through a zero-disparity oblique aperture. Same format as in Figure 2, but the pattern is now anticorrelated in the two eyes (Fig. 1E). Regardless of pattern orientation, and for all subjects, an early DVR in the opposite direction of that induced by correlated patterns is observed. It is, however, considerably weaker and delayed (Table 1). In most cases, a late DVR component in the orthogonal channel is also observed, with a different sign depending on the orientation of the aperture. Note that the sign of the late component is also reversed relative to that observed with correlated patterns (Fig. 2). The latency of each component is indicated by the black and gray tick marks.

Figure 7.

Response of off-axis binocular energy units to some of our stimuli. A, We simulated the response of a set of binocular energy units to the stimuli from our first and last experiments. All the units were centered on the edge of the aperture, and had a preferred orientation orthogonal to its long axis (see inset at top), but each unit had a different preferred phase disparity. This population of neurons correctly identifies the disparity of the terminators when the stimulus is correlated across eyes (black line); furthermore, the tuning is reversed with anticorrelated patterns (gray line). B, We simulated the response of a set of binocular energy units to the stimuli from our fourth experiment. All the units were centered on the texture-defined aperture edge and oriented parallel to its long axis (inset at top), but had different preferred phase disparity. When the center and surround patterns are correlated (zero disparity, black line), the population encodes the disparity of the terminators. When they are uncorrelated (gray line), there is no disparity tuning, indicating that the population is not capable of extracting the disparity of the texture-defined aperture itself.