Symmetry mediates the bootstrapping of 3-D relief slant to metric slant
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Symmetry mediates the bootstrapping of 3-D relief slant to metric slant Xiaoye Michael Wang 1
&
Mats Lind 2 & Geoffrey P. Bingham 1
# The Psychonomic Society, Inc. 2019
Abstract Empirical studies have always shown 3-D slant and shape perception to be inaccurate as a result of relief scaling (an unknown scaling along the depth direction). Wang, Lind, and Bingham (Journal of Experimental Psychology: Human Perception and Performance, 44(10), 1508–1522, 2018) discovered that sufficient relative motion between the observer and 3-D objects in the form of continuous perspective change (≥45°) could enable accurate 3-D slant perception. They attributed this to a bootstrap process (Lind, Lee, Mazanowski, Kountouriotis, & Bingham in Journal of Experimental Psychology: Human Perception and Performance, 40(1), 83, 2014) where the perceiver identifies right angles formed by texture elements and tracks them in the 3-D relief structure through rotation to extrapolate the unknown scaling factor, then used to convert 3-D relief structure to 3-D Euclidean structure. This study examined the nature of the bootstrap process in slant perception. In a series of four experiments, we demonstrated that (1) features of 3-D relief structure, instead of 2-D texture elements, were tracked (Experiment 1); (2) identifying right angles was not necessary, and a different implementation of the bootstrap process is more suitable for 3-D slant perception (Experiment 2); and (3) mirror symmetry is necessary to produce accurate slant estimation using the bootstrapped scaling factor (Experiments 3 and 4). Together, the results support the hypothesis that a symmetry axis is used to determine the direction of slant and that 3-D relief structure is tracked over sufficiently large perspective change to produce metric depth. Altogether, the results supported the bootstrap process. Keywords Bootstrap process . Geographical slant perception . Affine geometry . Stereomotion . Structure from motion . Skew symmetry
Statement of significance 3-D shape and slant perception are a fundamental part of the perception of the surrounding environment necessary to support action. Studying ways through which people can achieve perceived 3-D shape and slant accurately will not only shed light on how the human visual system works but also provide ideas that could be applied to, for example, computer vision. The current study offers empirical evidence suggesting how veridical slant perception can be achieved. * Xiaoye Michael Wang [email protected] 1
2
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA Department of Information Technology, Uppsala University, Uppsala, Sweden
Many theoretical and empirical studies have characterized the perception of 3-D objects to be intrinsically affine, or of relief structure,1 where the frontoparallel dimension of the object is perceived accurately while there is a homogeneous stretching or compression of distances orthogonal to the frontoparallel plane by an unknown scaling factor (e.g., Domini
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