Inaccurate representation of the ground surface beyond a texture boundary

Abstract

The sequential-surface-integration-process (SSIP) hypothesis was proposed to elucidate how the visual system constructs the ground-surface representation in the intermediate distance range (He et al, 2004 Perception 33 789-806). According to the hypothesis, the SSIP constructs an accurate representation of the near ground surface by using reliable near depth cues. The near ground representation then serves as a template for integrating the adjacent surface patch by using the texture gradient information as the predominant depth cue. By sequentially integrating the surface patches from near to far, the visual system obtains the global ground representation. A critical prediction of the SSIP hypothesis is that, when an abrupt texture-gradient change exists between the near and far ground surfaces, the SSIP can no longer accurately represent the far surface. Consequently, the representation of the far surface will be slanted upward toward the frontoparallel plane (owing to the intrinsic bias of the visual system), and the egocentric distance of a target on the far surface will be underestimated. Our previous findings in the real 3-D environment have shown that observers underestimated the target distance across a texture boundary. Here, we used the virtual-reality system to first test distance judgments with a distance-matching task. We created the texture boundary by having virtual grass- and cobblestone-textured patterns abutting on a flat (horizontal) ground surface in experiment 1, and by placing a brick wall to interrupt the continuous texture gradient of a flat grass surface in experiment 2. In both instances, observers underestimated the target distance across the texture boundary, compared to the homogeneous-texture ground surface (control). Second, we tested the proposal that the far surface beyond the texture boundary is perceived as slanted upward. For this, we used a virtual checkerboard-textured ground surface that was interrupted by a texture boundary. We found that not only was the target distance beyond the texture boundary underestimated relative to the homogeneous-texture condition, but the far surface beyond the texture boundary was also perceived as relatively slanted upward (experiment 3). Altogether, our results confirm the predictions of the SSIP hypothesis.

Figure 1

The slant hypothesis. A texture boundary is created when two different texture surfaces (depicted in side view as black and gray lines) abut on a flat ground surface. According to the SSIP hypothesis, the far texture surface will not be represented as coplanar with the near texture surface. Instead, the far texture surface will be subjected to the influence of the visual system's intrinsic bias. This leads the far texture surface to be represented with a slant error, η; hence, its upward slant representation (gray dash line). Accordingly, d’₁=d₁ and d’₂=d₂*sin(α)/sin(α+η), in which the latter is derived from the trigonometric relationship, d’₂/sin(α)=d₂/sin(180-α-η). Thus, the perceived egocentric distance of a target on the far texture surface (d=d’₁+d’₂) is less than the actual physical distance (d₁+d₂).

Figure 2

The horizontal compression hypothesis. Instead of the slant hypothesis (figure 1), the egocentric distance underestimation observed when the flat ground surface has a texture boundary could be explained by an alternative horizontal compression hypothesis. It predicts that a horizontal compression of the far texture surface representation leads to the egocentric distance of a target on the far surface (d) being perceived as less than the actual distance (d₁+d₂).

Figure 3

The VR displays used in Experiment 1. (a) In the discontinuous-texture condition, a grass-textured field and a cobblestone-textured field covered the flat ground surface. (b) In the homogeneous-texture condition, a continuous grass-textured field covered the flat ground surface. (c) An illustration (side view) of the general layout for measuring the judged target distance in the discontinuous-texture condition. The observer stood on the grass-textured field to view the test-target on the cobblestone-textured field. The texture boundary between the two textured-fields was always set halfway in between the observer and the test-target. To respond to the perceived distance, the observer turned around by 180° to view the grass-textured field and performed a distance-matching task.

Figure 4

Results of Experiment 1 with displays presented in the bi-ocular (a) and stereoscopic (b) modes. The average matched distances were underestimated in the discontinuous-texture condition compared to the homogeneous-texture condition (n=8).

Figure 5

The VR displays used in Experiment 2. (a) In the occlusion condition, a brick wall occluded part of the flat, grass-textured ground surface. (b) In the homogeneous-texture condition, a continuous grass-textured field covered the flat ground surface. (c) An illustration (side view) of the general layout when measuring the judged target distance in the occlusion condition. The observer stood on the grass-textured field to view the test-target on the grass surface beyond the brick wall. The brick wall (0.5m × 1m) was always set halfway in between the observer and the test-target. To respond to the perceived distance, the observer turned around by 180° to view the grass-textured field and performed a distance-matching task.

Figure 6

Results of Experiment 2 with displays presented in the bi-ocular (a) and stereoscopic (b) modes. The average matched distances were underestimated in the occlusion condition compared to the homogeneous-texture condition (n=8).

Figure 7

(a) A (side view) schematic of the layout used in the control experiment to test the equidistance tendency phenomenon explanation. In the far-wall condition shown, a brick wall (0.5m × 1m) was placed beyond the test-target. The distance of the far brick wall to the testtarget was always set at half the physical distance between the observer and the test-target. To respond to the perceived distance, the observer turned around by 180° to view the grass-textured field and performed a distance-matching task. (b) The average results indicate that no systematic distance overestimation was found in the far-wall condition compared to the homogeneoustexture condition (n=8).

Figure 8

The VR displays used in Experiment 3. (a) In the discontinuous-texture condition, an explicit texture boundary was created by a 90° phase shift between the near and far checkerboard-textured surfaces. (b) In the homogeneous-texture condition, regular checkerboard tiles covered the ground surface. For both conditions, a vertical brick wall was placed at the farend of the checkerboard-textured surface to block the horizon. (c) An illustration (side view) of the general layout when measuring the judged target distance in the discontinuous-texture condition. The observer stood on the near checkerboard-textured surface to view the test-target on the far checkerboard-textured surface. The distance of the texture boundary from the observer was either 3m or 5m. To respond to the perceived distance, the observer turned around by 180o to view the grass-textured field and performed a distance-matching task.

Figure 9

A (side view) schematic depicting the general layout in the surface-slant judgment measurement (discontinuous-texture condition) in Experiment 3. In the virtual environment, the observer stood on the flat, near checkerboard-textured surface to judge if the near and far checkerboard-textured surfaces were coplanar. The slant of the far checkerboard-textured surface was initially set at a random value between +12° (downward) and −12° (upward). The distance of the texture boundary from the observer was 3m, 4m or 5m.

Figure 10

Results of Experiment 3 in the distance judgment measurement (n=8). Graphs (a) and (b), respectively, plot the average results when the texture boundary was 3m and 5m from the observer. Overall, the average judged distances were underestimated in the discontinuoustexture condition (filled symbols) compared to the homogeneous-texture condition (open symbols).

Figure 11

Results of Experiment 3 in the surface-slant judgment measurement (n=8). Overall, the far checkerboard-textured surface had to be slanted downward for it to be perceived as coplanar with the near checkerboard-textured surface (filled diamonds). The derived, predicted slant errors, based on the judged distance (d) and the equation, d=d₁+d₂*sin(α)/sin(α+η), are plotted as the open circles. There is no significant difference in the magnitudes of the judged and predicted slant errors.