The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation

Abstract

Abstract:The visual system is sensitive to symmetries in the frontoparallel plane, and bilateral symmetry about a vertical axis has a particular salience. However, these symmetries represent only a subset of the symmetries realizable in three-dimensional space. The retinal image symmetries formed when viewing natural objects are typically the projections of three-dimensional objects-animals, for example-that have a symmetry in depth. To characterize human sensitivity to depth symmetry, experiments measured observers' ability to discriminate stereo displays that were symmetrically distributed in depth and those that were asymmetrically distributed. Disparity values were distributed about one of four planes passing through the z-axis and differing in frontoparallel orientation. Asymmetrical patterns were generated by perturbing one of these disparities. Symmetrical-asymmetrical discrimination thresholds were lowest for symmetry about the vertical plane and highest for the horizontal plane. Thresholds for discriminating repetitions and non-repetitions of depth values did not differ across the four planes, whereas discriminations for depth gradients differed from both the symmetry and repetition cases. The heightened sensitivity to symmetry in depth about the vertical plane is a 3-D analog of 2-D mirror-image symmetry performance and could be its source.

Regularity detection by haptics and vision.

“…Any such effects, because of body-centric coding of symmetrical spatial relations, would indicate that regularity detection does not merely reflect properties of our external, physical environment but, instead, is influenced by how we perceptually acquire and process information. For vision, the prediction that axis alignment should aid the detection of symmetry, but not of repetition, is supported by the results of Baylis and Driver (1994) and Farell (2015), but not by those of Friedenberg and Bertamini (2000), so the evidence to date is mixed, while for haptics this issue has only been tested once, by Lawson et al (in press), and here the results supported the prediction.…”

“…Baylis and Driver (1994) found an advantage for detecting symmetry if the stimuli were aligned with, rather than running across, the body midline, but no such effect for the detection of repetition. Farell (2015) replicated this result of an alignment advantage for detecting symmetry, but not repetition, for stimuli slanted in depth, as well as for stimuli presented in the usual frontoparallel plane. In contrast, Friedenberg and Bertamini (2000) found weak alignment effects with a general trend for an alignment advantage for repetition detection as well as symmetry detection.…”

Factors Affecting the Perception of 3D Facial Symmetry from 2D Projections

“…The difference between the inverted faces and the orthogonal faces, therefore, represents the loss of this bilateral symmetry. This is consistent with the findings of Farell [44] who found that symmetry with a vertical axis is easier to detect than symmetry with a horizontal axis. The current data show that this difference only occurs for the front-view versions of the faces.…”

“…Further research into 3D symmetry has demonstrated that the direction of symmetry affects its detection. Farell [44] showed that the thresholds to detect symmetry are lower when the symmetry is across a vertical plane than when it is across a horizontal plane. Although this effect was discovered using abstract stereo displays, it does have clear implications for the current research particularly when comparing inverted faces (which have a vertical plane of symmetry) with orthogonal faces (which have a horizontal plane of symmetry).…”

Influence of 3D Centro-Symmetry on a 2D Retinal Image

“…It raises two questions: (i) which 3D centro-symmetry or 3D rotational symmetry is actually inferred from 2D rotational symmetry in the human visual system and (ii) can any sensitivity to 3D centro-symmetry be helpful for the perception of 3D? The first question can be addressed by testing the human sensitivity to 2D rotation-symmetrical patterns with a 3D centro-symmetrical or with a 3D rotation-symmetrical depth distribution (see Figure 5, see also [38][39][40][41] for studies of the perception of 2D mirror symmetry from a dotted pattern with a depth distribution). Note, however, even if the human visual system is sensitive to 3D centro-symmetry, it is unclear how 3D centro-symmetry can be of any help in the perception of 3D.…”