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. Author manuscript; available in PMC: 2011 Jul 21.
Published in final edited form as: Vision Res. 2010 May 21;50(16):1571–1580. doi: 10.1016/j.visres.2010.05.017

Visual Constraints for the Perception of Quantitative Depth from Temporal Interocular Unmatched Features

Rui Ni 1, Lin Chen 2, George J Andersen 3
PMCID: PMC2909673  NIHMSID: NIHMS212486  PMID: 20493899

Abstract

Previous research (Brooks & Gillam, 2006) has found that temporal interocular unmatched (IOUM) features generate a perception of subjective contours and can result in a perception of quantitative depth. In the present study we examine in detail the factors important for quantitative depth perception from IOUM features. In Experiments 1 and 2 observers were shown temporal IOUM features based on three dots that disappeared behind an implicit surface. Subjects reported a perception of a subjective surface and were able to perceive qualitative depth. In Experiments 3 and 4 metrical depth was perceived when binocular disparity features were added to the display. These results suggest that quantitative depth from IOUM information is perceived when binocular matched information is present in regions adjacent to the surface. In addition, the perceived depth of the subjective surface decreased with an increase in the width of the subjective surface suggesting a limitation in the propagation of quantitative depth to surface regions where qualitative depth information is available.

Keywords: stereopsis, interocular delay, matched features, unmatched features, depth perception

Introduction

Interocular unmatched (IOUM) features are available when one object partially occludes another object in the visual scene. Under these conditions part of the occluded object is only visible to one eye resulting in unmatched features across the two eyes. Although these unmatched features were treated as noise by traditional theories of binocular vision (Julesz, 1971; Marr & Poggio, 1976), more recent research has shown that IOUM features are an important source of information and are processed by the human visual system to recover depth information (see Harris & Wilcox, 2009 for a thorough review). Previous studies have found that IOUM features (1) facilitate stereoscopic processing to locate disparity discontinuities (Gillam & Borsting, 1988), (2) recover depth of monocular components (Shimojo et al., 1988; Nakayama & Shimojo, 1990; Hakkinen & Nyman, 1996; Ono et al., 1992; Gillam et al., 1999: Pianta & Gillam, 2003a, 2003b), and (3) generate a perception of an occluding subjective surface (Nakayama & Shimojo, 1990; Anderson, 1994; Liu et al., 1994; Gillam & Nakayama, 1999; Brooks & Gillam, 2006, 2007)1.

Nakayama and Shimojo (1990) referred to depth perception from IOUM features as “da Vinci stereopsis” because it was first illustrated in drawings by Leonardo da Vinci. Their study assessed the importance of ecologically valid and invalid monocular features in determining the perceived depth of IOUM features. Under valid conditions the right-eye-only area was visible to the right side of the occluding object or the left-eye-only area was visible to the left side of the occluding object. Ecologically invalid conditions were examined by reversing these conditions (e.g., right-eye-only area visible to the left side). These geometric occlusion relations specify the constraints present during real world viewing conditions (Shimojo et al. 1988). The results of the Nakayama and Shimojo (1990) study suggest that observers are more likely to perceive the monocular target as more distant under valid as compared to invalid conditions. More recent research suggests that the unmatched features in the Nakayama and Shimojo study were actually matched features and that qualitative (ordinal) depth was perceived when unmatched features were present (Gillam, Cook, & Blackburn, (2003); see Gillam et al., (1999), Pianta & Gillam (2003a), and Anderson (1994) for examples of studies demonstrating quantitative depth that cannot be explained by conventional disparity matching processes).

IOUM features from partial occlusion (present in one eye) can also result in a perception of a subjective surface. In a study by Nakayama and Shimojo (1990), valid occlusion-induced unmatched features resulted in a perception of a subjective surface. In addition, Anderson (1994) found that when the vertical interocular differences were consistent with partial occlusion a subjective surface was perceived (outlined by subjective contours) that occluded the line segments. Studies have also found that the width of the monocular regions provided quantitative (metrical) depth information (Gillam et al., 1999; Gillam & Nakayama, 1999; Grove et al., 2002; Hakkinen & Nyman, 1996).

Interocular differences are common in daily life when one object occludes another in the visual scene. Such differences provide IOUM information that can change over time when the occluded object, the occluder, or the observer is in motion. Consider an example of an individual walking towards an occluded object. Under these conditions IOUM information will vary over time as the viewing distance changes unless the line of sight is perfectly aligned with both the occluding and the occluded edges. Previous research (Ogle, 1963; Wist & Gogel, 1966; Ross & Hogben, 1974) found that disparity information could be integrated within a limited temporal range to generate stereoscopic depth perception. Shimojo et al. (1988) examined the perceived depth of an occluded object that translated behind a thin aperture. The width of the aperture was manipulated such that the occluded object was only visible to one eye at a time. It was found that subjects perceived a single occluded object in depth when there was no temporal overlap between the two monocular sequences. This percept occurred only when the translation direction was consistent with the interocular order specified by occlusion. Their results suggest that real-world occlusion constraints were used by the visual system to perceive the depth of occluded objects.

More recently, Brooks and Gillam (2006) examined the perception of quantitative depth from IOUM features. Subjects were presented with an array of vertical white lines that were occluded as they passed by a camouflaged black rectangular target. Static dots were presented above and below the lines and target. A probe point was used to match the apparent depth of the subjective contour of the rectangular target. They manipulated the translation speed to produce different combinations of temporal interocular delay and quasi-disparity information (the disparity available if the two monocular half-images were simultaneously visible). Their results indicate that quantitative depth can be perceived from temporal IOUM features and that perceived depth increased as a function of increased quasi-disparity.

One important question regarding the perception of depth from IOUM features is whether such features are processed by a standard matching mechanism (see Harris and Wilcox, 2009, for a discussion of this issue). For example, quantitative depth in da Vinci stereopsis could be explained by double matching (Gillam et al. 2003). Similarly, the perception of quantitative depth found in stimuli presented by Liu et al. (1994) has been shown to result from binocular matching (Gillam, 1995; Liu et al, 1997). In a monocular gap condition examined by Gillam et al. (1999) quantitative depth may have been dependent, in part, on the binocular disparity of the outer edges (Pianta and Gillam, 2003b). These studies suggest that to understand the importance of IOUM features in depth perception one must consider the role of binocular matched information and monocular occlusion information that might be available.

In the present study we examined several constraints likely to be important for the perception of quantitative depth from temporal IOUM features. In addition, we assessed the role of binocular matched information and monocular occlusion information in the perception of depth. In Experiments 1 and 2 we examined whether qualitative or quantitative depth can be perceived from displays containing temporal IOUM information. Experiment 1 also examined whether the direction of motion must be consistent with the interocular order from occlusion. Experiments 2 and 3 examined whether IOUM information is sufficient to generate quantitative depth perception or whether binocularly matched information is needed to perceive quantitative depth. Experiment 4 examined whether quantitative depth from IOUM features may be propagated to regions where only qualitiative depth information from monocular occlusion is available.

Experiment 1: The perception of a subjective surface from TIOA

In Shimojo et al.’s study (1988), the translating direction of the bar was consistent with the temporal order resulting in a percept of a single occluded object in depth. For example, consider a bar translating rightward underneath an aperture. Under this condition the right monocular image should be visible followed by the left monocular image. When the bar translates leftward underneath an aperture, the left monocular image should be visible followed by the right monocular image. They referred to this condition as the “valid condition” (positive temporal interocular asynchrony or PTIOA).

In Experiment 1 we examined whether the consistency of motion direction and interocular order is necessary for the perception of a subjective surface from IOUM features. Subjects were shown displays of a homogeneous occluding surface (Figure 1a). Three dots translated horizontally until occluded by a camouflaged occluding surface. When occlusion occurred temporal unmatched information was available across the two monocular images. If the visual system uses IOUM information then a subjective surface should be perceived that is occluding the dots (see Figures 1a and 1b). However, consider a condition in which an occluding surface translates in the same direction but at a greater speed than the occluded object (defined by the three dots, See Figure 1c and 1d). Under these conditions the left monocular image disappears followed by the right monocular image. This makes the “invalid” occlusion condition (negative temporal interocular asynchrony, referred to as NTIOA) a valid condition according to real-world constraints. Thus, for both rightward and leftward translation directions (Figure 1c and 1d) both PTIOA and NTIOA are compatible with real-world constraints. Because these conditions are consistent with real world constraints we expect that both PTIOA and NTIOA conditions will result in a perception of a subjective surface.2

Figure 1.

Figure 1

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Schematic illustration of the stimuli used in Experiment 1. The left column is an illustration of the stimuli. The middle column illustrates the temporal profile of two monocular views. The right column is a top view illustration of the geometry of the stimuli. Three dots translated to the right (a) or to the left (b) and were occluded by a stationary subject surface. Under these conditions the temporal difference between two monocular images was positive (>0). In two other conditions, three dots translated to the right (c) or left (d) but were occluded by a flat subjective surface that translated at a greater speed in the same direction. Under these conditions the temporal difference between two monocular images was negative (<0). Figure 1e depicts four frames of the motion sequence for PTIOA.

In Experiment 1 subjects were required to judge whether the dots were occluded from the left or the right side. This measure assured that the observer’s judgments were based on their perception of a subjective occluding surface rather than the direction of dot translation. Given the results of previous research demonstrating temporal constraints for matched disparity stereopsis (Ogle, 1963; Wist & Gogel, 1966; Ross & Hogben, 1974) the visual system might integrate unmatched disparity information within a certain temporal window. To examine the temporal limits of the integration window TIOA was manipulated.

Methods

Subjects

The subjects were 6 undergraduate students from the University of California, Riverside who received monetary compensation for participating in the experiment. All observers had normal or corrected-to-normal visual acuity and were naive regarding the purpose of the experiment. All observers had normal stereo vision (according to the RANDOT Stereotests, at least 25 sec arc at 40cm viewing distance).

Apparatus

A Dell 670 workstation was used to produce the stereo images on a ViewSonic P225f CRT monitor with a 140Hz refresh rate and a 1024 × 768 resolution. The experiment was conducted in a darkened room with walls and ceiling painted black and black carpeting. The monitor frame, the keyboard, and the mouse were not visible during the experiment. Observers viewed the displays binocularly wearing a pair of CrystalEyes LCD shutter glasses with their head stabilized by a chin and head rest. Given the nature of LCD shutter glasses, there was a 7-ms asynchrony between left and right monocular images. The luminance of the stimuli was selected so that the image when viewed monocularly through the filtered eye was not detectable (i.e., no ghosting was visible). The distance between the observer and the display screen was 57 cm. Responses were made using a mouse.

Stimuli

Three vertically aligned white dots (63.4 cd/m2) were presented on a black background (0.3 cd/m2). The dots subtended 2.3 arc min (1 pixel) and were vertically separated by 1.67 deg. visual angle (see Figure 1). The dots translated horizontally (either leftward or rightward) at a constant speed of 2.2 deg/sec for both monocular images. The direction of dot motion was counterbalanced across all conditions. The dots translated for 1.8 sec before occluded by the subjective contour, were occluded for 1.8 sec by the subjective contour, and then reappeared at the original position on frame 1 and continued to translate in the image. This cycle was repeated until the subject responded. Thus, the subjective contour was decamouflaged every 3.6 sec until the subject responded. The only difference between the two monocular images was the temporal delay when occlusion occurred (i.e., the dots disappeared). Thus viewing the display monocularly will not result in a perception of depth.

Design

Two independent variables were examined: dot disparity (relative to the screen plane, −9 (uncrossed disparity), 0, and +9 (crossed disparity) arc min) and TIOA (−320, −240, −160, −80, 0, 80, 160, 240, and 320 ms, as shown in the middle column of Figure 1). Simulated depth values of the occluding surface are presented in Table 1.

Table 1.

The simulated depth of the subjective occluding surface in Experiment 1, 2, and 3 presented in terms of disparity (arc min).

Dots depth\TIOA 0 ms +/− 80 ms +/− 160 ms +/− 240 ms +/− 320 ms
−9 arc min −9 −7.8 1.8 12 22.2
0 0 10.2 21 31.8 42
+9 arc min 9 28.8 40.2 51 62.4
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Procedure

Subjects were shown demonstrations of the display in which the translating dots were occluded by a visible white surface (19.2 cd/m2). The surface was either stationary (as shown by Figure 1a and 1b) or translated (Figure 1c and 1d). If the surface was translating the velocity of the surface was greater than the velocity of the dots and thus occluded the dots during the presentation (as shown by Figure 1c and 1d). Subjects were informed about the direction of occlusion (e.g. the dots were occluded on the right side, as depicted in Figure 1a and 1d; or on the left side, as depicted in Figure 1b and 1c) and were instructed to indicate the direction of occlusion (right or left side) by pressing the right or left mouse buttons. After the subjects understood the task they were presented with 8 practice trials in which the occluding surface was visible in dark gray (2.3 cd/m2). During the practice trials the subjects were required to report on which side (right or left) the translating dots were occluded by the surface by pressing the right or left mouse button. Following a response the next trial was presented. Subjects were required to make a minimum of 7 correct responses during the practice trials before proceeding to the experiment to ensure that subjects understood the task. Subjects were allowed up to three sets of practice trials. All subjects were able to pass the practice block of trials. During the experiment subjects were presented 20 replications of the 27 conditions (540 trials) in random order. The trials were presented in 6 blocks with a rest period between blocks. Feedback was not used during the practice trials or the experiment.

Results

The percent correct for each subject in each condition was analyzed in a 3 (dot disparity) by 9 (TIOA) repeated-measures ANOVA (Analysis of Variance). Significant main effects were found for both TIOA (F (8, 40) =7.46, p<0.01) and dot disparity (F (2, 10) =10.70, p<0.01). These results indicate that accuracy increased with an increase in the absolute value of TIOA and with a decrease in dot disparity. The interaction between TIOA and dot disparity was significant (F (16, 80) =2.61, p<0.01), as shown in Figure 2. The results indicate that for most conditions examined both PTIOA and NTIOA conditions resulted in a perception of a subjective surface. There was an overall decrease in accuracy for the NTIOA as compared to the PTIOA conditions (see Figure 2). The percent correct was at chance for the 0 msec TIOA condition. In addition, the percent correct was near chance for the −80 msec TIOA and the 0 and 9 arc min disparity conditions. Informal observations and results from a pilot study suggest that for these conditions subjects did not consistently perceive a subjective surface.

Figure 2.

Figure 2

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Mean percent correct as a function of temporal interocular asynchrony and dot depth from Experiment 1. Error bars are +/− 1 standard error.

Experiment 2a: Perception of depth from unmatched information

In Experiment 1, we found that observers could perceive a subjective occluding surface from temporal IOUM features with a TIOA of up to 320 ms. In Experiment 2a a binocular probe was used to measure the perceived depth of the subjective surface. A similar technique has been found to be an effective and precise measurement for stereoscopic depth from IOUM features (Brooks & Gillam, 2006). In the present study the vertical extent of the 3 aligned dots was less than the vertical extent of the occluding surface. This manipulation ensured that the only information for the perception of quantitative depth was the temporal disparity between the two monocular images. If TIOA provides quantitative depth information then an increase in perceived depth should be perceived with an increase in TIOA.

Methods

Apparatus

The apparatus was the same as that used in Experiment 1.

Subjects

The subjects were 7 undergraduate students from University of California, Riverside, who received monetary compensation for their participation. All observers had normal or corrected-to-normal visual acuity and were naive regarding the purpose of the experiment. All observers had normal stereo vision (at least 25 sec arc at 40cm distance as measured using a RANDOT Stereotest).

Stimuli

The stimuli were the same as in Experiment 1 with the following exception: two red dots (19.2 cd/m2) were presented 2.33 deg above and below the center of the display respectively (see Figure 3) and were adjusted by the subject to match the apparent depth of the subjective surface. The disparity of the depth probe at the beginning of each trial was a random value between −10 arc min and +10 arc min. The temporal difference between the two monocular images was consistent with a stationary subjective surface occluding the translating dots (PTIOA). The subjective contour was decamouflaged every 3.6 sec until the subject responded.3

Figure 3.

Figure 3

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Schematic illustration of three frames of the moving stimuli used in Experiment 2. The two diamonds represent probe dots (red dots in the actual experiment) used to measure the depth of the subjective occluding surface. As can been seen from left to right, the dots were moving rightward until occluded by the subjective surface. After 1.8 sec the dots reappeared in their original positions.

Design

The independent variables were dot disparity (relative to the screen plane, −9, 0, and +9 arc min) and the TIOA (0, 80, 160, 240, and 320 ms.).

Procedure

The subjects were shown demonstrations of the stimuli in which the translating dots were occluded by a stationary white surface (19.2 cd/m2). Subjects were instructed to adjust the depth of the red dots to match the perceived depth of the subjective surface at the edge by pressing the up and down arrow keys. Pressing the up key decreased the disparity resulting in an increase in depth of the red dots whereas pressing the down key increased disparity resulting in a decrease in depth of the red dots. When the subject was satisfied with the depth match they pressed the space key to advance to the next trial. After they understood the task subjects were presented with 8 practice trials in which the occluding surface was visible in dark gray (2.3 cd/m2). An accurate response during the practice trials was recorded if the disparity difference (in either direction) between the red dots and the surface was equal to or less than 2 arc min. Subjects were required to make 7 accurate responses (out of 8 practice trials) to ensure that subjects understood the task. The practice trials were repeated if subjects failed to meet this criterion. Subjects who failed the practice criterion in three practice blocks were not run in the experiment. All 7 subjects passed the practice test criterion. During the experiment each observer was presented 20 replications of the 15 conditions. For each condition the direction of dot motion (rightward or leftward) was counterbalanced. A total of 300 trials were randomly assigned in 5 blocks. Breaks were taken between blocks. Feedback was not provided during the practice test or the experiment.

Results

The perceived depth for each subject in each condition was analyzed in a 3 (dot disparity) by 5 (TIOA) repeated-measures ANOVA. The main effect of TIOA was not significant (F (4, 24) =1.77, p=0.17). The main effect of dot disparity was significant (F (2, 12) =100.14, p<0.01) and is shown in Figure 4a. These results indicate that the subjective surface was perceived as closer than the occluded dots. There was no significant interaction between TIOA and dot disparity (F (8, 48) =1.21, p=0.31). These results suggest that temporal unmatched information---generated when occlusion occurs---is used for the perception of depth order but not for the perception of quantitative depth.

Figure 4.

Figure 4

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Mean perceived depth of the subjective surface as a function of TIOA for different dot disparity conditions. The results from Experiment 2a for PTIOA are shown in Figure 4a. The results from Experiment 2b for NTIOA are shown in Figure 4b. Error bars are +/− 1 standard error.

Experiment 2b

The conditions examined in Experiment 2a consisted of stimuli with PTIOA information. In this experiment we examined a depth matching task using NTIOA information. The settings and design were the same as in Experiment 2a except that the TIOA was negative (NTIOA) indicating that the dots were occluded by a subjective surface translating in the same direction. Six subjects from Experiment 2a were run in the experiment. The perceived depth for each subject in each condition was analyzed in a 3 (dot disparity) by 5 (NTIOA) repeated-measures ANOVA. The results of Experiment 2b were similar to the results obtained in Experiment 2a. The main effect of NTIOA was not significant, F (4, 20) =0.24, p=0.91. The main effect of dot disparity was significant, F (2, 10)=51.40, p<0.01, as shown in Figure 4b. The interaction of NTIOA and dot disparity was not significant, F(8, 40)=1.20, p=0.33. These results replicate the results obtained in Experiment 2a and suggest that both PTIOA and NTIOA information provide qualitative information for depth order.

Experiment 3a: Perception of depth from matched and unmatched information

The results of Experiments 2a and 2b indicate that IOUM features provided qualitative but not quantitative depth. In contrast, Brooks and Gillam (2006) found that IOUM features were used for the perception of quantitative depth. An important difference between our study and the Brooks and Gillam study concerns the presence of binocular features. In the stimuli used by Brooks and Gillam the display included a series of vertical lines whereas the present stimuli included a single subjective line defined by three dots. It is possible that the presence of additional lines, which provide binocularly matched features, may serve as a metrical reference for quantitative depth from IOUM features. To examine this issue we added binocularly matched features to the stimuli used in Experiment 2a and 2b by including an array of lines (defined by three dots; see Figure 5). If binocularly matched features are used as a metric for quantitative depth for IOUM features then perceived quantitative depth should occur when this information is present.

Figure 5.

Figure 5

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Schematic illustration of stimuli used in Experiment 3. Multiple columns of dots were presented that translated horizontally. Only one column of dots was occluded by the subjective surface at any moment in time. The two diamonds represent probe dots (red dots in the actual experiment) used to measure the depth of the subjective occluding surface. Dots in grey depict dots not visible due to occlusion.

Methods

Apparatus

The apparatus was the same as in Experiment 1.

Subjects

The subjects were 6 undergraduate students from University of California, Riverside, who received monetary compensation for participating in the experiment. All observers had normal or corrected-to-normal visual acuity and were naive regarding the purpose of the experiment. All observers had normal stereo vision (at least 25 sec arc at 40cm distance measured using a RANDOT Stereotest).

Stimuli

The stimuli were the same as in Experiment 2a with the following exception. To provide matched disparity information we included multiple columns of white dots that translated in the scene until occluded by a subjective surface (see Figure 5). The spatial separation of the columns was 1.67 deg. visual angle. The temporal difference between two monocular images was consistent with a stationary subjective surface occluding the translating dots.

Design

The independent variables were dot disparity (relative to the screen plane, −9, 0, and +9 arc min) and TIOA (0, 80, 160, 240, and 320 ms.).

Procedure

The demonstration, practice procedures, and task were the same as that used in Experiment 2a. All subjects passed the practice test. Each observer was presented with 20 replications of the 15 conditions with the direction of motion counterbalanced. A total of 300 trials were randomly assigned into 5 blocks. Breaks were taken between blocks.

Results

The perceived depth for each subject in each condition was analyzed in a 3 (dot disparity) by 5 (TIOA) repeated-measures ANOVA. Significant effects were found for both TIOA (F (4, 20) =5.02, p<0.01) and dot disparity (F (2, 10) =78.93, p<0.01), as shown in Figure 6. The mean perceived depth, for the 0, 4.8, 9.6, 14.4, and 19.2 TIOA conditions were 1.36, 1.72, 2.92, 3.26, and 3.69 min, respectively. Post hoc comparisons (Tukey HSD test) indicated significant differences (p<.05) between the 0 and 14.4, the 0 and 19.2, and between the 4.8 and 19.2 TIOA conditions. According to these results the subjective surface was perceived as closer than the translating dots and the perceived depth increased with an increase in TIOA. There was no significant interaction between TIOA and dot disparity (F (8, 40) =1.75, p=0.12). These results suggest that temporal IOUM information, when combined with binocularly matched information, provide information for both depth order and quantitative depth.

Figure 6.

Figure 6

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Mean perceived depth of the subjective surface as a function of TIOA from Experiment 3a (Figure 6a) and Experiment 3b (Figure 6b). Error bars are +/− 1 standard error.

Experiment 3b

Similar to Experiment 2b a second study was conducted for NTIOA conditions. Three Subjects from Experiment 3a participated in the experiment. The mean performance for each subject in each condition was analyzed in a 3 (dot disparity) by 5 (TIOA) repeated-measures ANOVA. The results of Experiment 3b were similar to the results of Experiment 3a. The main effect of TIOA (F (4, 8) =10.21, p<0.01) and dot disparity (F (2, 4) =10.47, p<0.01) were significant. The interaction between TIOA and dot disparity was not significant, (F (8, 16) =1.65, p=0.19). These results, considered with the results of Experiment 3a, suggest that both positive and negative TIOA information result in a perception of quantitative depth when combined with metrical depth information from binocularly matched features.

Experiment 4: Quantitative Depth Perception and Surface Propagation

The results of Experiments 3a and 3b indicate that---similar to the results of Brooks and Gillam (2006)---subjects perceive quantitative depth from IOUM features when binocularly matched features are present. An important difference between the stimuli used by Brooks and Gillam (2006) and the stimuli used in Experiments 3a and 3b is that in the Brooks and Gillam study the top and bottom horizontal edges of the subjective surface were revealed by the occluded vertical bar. This monocular occlusion information has been shown to be important for the perception of subjective contours (Shipley & Kellman, 1990) and the perception of qualitative depth order (Kaplan, 1969). The availability of this information suggests an interesting process of how quantitative depth of a subjective surface is perceived from IOUM features. To understand this process consider the perception of a subjective surface that is revealed by motion of an occluded vertical bar that extends beyond the vertical dimension of the subjective surface (see Figure 7). When the moving vertical bar reaches the edge of the subjective surface quantitative depth is perceived from IOUM. As the occluded vertical bar continues to translate the upper and lower extents of the bar are still visible and a subjective surface is perceived from monocular occlusion (middle panel Figure 7). However, monocular occlusion only specifies qualitative depth. Thus, in order for the visual system to perceive quantitative depth for this region of the subjective surface the visual system must propagate the quantitative depth from the edge to the central region of the surface where qualitative depth information is available. An important question is whether there are spatial constraints in propagating quantitative depth to regions where only qualitative depth information is locally available. To examine this issue we systematically varied the horizontal extent of the subjective surface. If there are spatial constraints to the propagation process then for large spatial extents the ability of the visual system to propagate quantitative depth from IOUM features will decrease and the perception of quantitative depth will degrade.

Figure 7.

Figure 7

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Schematic illustration of three frames of the moving stimuli used in Experiment 4. The diamond below the cross depicts the probe (a red dot in the actual experiment) used to measure the depth of the subjective occluding surface. The grey line in the middle panel depicts the line segment not visible due to occlusion.

Methods

Subjects

The subjects were 7 undergraduate students from University of California, Riverside, who received monetary compensation for participating in the experiment. All observers had normal or corrected-to-normal visual acuity and were naive regarding the purpose of the experiment. All observers had normal stereo vision (at least 25 sec arc at 40cm distance measured using a RANDOT Stereotest).

Apparatus

The apparatus was the same as in Experiment 1.

Stimuli

As shown in Figure 7, the stimuli were similar to those used in Brooks and Gillam’s study (2006), except that a single white vertical bar (2 arc min by 48 arc min) was presented that translated horizontally on a black background. A white fixation cross was presented in the center of the screen. An invisible black rectangle was positioned 36 arc min above the white fixation cross. The rectangle (24 min in height) was revealed when the translating bar was partially occluded. The vertical white bar translated in the zero disparity plane leftwards on half the trials and rightwards on the remaining trials. The travel path of the white vertical bar was defined as 3 times the width of the black rectangle with the path midpoint centered on the rectangle. When the bar reached the left edge of the subjective surface the occluded region disappeared with a TIOA value of 50, 100 or 200 msec. When the bar reached the right edge of the subjective surface the occluded region reappeared with the same TIOA value. When the bar reached the end of its motion path it reappeared at the opposite side of the display. The motion path was repeated until subjects made their judgment. A red probe dot (6 arc min in diameter) was placed 36 min below the fixation cross. The depth of the probe dot was adjusted by pressing the UP and DOWN arrow keys.

Design

The independent variables were the TIOA (50, 100, and 200 ms), the translation speed of the bar (0.5, 1.0, 1.5, and 2.0 deg/sec), and the width of the occluding surface (0.6, 1.2, 1.8, and 2.4 deg in visual angle). In addition, combinations of speed and TIOA resulted in three constant values of quasi-disparity (3 arc min, 6 arc min, and 12 arc min). The 3 arc min quasi-disparity condition occurred for the 50 msec with 1.0deg/sec and 100 msec with 0.5 deg/sec combinations. The 6 arc min quasi-disparity condition occurred for the 50 msec with 2 deg/sec, 100 msec with 1 deg/sec, and 200 msec with 0.5 deg/sec combinations. The 12 arc min quasi-disparity condition occurred for the 100 msec with 2.0 deg/sec and the 200 msec with 1.0 deg/sec combinations.

Procedure

The demonstration, practice test and experimental task were similar to that used in Experiment 2a. All 7 subjects passed the practice test prior to the experimental session. Subjects were instructed to judge the depth of the rectangular region aligned with the probe point. During the experiment each observer responded to 10 replications of the 48 display conditions. The translation direction was counterbalanced across trials. The 480 trials were randomly assigned in 6 blocks of trials. Rest breaks were taken between blocks.

Results

The perceived depth for each subject in each condition was analyzed in a 3 (TIOA) by 4 (dot translating speed) by 4 (surface width) repeated-measures ANOVA. The main effects of TIOA (F (2, 12) =31.7, p<0.01), the bar translating speed (F (3, 18) =37.6, p<0.01), and surface width (F (3, 18) =24.6, p<0.01) were significant (p<.05). These results (see Figure 8) indicate an increase in perceived depth with an increase in TIOA and an increase in speed. The results also indicate a decrease in perceived depth with an increase in the width of the rectangular region. There were also significant interactions between TIOA and speed (F (6, 36) =19.4, p<0.01), between TIOA and surface width (F (6, 36) =4.7, p<0.01), and among TIOA, speed, and surface width (F (18, 108) =5.5, p<0.01). The interaction between TIOA and speed was not significant (F (9, 54) =1.2, p> 0.05). These results are consistent with the results of Brooks and Gillam (2006) and indicate that quantitative depth can be perceived from TIOA information. In addition, the results indicate that the perception of quantitative depth from TIOA information can propagate to regions with qualitative depth information from monocular occlusion.

Figure 8.

Figure 8

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Mean perceived depth of the subjective surface, from Experiment 4, as a function of TIOA, speed, and surface width. Error bars are +/− 1 standard error.

An important issue is whether the effects of the width of the subjective surface on perceived depth varied when quasi-disparity was constant. To address this issue we conducted three separate one-way ANOVAs (for the 3, 6, and 12 arc min quasi-disparity conditions) based on different combinations of speed and TIOA (see Figure 9). The main effect for the 3 min arc quasi-disparity condition was significant, F(3,18) = 18.8, p<.05 (see Figure 9a). Post hoc comparisons (Tukey HSD test) indicated significant differences (p<.05) between the 0.6 and 1.8, the 0.6 and 2.4, the 1.2 and 1.8, and the 1.2 and 2.4 deg width conditions. The main effect for the 6 min arc quasi-disparity condition was significant, F(3,18) = 6.6, p<.05 (see Figure 9b). Post hoc comparisons indicated significant differences between the 0.6 and 2.4, and between the 1.2 and 2.4 deg width conditions. The main effect for the 12 min arc quasi-disparity condition was significant, F(3,18) = 25.0, p<.05 (see Figure 9c). Post hoc comparisons indicated significant differences between all pairwise comparisons except the 1.2 and 1.8, and between the 1.8 and 2.4 deg width conditions. Overall these results suggest that perceived depth declined with an increase in the width of the subjective surface. One exception to this pattern occurred for the 0.6 deg width surface under the 12 min arc quasi-disparity condition (see Figure 9c). One possible explanation for this result concerns the velocity of the displays for different levels of quasi-disparity the ability of observers to see a subjective surface. Specifically, the velocity conditions for the 12 min arc quasi-disparity condition were higher (average velocity of 1.5 deg/sec) than the 6 min arc (average velocity of 1.16 deg/sec) and 3 min arc (average velocity of 0.75 deg/sec) quasi-disparity conditions. It is possible that subjects had difficulty perceiving a subjective surface when the width of the surface was very narrow and the velocity was high.

Figure 9.

Figure 9

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Mean perceived depth of the subjective surface as a function of the occluding surface width from Experiment 4. Figures 9a, 9b, and 9c are the results for constant quasi-disparity values of 3 arc min, 6 arc min, and 12 arc min respectively. Error bars are +/− 1 standard error.

General Discussion

Previous research has shown that IOUM features are used to perceive quantitative depth (Brooks and Gillam, 2006). In the present study we examined the importance of several visual constraints for the effective use of this information. The first experiment examined temporal constraints for the perception of a subjective surface from IOUM features. The results indicated that subjects perceived a subjective surface across a wide range of interocular delay conditions. Previous research has also examined the temporal constraints of processing disparity information. For example, Ogle (1963) found that interocular delays of up to 100 msec resulted in a perception of depth from disparity. Wist and Gogel (1966) found that an interocular delay of up to 32 msec had little effect on the perception of depth from binocularly matched features. Our results suggest that the visual system can integrate IOUM information from TIOA for temporal offsets of up to 320 msec. The increased range of temporal integration when IOUM information is present suggests that a greater range of temporal integration can occur when both matched and unmatched information, present under real world viewing conditions, is available.

In addition, the results of Experiment 1 indicate that both PTIOA and NTIOA generate a perception of a subjective surface under real-world constraints. However, as presented in Figure 2, there was an advantage of PTIOA over NTIOA for most conditions. One explanation for this asymmetric result is that although NTIOA conditions are valid under real world viewing conditions it may represent a real world situation that observers experience with low frequency and as a result is difficult to perceive. A second possibility is that the motion of the decamouflaged occluder requires spatial-temporal processing that can interfere with the temporal integration of IOUM information. As a result the subjective surface is difficult to perceive when the dots and subjective surface are translating in the same direction. An important issue for future research will be to examine these possibilities in greater detail.

It is possible that subjects may have used the sign of TIOA---which indicates the disappearance order of the two monocular images---to judge the location (left or right) of the occluding surface. However, during debriefing no subjects in Experiment 1 reported that they noticed any temporal differences for either PTIOA or NTIOA conditions. Instead subjects reported perceiving a black surface occluding the white translating dots.

The results of Experiments 2a and 2b indicate that TIOA information in isolation (i.e., without the presence of binocular features) can result in a perception of qualitative depth. In Experiments 3a and 3b binocular features were added to the stimuli. Under these conditions quantitative depth was perceived. The results of these experiments, considered together, suggest that an important constraint in the use of TIOA information for quantitative depth is the presence of binocular matched features which serve as a metric for quantitative depth.

The results of Experiment 4 confirm the finding by Brooks and Gillam (2006) that quantitative depth from TIOA is perceived from a partially occluded moving object. In addition, the results of Experiment 4 indicate that the perceived depth of a subjective surface decreased with an increase in its horizontal extent. This decrease occurred under conditions in which quasi-disparity remained constant. The decrease in perceived depth was not due to a lack of binocular references (i.e. the non-occluded parts of the line above and below the camouflaged region). Thus, these results indicate that there are spatial limitations in propagating quantitative depth from TIOA information. In Experiment 4 subjects matched the perceived depth of the center of the subjective region when the horizontal extent of the region was varied. An important issue for future research will be to determine whether variations in the horizontal extent of the subjective surface will also alter the perceived depth of the edges of the surface.

The results of the present study suggest that the presence of binocularly matched features are used a reference for quantitative depth from quasi-disparity. An important issue is whether the depth probe used in the present study might have also been used as a reference because the probe contained binocularly matched information that varied when subjects responded. If the depth probe was used as a reference then quantitative depth should have occurred in Experiments 2 – 4 (the experiments in which the probe was used). However, the results of Experiment 2, when a depth probe was used, indicate that quantitative depth was not perceived. An important difference between the conditions examined in Experiment 2 as compared to Experiments 3 and 4 is that in Experiments 3 and 4 the display contained additional binocularly matched features that were constant during the trial. This observation suggests that it is not binocularly matched features per se that are important but that the binocularly matched features that are constant.

Anderson and Sinha (1997) suggested that an object translating behind an aperture is decomposed into translating segments and unmatched features from occlusion which are used to generate subjective contours. A similar process might be used by the visual system when viewing monocular images of the displays in Experiment 4. An important characteristic of the displays in Experiment 4 is that the two ends of the vertical bar were visible when the central part of the bar was occluded. This may have allowed for modal completion of the bar from monocular occlusion. A weak subjective surface may be perceived from the monocular images when only a single vertical bar is present. This weak perception could be enhanced by simply adding additional lines. However, only qualitative depth can be perceived because the only information available is monocular occlusion. This suggests that the subjective surface in this experiment may be generated prior to binocular processing. The upper and lower regions of the vertical bar contain matched disparity information. Matched disparity information is still present when the bar is partially occluded by the subjective surface. This suggests that the presence of matched disparity information may be used by the visual system as a reference for quantitative depth and used to propagate quantitative depth from the unmatched disparity information from TIOA.

In summary, the results of the present study indicate that the visual system can make use of IOUM features present when occlusion occurs to segregate a homogeneous occluding surface from the background. The visual system can integrate information from two monocular views over a long temporal gap (up to 320 ms in the present study) to produce a perception of a subjective surface based on real-world occlusion constraints. The ambiguity of perceived quantitative depth from TIOA information is eliminated by the presence of binocular matched information. These results suggest that the visual system integrates the depth order information from TIOA features and utilizes metrical information from binocularly matched features for the perception of quantitative depth that is propagated over time and space.

Acknowledgments

This research was supported by NIH EY18334, NIH AG031941 and the Ministry of Science and Technology of China (2005CB522800CB522004CB318101). We thank Kevin Brooks and an anonymous reviewer for their helpful comments and suggestions. Rui Ni is now at the Department of Psychology, Wichita State University, Wichita, KS 67260.

Footnotes

1

Although these studies conclude that IOUM features are used for depth perception Gillam (1995) has questioned whether some of these studies have excluded the possibility that matched features might be used.

2

Constant quasi-disparity requires an assumption of stationarity of the subjective edge or knowledge of the velocity of the occluder. Thus the NTIOA displays, although compatible with real-world constraints, are conditions in which quasi-disparity varied.

3

A control experiment was conducted to determine whether the perception of quantitative depth was dependent on the frequency with which the edge was decamouflaged. Four subjects participated in the study in which TIOA (0,80, 160, 240, and 320 msec) and rate of presentation of the decamouflaged edge (2.9, 2.2, 1.5, and 0.80 sec for each cycle) were varied. The main effects of TIOA (F(3,27) = 1.56), presentation rate (F(3,9) = 0.71), and the interaction of TIOA and presentation rate (F(12,36) = 1.09) were not significant, p>.05, indicating that the perception of quantitative depth was not dependent on the presentation rate.

Portions of this research were presented at the 2006 and 2008 meeting of the Vision Sciences Society, Florida.

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Contributor Information

Rui Ni, University of California, Riverside.

Lin Chen, The Key Lab of Cognitive Sciences, Chinese Academy of Sciences, Beijing.

George J. Andersen, University of California, Riverside

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