Skip to main content
NCBI home page
NIHPA Author Manuscripts logoLink to NIHPA Author Manuscripts
. Author manuscript; available in PMC: 2014 Apr 6.
Published in final edited form as: Percept Psychophys. 2008 May;70(4):707–713. doi: 10.3758/pp.70.4.707

Perceived relative distance on the ground affected by the selection of depth information

Jun Wu 1, Zijiang J He 2, Teng Leng Ooi 3
PMCID: PMC3977006  NIHMSID: NIHMS541313  PMID: 18556932

Abstract

Our visual space does not appear to change when we scan or shift attention between locations. This appearance of stability implies that the depth information selection process is not crucial for constructing visual space. But we present evidence to the contrary. We focused on space perception in the intermediate distance, which depends on the integration of depth information on the ground. We propose a selection hypothesis that states the integration process is influenced by where the depth information is selected. Specifically, the integration process inaccurately represents the ground when one samples depth information from only the far-ground surface, instead of sequentially from the near to far ground. To test this, observers matched the depth/length of a sagittal bar (test) to the width of a laterally oriented bar (reference) in three conditions in the full-cue environment that compelled the visual system to sample from different parts of the ground. These conditions had the lateral reference bar placed (i) adjacent to the test bar, (ii) at the far-ground, and (iii) at the near-ground. We found that the sagittal bar was perceived as shorter in conditions (i) and (ii), than (iii). This finding supports the selection hypothesis as only condition (iii) led to more accurate ground surface integration/representation and less error in relative distance/depth perception. Also, we found that performances in all three conditions were similar in the dark, which has no depth information on the ground, indicating that the results cannot be attributed to asymmetric visual scanning but rather to differential information selection.

The ground theory of space perception claims a prominent role for the ground surface in localizing an object in the intermediate distance range (Gibson, 1950, 1979; Sedgwick, 1986). This is presumably due to the ecological significance of the ground surface (Gibson, 1950, 1979). Since its conception, the ground theory has found empirical supports from various laboratories. For example, it has been shown that the perceived distance of an object on the ground can be affected by the structure of the ground surface (Feria, Braunstein, & Andersen, 2003; He, Wu, Ooi, Yarbrough, & Wu, 2004; Sinai, Ooi, & He, 1998, Wu-B, Ooi, & He, 2004; He, & Ooi, in press). A homogeneous ground surface, in conjunction with the object's angular declination, allows the object to be reliably localized (Ooi, Wu, & He, 2001, 2006; Philbeck & Loomis, 1997; Wu-J, He, & Ooi, 2005). When the object is above the ground, the visual system can use the object's relative distance information with respect to the ground surface to localize the object (Madison et al, 2001; Meng & Sedgwick, 2001; Ni, Braunstein, & Andersen, 2004; Ooi & He, 2006; Wu-J, He, & Ooi, 2004). Furthermore, a bias for using the ground surface is revealed in studies that measured the visual system's performances under different types of large surface conditions, e.g., ground-like versus ceiling-like surfaces (Bian, Braunstein, & Andersen, 2005; McCarley & He, 2000, 2001).

How does the visual system represent the ground surface for space perception? One possible way is based on the Sequential Surface Integration Process (SSIP) (He et al, 2004; Ooi & He, in press; Wu-B et al, 2004). The SSIP hypothesis proposes that the visual system depends on both the external depth cues on the ground and the visual system's intrinsic bias to form the represented surface, and that it constructs the ground surface representation from the near to far distance. In a full cue visual environment, the SSIP begins its operation by utilizing the reliable depth cues on the near ground surface (e.g., binocular disparity and motion parallax information) to form an accurate representation of the near ground surface. The near ground representation is then used as a template by the SSIP to integrate with the farther patches of ground surface, whose predominant depth information is the texture gradient. Thus, as the process extends from near to far, the SSIP is able to construct an accurate global ground surface representation. In a viewing condition where the ground surface is not visible (e.g., in complete darkness), the intrinsic bias of the visual system is treated as the ground surface. Our previous studies have found that the intrinsic bias takes the form of an implicit surface that curves upward from the ground (Ooi et al, 2001, 2006, Wu-J, He, & Ooi, 2006). The local slant of the surface increases as the distance increases; but for our current purposes, we will assume that the shape of the intrinsic bias is approximately a plane surface with a constant slant. In a reduced cue environment with limited reliable near depth cues, the visual system increases its reliance on the intrinsic bias to represent the ground surface, leading to an inaccurate ground surface representation (Sinai et al, 1998; Wu-B et al, 2004, in press).

In the present paper, to further understand how the visual system constructs the ground surface representation, we focus on the idea of a selection process influencing the SSIP. This selection hypothesis argues that the SSIP, like many other perceptual processes, is affected by a selection process that samples the depth information on the ground surface. Confirming this hypothesis would mean that the ground surface representation, and thus, our space perception, is affected by where the depth information on the ground is sampled. At first blush, this hypothesis appears somewhat counterintuitive because it is inconsistent with the general view that our perceptual space is formed by an automatic process that does not depend on an attention selection process. As such, only few studies have addressed the concern whether perceived distance is affected by attention (Gogel & Tietz, 1977).

In the current study, we tested a prediction of the selection hypothesis that the perceived relative distance/depth of a bar-target on the ground surface depends on how the visual system selects the available depth information on the ground. We capitalized on the foreshortening phenomenon, in which the sagittal distance in the depth dimension (relative distance/depth) is underestimated compared to the lateral distance (width).

Our first experiment tested whether the selection process can affect the perceived foreshortening of a target on the ground in the full cue environment (figure 1). In the L-shaped condition (figure 1A), an observer is asked to perceptually match the sagittal length (L) of the L-shaped target to its lateral width (W). It is expected that the observer will require the length of the L-shaped target to be longer to match its width, i.e., the aspect ratio (W/L) of the matched L-shaped target will be smaller than 1 (Loomis & Philbeck, 1999; Loomis, Philbeck, & Zahorik, 2002). In addition, our previous studies have found that the foreshortening of the L-shaped target is affected by the extent of the visible ground surface supporting the target (Ooi et al, 2006; Wu-B et al, 2004). For instance, when the visual field of view is limited to a small ground surface area (<20 deg) surrounding a distant L-shaped target, the foreshortening is larger than when the visual field of view is unrestricted (Wu-B et al, 2004). This is because by sampling only the limited visual information of the distant target and its vicinity, which excludes the near ground surface information, denies the SSIP from forming an accurate template of the near ground representation for integration with the distant ground surface. Thus, the representation of the distant ground surface is heavily affected by the intrinsic bias of the visual system. In turn, the global representation of the ground surface has a slant error and the foreshortening is increased.

Figure 1.

Figure 1

Open in a new tab

Illustration of the display conditions (top view). In (A-C), the observers matched the sagittal length of the test target to the lateral width of the reference target. In (D), they matched the lateral widths of both the test and reference targets.

From the foregoing, one can predict that less foreshortening will be found in the stimulus display in the near-reference condition (figure 1B), i.e., a larger matched ratio between the reference target and the test target (W/L) will be found compared to that in the L-shaped condition (figure 1A). Here, the observer has to match the sagittal length/depth of the test target to the lateral width of a reference target that is located on the near ground surface (this display modifies the L-shaped target by spatially separating its limbs). The foreshortening effect is predicted to be less because the observer can now scan the ground surface between the near-reference target and the test target to perform the matching task. As a result, the SSIP is able to utilize the reliable near depth cues on the near ground surface to form a more accurate ground surface representation.

The stimulus display in the far-reference condition (figure 1C) reverses the stimulus design of the near-reference condition (figure 1B) by placing the reference target beyond the test target on the far ground surface. As such, although the observer can scan a larger area of ground surface to view the test target and the far-reference target during the matching task, he/she concentrates mainly on the ground surface area between the test and reference targets. Less attention is paid to the near ground surface; thus, preventing the reliable near depth cues from being sufficiently sampled to form an accurate global ground surface representation. Consequently, the selection hypothesis predicts that a smaller matched ratio (W/L) will be found in the far-reference condition (figure 1C) than in the near-reference condition (figure 1B).

Experiment 1 assumes that the specific act of scanning and sampling of the depth information on a particular area of the ground surface affects the accuracy of the ground surface representation, and hence, the foreshortening effect. The validity of this assumption requires that the impact of the scanning process on depth perception is the same whether the reference target is at the near or far ground surface. To evaluate this same-scanning-process hypothesis, our second experiment tested the same three display conditions in the dark where the ground surface is not visible. The ground representation in the dark is contributed solely by the intrinsic bias, which can be approximated as a slant surface with its far-end above the floor (Ooi et al, 2001, 2006). The foreshortening effect in the dark is dependent on the intrinsic bias and not the ground surface information (which is not visible). Thus, this predicts that the foreshortening in all three stimulus-conditions will be the same – unless – a scanning process that varies with scanning distance also influences the foreshortening effect.

The above analysis and predictions not withstanding, it could still be argued that our favored empirical outcomes have an alternative explanation. It could be that the (lateral) reference target in the near-reference condition is simply estimated as longer than those in the far-reference and L-shaped conditions. Thus, for both experiments 1 and 2, to investigate the possibility of an increasing overestimation of the lateral width of the reference target with viewing distance, we tested our observers in a control condition where both the test and reference targets had the same (lateral) orientation (figure 1D).

Experiment 1: Full cue environment

Method

Participants

Eleven naïve observers with informed consent and normal or corrected-to-normal visual acuity (at least 20/20) participated in the experiment. Of these, seven observers were tested with the monocular viewing protocol. The subsequent, binocular viewing protocol was conducted with three of the same observers who participated in the monocular viewing protocol, and four new observers who did not.

Displays and test site

The experiment was conducted on a large homogeneous, horizontal grass field, from which the viewing distance to the nearest tree or building was at least 20m from the observer. A discreet, short wooden stick marked the observer's starting position. The lateral reference target in each of the 4 conditions was a white PVC pipe (1” diameter) with a fixed length of either 44cm for the test trials or 30cm for the catch trials. The variable length test target was made up of two white PVC pipes, in which a 1” diameter pipe was inserted into a 1.2” diameter pipe. This allowed the pipes to slide over one another to obtain the desired length during a trial. The test target in all conditions, including the sagittal limb of the L-shaped target in the L-shaped condition, was set at one of three test distances (5m, 6m, or 7m) from the observer. Whereas the distance of the lateral reference target in the L-shaped condition changed with the test distance, it remained fixed at a selected viewing distance in the remaining 3 conditions (figure 1).

Tasks and Procedures

The observers performed the matching task with both binocular and monocular (dominant eye) viewing protocols. Before a trial, the observer stood with his/her back facing the test scene to allow the experimenter to set up the stimulus. Once set, the experimenter walked several meters away from the stimulus and informed the observer to turn around to compare the sagittal length of the test target to the width of the reference target. To match the length and width, the observer instructed the experimenter to adjust the length of the test target in an amount proportional to its perceived length. He/she then turned his/her back to the test scene to allow the experimenter to make the adjustment, after which, the experimenter again instructed the observer to turn around to make another judgment. This procedure was repeated until the observer judged the length and width as equal. No feedback was given to the observer regarding the performance.

We ran 2 blocks of trials in the monocular viewing protocol. The first block tested the L-shaped condition (figure 1A) to investigate if the observers could match the length and width of the target on the basis of retinal image size. With this retinal image size response criterion, the observers were told to imagine taking a photograph of the L-shaped target, and based on the perceived size on the photograph to match the length and width. The order of testing the target distance was randomized.

The second block tested all 4 conditions in figure 1 and was run after a 15 minutes break following the first test block. The observers now performed the task using the physical size response criterion (Loomis & Philbeck 1999; Loomis et al, 2002; Ooi et al, 2006; Sedgwick, 1986; Wu et al, 2004). The observer was told to imagine that she/he had walked up to the test target and looked down directly at it, in order to match the physical length and width. The test order of the target distance and condition was randomized.

The 4 conditions in figure 1 were also tested with the binocular viewing protocol using similar procedures as above and with the physical size response criterion. However, only one target distance (6m) was tested.

The observers practiced the matching task according to the specified response criterion for 5-10 minutes before each test block. Each block consisted of four-fifth test-trials (reference target = 44cm) and one-fifth catch trials (reference target = 30cm). Only the data from the test-trials were analyzed. Each target distance was tested twice.

Results

Monocular viewing

The filled triangles, squares and circles in figure 2A plot the average matched ratios (W/L) of the three stimulus conditions in figures 1A, 1B and 1C, respectively, using the physical size response criterion. Overall, the matched ratios are smaller than 1, indicating that a target's sagittal length is underestimated relative to its lateral width. The matched ratios decrease with the test target distance [F(2,12)=77.458, p<0.00001; 2-way ANOVA with repeated measures], indicating that the relative underestimation of the sagittal length increases with distance. Comparison among the three conditions reveal that the matched ratios are larger in the near-reference condition than in the far-reference condition [Main effect of display condition: F(1,6)=36.016; p<0.001; Interaction effect (distance × display): F(2,12)=0.214, p=0.810; 2-way ANOVA with repeated measures] and in the L-shaped condition [Main effect of display condition: F(1,6)=72.11, p<0.0005; Interaction effect (distance × display): F(2,12)=1.539, p=0.254, 2-way ANOVA with repeated measures].

Figure 2.

Figure 2

Open in a new tab

Average results of Experiment 1 performed in the full cue environment. The filled and open symbols depict the average data with monocular and binocular viewing, respectively. (A) The average matched ratio (width of lateral bar/length of sagittal bar) is plotted as a function of the distance of the sagittal bar, for the conditions in figure 1A-1C. The dash line predicts the matched ratios that would be obtained had the observer's judgment been based solely on the retinal image size. (B) The average matched width of the lateral test bar with respect to the lateral reference bar (44cm) at a viewing distance of 2.5 m. (C) The corrected matched ratios of the data in (A). See text for details.

Figure 2B plots the data of the control condition (figure 1D), which tested the possibility that the lateral width of a distant target is overestimated relative to the width of a near target. Consistent with this, the average data show a tendency for the matched width to decrease with distance. However, 1-way ANOVA with repeated measures fails to reveal a significant effect of distance [F(3,18)=1.826; p=0.179]. Nevertheless, to account for the residual contribution of an overestimation of the reference target to the matched ratios (the second factor) in the far-reference and L-shaped conditions (figure 2A), we first calculated the ratio of the matched width of the test target at 9.5m to the width of the reference target (44 cm) (figure 2B). We then divided each of the matched ratio from the far-reference condition by the calculated ratio, and plotted the results as the filled circles in figure 2C. We also calculated the ratios at the 5m, 6m, and 7m target distances in figure 2B. We divided the matched ratios in the L-shaped condition by the calculated ratios at each corresponding test target distance (figure 2A). The corrected matched ratios are plotted as filled triangles in figure 2C. Clearly, the data in figure 2C reveal that after correcting for the overestimation of the reference target, the matched ratios in the near-reference condition remain larger (i.e., smaller foreshortening) than in the far-reference [F(1,6)=16.950, p<0.01; F(2,12)=0.122, p=0.886] and L-shaped conditions [F(1,6)=33.860, p<0.0025; F(2,12)=0.576, p=0.577]. These findings support the prediction of the selection hypothesis. Furthermore, notice that the matched ratios of the far-reference and L-shaped conditions are similar, even though the former condition requires the observer to scan a larger ground area. This suggests that at the far distance, the accuracy of the ground surface representation is not critically dependent on the size of the ground area sampled.

The gray triangles in figure 2A plot the average matched ratios from the L-shaped condition based on the retinal image size response criterion. The matched ratios are significantly smaller than those obtained with the physical size criterion (filled triangles) [F(1,6)=20.871, p<0.005; F(2,12)=1.087, p=0.368]. This finding suggests that the matched ratios can be influenced by the response criterion used during the experiment (Gilinsky, 1955). The dash line in figure 2a indicates where the data would fall had the observers' performances been strictly based on the retinal image size response criterion. Clearly, the open triangles are above the dash line, indicating that even with explicit instructions, observers can only partially “ignore” the depth information on the ground surface (Burbeck, 1987; Gilinsky, 1955; McKee & Welch, 1992).

Binocular viewing

The average results with binocular viewing (open symbols) using the physical size response criterion have a similar trend as with monocular viewing (filled symbols). As shown in figure 2A, the matched ratios are larger in the near-reference condition than in both the far-reference [t(6)=8.92, p<0.001] and L-shaped conditions [t(6)=10.34, p<0.001]. This trend remains the same after correcting for the overestimation of the reference target [figure 2C; near vs. far: t(6)=6.78, p<0.001; near vs. L-shaped: t(6)=6.81, p<0.001].

Experiment 2: Dark Environment

Method

Participants

Eight naïve observers with informed consent and normal or corrected-to-normal visual acuity (at least 20/20) participated in the experiment. Three of the observers also participated in Experiment 1.

Displays and test site

The targets were phosphorescent stripes with almost similar angular widths (0.25” at 2.5m and 1” at 9.5m). The lateral width of the reference target was either 30cm (test trials) or 40cm (catch trials). The 4 conditions from Experiment 1 were tested in a dark room. While the targets were always placed on the floor, the observers were told that the targets could be either on, or above, the floor.

Procedures

The observers performed the matching task binocularly. Before the experiment, they spent 15-20 minutes practicing the matching task in the lighted hallway outside the test room. The practice session was necessary particularly for observers who had never performed the matching task using the physical size response criterion in the dark. This is because we have noticed in the past that without any training in using the physical size response criterion to perform the matching task, some observers can have a strong bias for using the retinal image size response criterion in the dark. Practicing in the light environment allows the observer to easily notice the foreshortening phenomenon and become familiar with the physical size response criterion, which leads to a stable performance.

After the practice, the observer was led to the test room without vision, to sit on a chair facing a wall near the starting position. A black curtain divided this waiting area (dark) and the test area (temporarily lighted). Once the phosphorescent targets were set up, the experimenter switched off the light in the test area and instructed the observer to stand, turn around, and step onto two phosphorescent elements on the floor (marking the starting position) facing the test area. The experimenter drew the black curtain open for the observer to begin the trial. The observer's task was to instruct the experimenter to adjust the sagittal length of the target to match the lateral width. In between instructions, the observer closed his/her eyes and the experimenter drew the curtain close to make the adjustments. This was repeated until the observer finished judging the length and width to be equal. The observer received no feedback regarding the performance.

Before the proper experiment, the observer was given several practice trials in the dark. All 4-display conditions were tested in a single block, in which the trial order was randomized. Each trial was repeated twice. As in Experiment 1, four-fifth of the trials were test trials (reference target = 30cm) and one-fifth were catch trials (reference target = 40cm).

Results

We measured the matched ratios for all four conditions in figure 1 in the dark, using the physical size response criterion. Figure 3A plots the average matched ratios for the three test conditions in figure 1. Overall, the matched ratios are smaller than those in the full cue conditions in Experiment 1 (figure 2A), indicating a stronger foreshortening when the ground surface is not visible in the dark, consistent with our previous study (Ooi et al, 2006). But similar to the full cue condition, the matched ratios decrease with target distance [F(2,14)=34.135, p<0.00005; 2-way repeated ANOVA with repeated measured].

Figure 3.

Figure 3

Open in a new tab

Average results of Experiment 2 performed in the dark environment (binocular viewing only). (A) The average matched ratio (width of lateral bar/length of sagittal bar) is plotted as a function of the distance of the sagittal bar, for the conditions in figure 1A-1C. (B) The average matched width of the lateral test bar with respect to the lateral reference bar (44cm) at a viewing distance of 2.5 m. (C) The corrected matched ratios of the data in (A). See text for details.

Figure 3A also reveals that the matched ratios in the near-reference condition (squares) are lower than in the far-reference condition (circles) [Main effect of display condition: F(1,7)=18.289, p<0.005; Interaction effect (Distance × display): F(2, 14)=0.304, p=0.743], and similar to the L-shaped condition [F(1,7)=3.531, p=0.1023; F(2,14)=0.639, p=0.543]. This differs from that in Experiment 1, where the matched ratios are significantly larger in the near-reference condition (figure 2A).

As in Experiment 1, we addressed the possibility that misperceiving the lateral width of the reference target affected the matched ratios in the L-shaped and far-reference conditions. The data from the control condition (figure 3B) show that observers progressively underestimated the lateral width with distance [F(3,21)=3.169, p<0.05; 1-way ANOVA with repeated measures]. This trend is opposite to that in the full cue environment (figure 2B). Following the same procedure as in Experiment 1, we calculated the correction ratio (reference width/target length) from the data in figure 3B and used them to correct the matched ratios in figure 3A.

With correction, the matched ratios in all three conditions become similar (figure 3C) [Main effect of display condition: F(2,14)=0.140, p=0.870; Interaction effect (Distance × display): F(4,28)=0.751, p=0.565]. This finding supports the same-scanning process hypothesis, which predicts that the judged relative depth of a target is not affected by the idiosyncrasies of scanning itself while performing the matching task. And given that the ground surface is not visible in the dark, the results in figure 3 reinforce the conclusion of Experiment 1, which supports the selection hypothesis.

General Discussion

The selection hypothesis proposes that the Sequential Surface Integration Process (SSIP), which represents the ground surface, is influenced by where depth information on the ground surface is sampled. To test the selection hypothesis, our study capitalized on the fact that the SSIP uses the depth information on the near ground to form an accurate ground surface representation (He et al, 2004; Wu-B et al, 2004). Supporting the hypothesis, we found that judged relative distance/depth on the ground is more accurate (less foreshortening) when the observer samples the large ground area that includes the near ground surface, than when he/she samples the ground area that encompasses only the far ground surface.

The selection hypothesis provides an explanation for a puzzle in space perception. A number of studies have revealed that human observers can accurately judge egocentric distance on the ground but not exocentric distance, which is underestimated (Loomis, DaSilva, Fujita, & Fukusima, 1992). A possible reason for the underestimation of exocentric distance, according to the selection hypothesis, is that the nature of the exocentric distance judgment task (e.g., the L-shaped task) encourages the visual system to attend locally to the ground surface information in the vicinity of the target rather than to the global ground surface. On the other hand, the egocentric distance task (e.g., the blindfolded walking task) encourages the observer to scan the ground from near his/her feet up to the target. Being able to sample the near ground information leads to an accurate ground surface representation and egocentric distance perception.

The notion of a selection process also adds a new dimension to our understanding of visual perception and cognition. It is often assumed that a process with unlimited capacity constructs our perceptual space. As such, information selection controlled by focal attention is not critical for the construction of the perceptual space but only affects the selection of objects and the assessment of distances within the stable perceptual space. Indeed, our every day experience of a stable visual space appears to reinforce this assumption. After all, when we look around, or shift attention from one place to another, we seldom notice changes in object distance or visual space. Yet, the selection hypothesis predicts that our space perception changes when we look around. In particular, when one ignores the near ground surface, space perception becomes less veridical. Our current study, which relies on psychophysical measurements in the natural environment (Experiment 1) shows that perceived relative distance/depth depends on which part of the ground surface information is sampled. Therefore, our study raises an interesting question for future research — why do we not perceive objects “morph” as we look around?

Acknowledgments

This study was supported by a grant from the NIH (R01 EY014821) to Z.J.H. and T.L.O.

Contributor Information

Jun Wu, University of Louisville, Louisville, Kentucky.

Zijiang J He, University of Louisville, Louisville, Kentucky.

Teng Leng Ooi, Pennsylvania College of Optometry, Elkins Park, Pennsylvania.

References

  1. Bian Z, Braunstein ML, Andersen GJ. The ground dominance effect in the perception of 3-D layout. Perception & Psychophysics. 2005;67:802–815. doi: 10.3758/bf03193534. [DOI] [PubMed] [Google Scholar]
  2. Burbeck CA. Locus of spatial-frequency discrimination. J Opt Soc American A. 1987;4:1807–1813. doi: 10.1364/josaa.4.001807. [DOI] [PubMed] [Google Scholar]
  3. Feria CS, Braunstein ML, Andersen GJ. Judging distance across texture discontinuities. Perception. 2003;32:1423–1440. doi: 10.1068/p5019. [DOI] [PubMed] [Google Scholar]
  4. Gibson JJ. The Perception of the Visual World. Boston, Mass: Houghton Mifflin; 1950. [Google Scholar]
  5. Gibson JJ. The Ecological Approach to Visual Perception. Hillsdale, NJ: Erlbaum; 1979. [Google Scholar]
  6. Gilinsky AS. The effect of attitude upon the perception of size. Am J Psychol. 1955;68:173–192. [PubMed] [Google Scholar]
  7. Gogel WC, Tietz JD. Eye fixation and attention as modifiers of perceived distance. Perceptual and Motor Skills. 1977;45:343–362. doi: 10.2466/pms.1977.45.2.343. [DOI] [PubMed] [Google Scholar]
  8. He ZJ, Wu B, Ooi TL, Yarbrough G, Wu J. Judging egocentric distance on the ground: occlusion and surface integration. Perception. 2004;33:789–806. doi: 10.1068/p5256a. [DOI] [PubMed] [Google Scholar]
  9. Loomis JM, DaSilva J, Fujita N, Fukusima S. Visual space perception and visually directed action. Journal of Experimental Psychology: Human Perception & Performance. 1992;18:906–921. doi: 10.1037//0096-1523.18.4.906. [DOI] [PubMed] [Google Scholar]
  10. Loomis JM, Philbeck JW. Is the anisotropy of perceived 3-D shape invariant across scale? Perception & Psychophysics. 1999;61:397–402. doi: 10.3758/bf03211961. [DOI] [PubMed] [Google Scholar]
  11. Loomis JM, Philbeck JW, Zahorik P. Dissociation of location and shape in visual space. Journal of Experimental Psychology: Human Perception and Performance. 2002;28:1202–1212. [PMC free article] [PubMed] [Google Scholar]
  12. Madison C, Thompson W, Kersten D, Shirley P, Smits B. Perception & Psychophysics. 2001;63:187–194. doi: 10.3758/bf03194461. [DOI] [PubMed] [Google Scholar]
  13. McCarley JS, He ZJ. Asymmetry in 3-D perceptual organization: Ground-like surface superior to ceiling-like surface. Perception & Psychophysics. 2000;62:540–549. doi: 10.3758/bf03212105. [DOI] [PubMed] [Google Scholar]
  14. McCarley JS, He ZJ. Repetition Priming of 3-D Perceptual Organization. Perception & Psychophysics. 2001;63:195–208. doi: 10.3758/bf03194462. [DOI] [PubMed] [Google Scholar]
  15. McKee SP, Welch L. The precision of size constancy. Vision Research. 1992;32:1447–1460. doi: 10.1016/0042-6989(92)90201-s. [DOI] [PubMed] [Google Scholar]
  16. Meng JC, Sedgwick HA. Distance perception mediated through nested contact relations among surface. Perception & Psychophysics. 2001;63:1–15. doi: 10.3758/bf03200497. [DOI] [PubMed] [Google Scholar]
  17. Ni R, Braunstein ML, Andersen GJ. Perception of scene layout from optical contact, shadows and motion. Perception. 2004;33:1305–1318. doi: 10.1068/p5288. [DOI] [PubMed] [Google Scholar]
  18. Ooi TL, He ZJ. Localizing suspended objects in the intermediate distance range (>2 meters) by observers with normal and abnormal binocular vision [Abstract] Journal of Vision. 2006;6(6):853a. http://journalofvision.org/6/6/853. [Google Scholar]
  19. Ooi TL, He ZJ. A distance judgment function based on space perception mechanisms – revisiting Gilinsky's equation. Psychological Review. doi: 10.1037/0033-295X.114.2.441. in press. [DOI] [PubMed] [Google Scholar]
  20. Ooi TL, Wu B, He ZJ. Distance determined by the angular declination below the horizon. Nature. 2001;414:197–200. doi: 10.1038/35102562. [DOI] [PubMed] [Google Scholar]
  21. Ooi TL, Wu B, He ZJ. Perceptual space in the dark affected by the intrinsic bias of the visual system. Perception. 2006;35:605–624. doi: 10.1068/p5492. [DOI] [PubMed] [Google Scholar]
  22. Philbeck JW, Loomis JM. Comparison of two indicators of perceived egocentric distance under full-cue and reduced-cue conditions. Journal of Experimental Psychology: Human Perception & Performance. 1997;23:72–85. doi: 10.1037//0096-1523.23.1.72. [DOI] [PubMed] [Google Scholar]
  23. Sedgwick HA. Space Perception. In: Boff KR, Kaufman L, Thomas JP, editors. Handbook of Perception and Human Performance. Wiley; New York: 1986. pp. 21.1–21.57. [Google Scholar]
  24. Sinai MJ, Ooi TL, He ZJ. Terrain influences the accurate judgement of distance. Nature. 1998;395:497–500. doi: 10.1038/26747. [DOI] [PubMed] [Google Scholar]
  25. Wu B, He ZJ, Ooi TL. The linear perspective information in ground surface representation and distance judgment. Perception & Psychophysics. doi: 10.3758/bf03193769. in press. [DOI] [PubMed] [Google Scholar]
  26. Wu B, Ooi TL, He ZJ. Perceiving distance accurately by a directional process of integrating ground information. Nature. 2004;428:73–77. doi: 10.1038/nature02350. [DOI] [PubMed] [Google Scholar]
  27. Wu J, He ZJ, Ooi TL. Stimulus duration and binocular disparity factors in representing the ground surface and localizing object in the intermediate distance range [Abstract] Journal of Vision. 2004;4(8):21a. http://journalofvision.org/4/8/21/ [Google Scholar]
  28. Wu J, He ZJ, Ooi TL. Visually perceived eye level and horizontal midline of the body trunk influenced by optic flow. Perception. 2005;34:1045–1060. doi: 10.1068/p5416. [DOI] [PubMed] [Google Scholar]
  29. Wu J, He ZJ, Ooi TL. The slant of the visual system's intrinsic bias in space perception and its contribution to ground surface representation [Abstract] Journal of Vision. 2006;6:730a. http://journalofvision.org/6/6/730/ [Google Scholar]

RESOURCES