Recent findings suggest that the slow eye movement system, the optokinetic response (OKR) in particular, provides the extra-retinal signal required for the perception of depth from motion parallax (Nawrot, 2003). Considering that both the perception of depth from motion parallax (Ono, Rivest & Ono, 1986; Rivest, Ono & Saida, 1989) and the eye movements made in response to head translations (Schwarz & Miles 1991; Paige, Telford, Seidmen, & Barnes, 1998) appear to scale with viewing distance, changes in perceived depth from motion parallax were studied as a function of viewing distance. If OKR is used in the perception of depth from motion parallax, a change in the OKR signal, caused by a change in viewing distance, should accompany a change in perceived depth from motion parallax. Over a range of viewing distances, binocular stereopsis was used to index perceived depth from motion parallax. At these viewing distances the gain of the OKR portion of the compensatory eye movement was also determined. The results show that the change in OKR gain is mirrored by the change in perceived depth from motion parallax as viewing distance increases. This suggests that the OKR eye movement signal serves an important function in the perception of depth from motion.

*d*is the specified depth,

_{S}*D*is the distance to the stimulus,

_{S}*δ*is the binocular disparity, and

*i*is the inter-ocular distance. For the MP stimulus, the commonly used distance-squared law (Rogers & Graham, 1982) is: where

*d*is the specified depth,

_{M}*D*is the distance to the stimulus,

_{M}*μ*is the disparity equivalence given by stimulus translation or displacement, and

*t*is the distance the head translated laterally. The psychophysical study described here will determine the disparity of the BD stimulus that generates perceived depth that matches the perceived depth in the MP stimulus; that is the stimulus parameters giving

*d*=

_{S}*d*. We can model this comparison of BD and MP by equating Equation 1 and Equation 2: If all the variables in Equation 3 maintained the same relationships over changes in viewing distances, the perceived depths in the BD and MP stimuli would be equal when the specified parameters were equal. As the findings of Ono et al., (1986) tell us, this does not occur. So we have to consider which of the variables in Equation 3 might differ between the BD and MP stimuli.

_{M}*D*and

_{S}*D*. Such a difference is unlikely due to the unobstructed view of experimental apparatus. In the current study, the difference between BD and MP viewing was whether the observer’s eyes were occluded sequentially by the shutter glasses (BD) or a single eye was briefly occluded (MP). Indeed, Bradshaw et al (1998, 2000) conclude from a BD and MP matching paradigm that BD and MP use “the same estimate of viewing distance to scale size and depth estimates.” If

_{M}*D*=

_{S}*D*, then they cancel in Equation 3 and do not explain the failure of constancy with motion parallax.

_{M}*δ*and

*μ*, over viewing distance Both parameters are quantified as proximal retinal stimuli, and the effect of viewing distance is only apparent when these proximal stimuli are used in the interpretation of depth. Moreover, the cue combination paradigm of Rogers and Collett (1989) suggests a very close perceptual equivalence for equivalent

*δ*and

*μ*parameters, at least when presented at a single 57 cm viewing distance. Therefore, if

*δ*=

*μ*, then they also cancel in Equation 3. (The reader should not confuse this theoretical equivalence in discussion of the distance-square law with the following study that uses a variable value of

*δ*to match a standard value of

*μ*.)

*i*(the observer’s interocular distance) remains constant over changes in viewing distance, the only term in Equation 3 that can produce a difference in the perceived-depth matches as a function of viewing distance is

*t*, the measured lateral translation of the head. Why might

*t*be mis-estimated?

*t*—meaning the internal parameter that affects the perceived depth in a MP display—is provided by the OKR eye movement signal. We have known since the original study by Rogers and Graham (1979) that head movements are not required for the unambiguous perception of depth from MP. Instead, Nawrot (2003) proposes that the model parameter

*t*is served by an OKR eye movement signal. The current study investigates whether changes in viewing distance (

*D*) produce a change in the perception of depth (

_{M}*d*) from motion parallax (

_{M}*μ*) that co-varies with changes in the OKR signal.

*t*. Consider, a fixed magnitude head movement (

*t*) generates a smaller OKR eye movement as viewing distance increases; the use of OKR gain in the model preserves this relationship. When OKR gain is high (which occurs with near viewing distances and when the gain of TVOR is low), the resulting depth estimate is similar to the depth estimate generated by a smaller effective

*t*. The predictions illustrated in Figure 1 stem from this hypothesis.

*t*(a decrease in OKR) with viewing distance.

Viewing Distance | cm | 57 | 90 | 143 | 227 |
---|---|---|---|---|---|

Dot Size. | Minarc (pix) | 2.0 (1) | 2.5 (2) | 2.4 (3) | 2.0 (4) |

# Dots | 5000 | 3750 | 2500 | 1250 | |

# cycles | (0.4c/ deg) | 5.3 | 3.4 | 2 | 1.4 |

Peak DE | Minarc (pix) | 8.0 (4) | 7.6 (6) | 8.0 (10) | 8.2 (16) |

BD range | minarc | 2.0 – 14.0 | 2.5 – 14.0 | 1.6 – 14.4 | 2.0 – 14.3 |

# stim. intervals | 7 | 10 | 9 | 7 |

*r*

^{2}= 0.999). The calibration of this device remained very stable as it was checked periodically throughout the experiment. Because the device prevented tilting or rolling of the head, observers typically made head movements only within the central 12 cm of the device’s travel.

*r*= 0.97 were excluded from the analysis, (about one quarter of the trials collected). Using this line, the

*actual*eye movement recording was converted to units of degrees left and right of center. Using the head movement recording, the

*expected*eye movements were determined in degrees left and right of center. Eye movement gain was determined by comparing the actual and expected eye movements for the central 7 to 10 degrees of translation to the left or right, excluding more extreme sections when both eye and head were slowing, reversing, and then accelerating. A regression was used to determine the relationship between actual and expected eye movements in this central section of each recording. Because the recording rate was fixed, the number of points included in the analysis depended on how fast the observer’s head moved. The slope of the regression gave the gain of the eye movement for the accompanying head movement. The average gain for each trial was determined from four translations, two to the left, and two to the right.

*pOKRG*) with viewing distance. Optokinetic response gain was calculated by subtracting dark gain (TVOR alone) from light gain (TVOR + OKR). As expected, eye movement gain was very close to 1.0 in light conditions at all viewing distances. In dark conditions the eye movement gain was less than 1.0, representing under-compensation, but these dark gain values increased with larger viewing distances. Although the TVOR gain values are lower than those found by Paige and Tomko (1991), these values are within the range reported by Schwarz and Miles (1991). As will be discussed below, the frequency and amplitude of the head movement most likely plays a role both in eye movements (Telford et al., 1997; Paige et al., 1998) and in the perception of depth from motion parallax.

Viewing Distance | Calibration r^{2} | LIGHT GAIN | DARK GAIN | OKR Gain | pOKRG | |
---|---|---|---|---|---|---|

57 | AVE | 0.994 | 1.033 | 0.775 | 0.257 | |

St Err | 0.002 | 0.022 | 0.036 | 0.032 | ||

90 | AVE | 0.986 | 1.017 | 0.785 | 0.232 | 0.903 |

St Err | 0.002 | 0.037 | 0.034 | 0.030 | ||

143 | AVE | 0.988 | 0.993 | 0.795 | 0.198 | 0.770 |

St Err | 0.003 | 0.032 | 0.051 | 0.038 | ||

227 | AVE | 0.995 | 0.970 | 0.801 | 0.169 | 0.658 |

St Err | 0.001 | 0.021 | 0.045 | 0.039 |

*δ*(binocular disparity) matching a standard

*μ*(disparity equivalence) at each viewing distance. The green line in Figure 5B gives the corresponding

*d*values. The red line in Figure 5A gives the expected

_{M}*δ*value if

*δ*measured at 57 cm changed with increased viewing distance as a function of the change in OKR gain (pOKRG) at these viewing distances as shown in Equation 4: Likewise, the red line in Figure 5B plots the corresponding

*d*

_{M}values (Equation 3). The function shown in Equation 5 demonstrates that changes in

*μ*and

*d*parallel the changes in OKR gain. This suggests a possible general form of the distance-square law for motion parallax.

_{M}*t*) is shown in Equation 6. While the specific metric of the OKR eye movement signal remains to be determined, we do know OKR gain and we know it maintains an inverse relationship with head movement magnitude. As OKR gain decreases, a larger head movement (

*t*) is required to generate the same magnitude of OKR eye movement. An estimate of the total compensatory eye movement (assuming gain = 1) is generated with the function,

*θ*= arctan (

*t*/

*D*). However, since the visual system relies on the OKR component of the eye movement, not the total eye movement, and OKR gain is ≪ 1, the estimate of the OKR eye movement needed in the distance-square law is given by

_{M}*θ*/

*OKRGain*. As shown with the blue line in Figure 6, this function generates a reasonable approximation of the MP-BD matching procedure data. An even better approximation of the psychophysical data would be generated by higher OKR gain values at nearer viewing distances (57 cm to 143 cm) and lower OKR gain values at the 227 cm viewing distance.