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Taro Maeda, Eimei Oyama, Hideyuki Ando, Susumu Tachi; The spatial perception of continuous curves with discrete light spot stimuli. Journal of Vision 2002;2(7):478. doi: https://doi.org/10.1167/2.7.478.
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© ARVO (1962-2015); The Authors (2016-present)
In depth perception studies, it has been observed empirically that a physically equidistant curve is not perceived as equidistant. An experiment is reported here regarding this perceptual phenomenon, in which discrete light spots on an arc of a circle appear to an observer at the circle's center as neither a continuous “egocentrically equidistant” curve nor a continuous “constant curvature” curve, whereas these phenomenal curves are perceived as different from each other. In spatial perception, a pair of parallel lines has two geometrical interpretations, “parallel” and “equidistant”. Classical empirical phenomena such as the equidistant and parallel alleys suggest that these interpretations are respectively psychophysical entities that are different from each other and the physical entity. Similarly, an arc on a circle also has the above -mentioned interpretations, “egocentric equidistance” and “constant curvature”. Are these interpretations also psychophysical entities? Our neural network model, the ISLES model, explains the phenomena of equidistant and parallel alleys as the results of developmental learning at each level of the psychometric scale. In this model, when the perception of parallelity is developmentally learnt from observations of physically parallel lines, the invariant is the order, and the psychometric scale for learning is an ordinal scale. When the perception of equidistance is learnt, the invariant is the interval, and the psychometric scale for learning is an interval scale. The ISLES model also predicts the difference between the phenomenal curves,“egocentric equidistance” and “constant curvature” in the same way. The prediction leads from only the hypothesis that the psychometric scale for learning curvature should be an ordinal scale whereas the psychometric scale for learning egocentric distance should be an interval scale. These results suggest the existence of homogeneous mechanisms in spatial perception of geometrical constancies.
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