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Tadamasa Sawada, Zygmunt Pizlo; Detection of mirror-symmetry of a volumetric shape from its single 2D orthographic image. Journal of Vision 2008;8(6):543. doi: 10.1167/8.6.543.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose. Many objects in our environment are symmetric. This means that symmetry is a potentially useful constraint in recovering 3D shapes from their 2D retinal images. However, symmetric objects rarely produce symmetric retinal images. This study tested, for the first time, human ability to detect symmetry of a volumetric object from its single 2D image. Method. Orthographic images of opaque polyhedra were used as stimuli. Mirror-symmetric polyhedra and three types of asymmetric polyhedra were used. Parallelism of line segments that connect pairs of symmetric points is the main (perhaps even the only) invariant of an orthographic projection of mirror-symmetric objects. Asymmetric polyhedra were produced by distorting the symmetric ones, so that: (i) all contours of faces were planar, and all pairs of vertices formed a set of parallel line segments, (ii) all contours of faces were planar, but the pairs of vertices did not form parallel lines segments, and (iii) the contours were not planar and the pairs of vertices did not form parallel line segments. Signal detection experiment was performed for two general conditions. In one condition, the subject was asked to discriminate between symmetric and asymmetric polyhedra, for several levels of distortion of symmetry. In another condition, the subject was asked to discriminate between clearly asymmetric polyhedra and polyhedra, which were less asymmetric, again for several levels of distortion of symmetry. Results. In all conditions and in all trials a single 2D image of a 3D polyhedron produced a 3D percept of a polyhedron. Discrimination involving asymmetric polyhedra (iii) led to best performance. Discrimination involving asymmetric polyhedra (i) and (ii) led to similar performance. Conclusions. Planarity of faces is a constraint that contributes to symmetry detection. A computational model of mirror-symmetry detection, involving planarity and compactness constraints, will be presented and compared to the results of the subjects.
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