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J. Farley, Hideko F. Norman, Young-lim Lee, DaSha Stockton, Joseph S. Lappin; The visual perception of length along intrinsically curved surfaces. Journal of Vision 2002;2(7):84. doi: 10.1167/2.7.84.
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© ARVO (1962-2015); The Authors (2016-present)
Past investigations of the perception of length along 3-D surfaces (e.g., Gilinsky, 1951; Norman, Lappin, & Norman, 2000) have demonstrated that observers' perceptions of lengths along flat and cylindrically curved surfaces are systematically distorted. In the current experiments, we extended the past research and evaluated observers' perceptions of length and spatial extent along physically curved surfaces that possessed intrinsic curvature. The surfaces with positive and negative Gaussian curvatures were a hemisphere and a hyperbolic paraboloid with radii of curvature of 14 cm. The surfaces were covered with a random texture (to create a “carrier” for binocular disparity, etc.). Observers viewed these surfaces at two distances (50 and 180 cm) and on each trial were required to estimate the length between one of 40 possible pairs of surface regions by adjusting a 2-D line on a PC monitor until its length matched that of the curved length. The observers judged each of the 160 surface lengths (40 pairs × 2 surfaces × 2 viewing distances) ten times, and thus completed a total of 1600 judgments. The results showed that the observers were reliable and precise in their judgments (average Pearson r's of 0.97), but in general they were not accurate. The slopes of the regression functions relating adjusted length to actual length varied widely between 0.8 to 1.5. The magnitude of these large perceptual distortions varied across observers. There were smaller effects of distance, such that the perceptual distortions were typically larger at the nearer viewing distance. Thus, in conclusion, it is apparent from the results of this experiment and from past investigations that the perception of length and spatial extent is not veridical in any context, whether evaluating distances in empty space, or between locations on flat or curved surfaces, even in full-cue situations where binocular disparity and other optical information is available.
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