The visual system's intrinsic bias and knowledge of size mediate perceived size and location in the dark

Abstract

Dimly lit targets in the dark are perceived as located about an implicit slanted surface that delineates the visual system's intrinsic bias (Ooi, Wu, & He, 2001). If the intrinsic bias reflects the internal model of visual space-as proposed here-its influence should extend beyond target localization. Our first 2 experiments demonstrated that the intrinsic bias also influences perceived target size. We employed a size-matching task and an action task to measure the perceived size of a dimly lit target at various locations in the dark. Then using the size distance invariance hypothesis along with the accurately perceived target angular declination, we converted the perceived sizes to locations. We found that the derived locations from the size judgment tasks can be fitted by slanted curves that resemble the intrinsic bias profile from judged target locations. Our third experiment revealed that armed with the explicit knowledge of target size, an observer perceives target locations in the dark following an intrinsic bias-like profile that is shifted slightly farther from the observer than the profile obtained without knowledge of target size (i.e., slightly more veridical). Altogether, we showed that the intrinsic bias serves as an internal model, or memory, of ground surface layouts when the visual system cannot rely on external depth information. This memory/model can also be weakly influenced by top-down knowledge.

Figure 1

Influence of intrinsic bias on space perception in the dark and reduced-cue environments. (A) The intrinsic bias takes the form of an implicit slant/curved surface and it acts like a representation of the ground surface when the physical ground surface is not visible in the dark. (B) A dimly-lit target on the non-visible ground surface in the dark is perceived at the intersection between the eye-to-target projection line and the intrinsic bias. The perceived distance of the dimly-lit target increases as the angular declination of the dimly-lit target (α₁<α₂) decreases. (C) The dimly-lit target in a reduced cue environment is located on an implicit slanted surface that is less slanted than the intrinsic bias.

Figure 2

Relationship between perceived distance and perceived size. (A) The well-known size-distance invariance hypothesis (SDIH) states that the perceived size (s) of a target is proportional to the perceived target distance (d_eye). (B) To estimate the perceived target location in the dark, we can derive the perceived eye-to-target distance (d_eye) by measuring the perceived target size (s). Should the intrinsic bias contribute to size perception in the dark, the estimated location will be found about the curved profile of the intrinsic bias. (C) If the knowledge of target size can affect space perception, the perceived target location will deviate from the intrinsic bias that is revealed without the knowledge of target size.

Figure 3

Experiment 1: Perceived target size from the perceptual matching task as a function of angular declination. The top cartoon illustrates the test setting in the dark. The graph shows that the matched target size increases significantly as the angular declination decreases. The data from the two target heights (on the floor and 50 cm above the floor) overlap, indicating that angular declination, rather than target height, determines the perceived target size in the dark. The matched sizes are similar in the two viewing conditions.

Figure 4

Experiment 1: Derived judged location from the matched target size. We transformed the matched target size (s_m) to perceived eye-to-target distance (d_eye) using the relationship, d_eye=s_m/tan(β/2). The derived judged target location is plotted with the derived d_eye and the physical angular declination (α) (polar coordinate with the origin at the average eye position on the y-axis). The derived judged locations (triangle symbols) are deviated from the physical target locations (plus symbols) and fall instead along an implicit curved surface (the intrinsic bias).

Figure 5

Experiment 2: Judged target size from the blind walk-gesture-height-size task as a function of angular declination. The judged sizes from both target heights transcribe the same curve and increase as the angular declination decreases. This trend is similar to that obtained with the perceptual size matching task in Experiment 1 (figure 3).

Figure 6

Experiment 2: Using the perceived eye-to-target distance (d_eye) as a function of angular declination for comparison among the three different measures from Experiments 1 and 2. First, we transformed the gestured target size (s_g) from Experiment 2 to d_eye (filled square). Second, we calculated d_eye based on the judged target location from Experiment 2 using the formula, d²_eye =d²_w+(H-h_g)², where d_w and h_g are the walked horizontal distance and gestured height, respectively, and H is the eye height (open square). The d_eye data from the perceptual size matching judgments of Experiment 1 are represented by filled circles. Overall, the perceived d_eye increases as the angular declination decreases. The perceived d_eye based on s_g from the blind walk-gesture size task (filled squares) appears longer than those based on the judged location from the blind walk-gesture height task (open square) and the perceptual matching task s_m (filled circles).

Figure 7

Experiment 2: Comparing measured and derived judged locations. The graph plots the judged target locations from the blind walk-gesture height task, the derived target locations from the blind walk-gesture size task (s_g) of Experiment 2 and from the perceptual size matching task (s_m) of Experiment 1. The judged locations (open square) and derived locations from the perceptual size matching task of Experiment 1 (filled triangle) cluster together and is well fitted by the same intrinsic bias profile taken from figure 4. The derived locations from the blind walk-gesture size task (filled square) are also fitted by the intrinsic bias profile when shifted rightward.

Figure 8

Experiment 2: Physical versus perceived angular declination. We correlated each observer's average judged angular declination at each target location (based on the blind walk-gesture height task) with the physical angular declination of the target. The regression line has a slope close to unity suggesting that the observers accurately perceived the angular declination.

Figure 9

Experiment 3: Judged target locations from the blind walking-gesturing task. Generally, the data from the same-angular-size (filled circle) and same-physical-size (open circle) conditions cluster about an implicit slanted curve, suggesting that the perceived locations are largely determined by the intrinsic bias. However, a closer comparison between the two conditions reveals that the data from the same-physical-size condition (open circle) are shifted rightward, due to the far targets being perceived as farther than those in the same-angular-size condition (filled circle). This indicates the impact of explicit knowledge of target size (figure 2c). The filled squares from the left to right represent the data from the same-angular-size condition where the targets were placed at the eye level and at distances, 3.25, 5.0, and 6.75m, respectively.

Figure 10

Experiment 3: Derived perceived eye-to-target distance. We derived the perceived eye-to-target distance (d_eye) from the formula, d²_eye=d²_w+(H-h_g)², where d_w and h_g are, respectively, the walked horizontal distance and gestured height and H is the eye height. The graph plots d_eye as a function of the physical angular declination (α) of the target for both conditions (filled circles: same-angular-size; open circles: same-physical-size). Clearly, d_eye increases as α decreases and is longer (farther) in the same-physical-size condition than in the same-angular-size condition, and their difference increases as the angular declination decreases.

Figure 11

Experiment 3: Catch-trials in the same-physical-size condition. The graph compares the average judged locations in the catch trials with those from the test trials at the same target distance and eye level. Distances are underestimated with both the test and catch targets. Furthermore, catch and test targets with the same angular size are perceived at the same distance despite the difference in their physical distances (and physical sizes), with targets having the smaller angular size being perceived as farther. This reveals the effect of angular size on perceived distance.