Symmetry mediates the bootstrapping of 3-D relief slant to metric slant

  • Xiaoye Michael WangEmail author
  • Mats Lind
  • Geoffrey P. Bingham


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.


Bootstrap process Geographical slant perception Affine geometry Stereomotion Structure from motion Skew symmetry 


Open practice statement

Data and materials for all experiments are available upon request to the corresponding author, and none of the experiments were preregistered.


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Copyright information

© The Psychonomic Society, Inc. 2019

Authors and Affiliations

  1. 1.Department of Psychological and Brain SciencesIndiana UniversityBloomingtonUSA
  2. 2.Department of Information TechnologyUppsala UniversityUppsalaSweden

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