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Special Issue "Symmetry Processing in Perception and Art"

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A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 March 2011)

Special Issue Editor

Guest Editor
Dr. Christopher W. Tyler

Smith-Kettlewell Brain Imaging Center, Smith-Kettlewell Eye Research Institute, 2318 Fillmore Street, San Francisco, CA 94115, USA
Website | E-Mail
Fax: +1 415 345 8455
Interests: human symmetry perception; mathematical systems analysis; complexity theory; texture analysis; self-referential systems; symmetry in art; consciousness

Special Issue Information

Dear Colleagues,

Although symmetry is a fundamental organizing principle of the universe in both abstract conceptual sense and the explicit form of mirror symmetry in organisms, visual symmetry is not much in evidence in the natural world. A view of any purely natural scene shows few exactly symmetric objects, and those that are approximately symmetric are usually life forms of some sort. Thus, at the level of our perception, symmetry is something that is imposed on the world by animate organisms, either by virtue of their biological make-up or by the constructions of human civilization. This view is paradoxical in relation to artistic depictions, in which the background and compositional structure is often symmetrical, while the figures representing the action are usually asymmetrical. Similarly, symmetries of various kinds play a huge role in the composition of music, and may be regarded as the key factor that distinguishes this artificial auditory environment from undifferentiated noise. Thus, symmetry is a largely human concoction that weaves an interesting perceptual counterpoint through our understanding of, and interactions with, the world on the human scale of visual and auditory perception.

This conceptualization provides the motivation for a Feature Issue bringing together contributions on the rigorous analysis of human symmetry processing through art and perceptual studies of all varieties. Submissions are encouraged from the fields of neuroscience and neuroimaging, as well as the quantitative analysis of symmetry perception in art productions and laboratory materials, with a particular emphasis on the neural and evolutionary mechanisms underlying the unique human appreciation of symmetry and the drive to propagate it through our societal environment.

Dr. Christopher W. Tyler
Guest Editor

Keywords

  • symmetry
  • perceptual
  • evolutionary
  • neuroscience
  • neuroimaging
  • composition
  • counterpoint

Published Papers (7 papers)

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Research

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Open AccessArticle Folded Sheet Versus Transparent Sheet Models for Human Symmetry Judgments
Symmetry 2011, 3(3), 503-523; doi:10.3390/sym3030503
Received: 6 April 2011 / Revised: 8 July 2011 / Accepted: 8 July 2011 / Published: 22 July 2011
PDF Full-text (2910 KB) | Supplementary Files
Abstract
As a contribution to the mysteries of human symmetry perception, reaction time data were collected on the detection of symmetry or repetition violations, in the context of short term visual memory studies. The histograms for reaction time distributions are rather narrow in the
[...] Read more.
As a contribution to the mysteries of human symmetry perception, reaction time data were collected on the detection of symmetry or repetition violations, in the context of short term visual memory studies. The histograms for reaction time distributions are rather narrow in the case of symmetry judgments. Their analysis was performed in terms of a simple kinetic model of a mental process in two steps, a slow one for the construction of the representation of the images to be compared, and a fast one, in the 50 ms range, for the decision. There was no need for an additional ‘mental rotation’ step. Symmetry seems to facilitate the construction step. I also present here original stimuli showing a color equalization effect across a symmetry axis, and its counterpart in periodic patterns. According to a “folded sheet model”, when a shape is perceived, the brain automatically constructs a mirror-image representation of the shape. Based in part on the reaction time analysis, I present here an alternative “transparent sheet” model in which the brain constructs a single representation, which can be accessed from two sides, thus generating simultaneously a pattern and its mirror-symmetric partner. Filtering processes, implied by current models of symmetry perception could intervene at an early stage, by nucleating the propagation of similar perceptual groupings in the two symmetric images. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
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Open AccessArticle Mirror Symmetry Is Subject to Crowding
Symmetry 2011, 3(3), 457-471; doi:10.3390/sym3030457
Received: 19 April 2011 / Revised: 9 June 2011 / Accepted: 28 June 2011 / Published: 13 July 2011
Cited by 2 | PDF Full-text (625 KB)
Abstract
Mirror symmetry is often thought to be particularly salient to human observers because it engages specialized mechanisms that evolved to sense symmetrical objects in nature. Although symmetry is indeed present in many of our artifacts and markings on wildlife, studies have shown that
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Mirror symmetry is often thought to be particularly salient to human observers because it engages specialized mechanisms that evolved to sense symmetrical objects in nature. Although symmetry is indeed present in many of our artifacts and markings on wildlife, studies have shown that sensitivity to mirror symmetry does not serve an alerting function and sensitivity to symmetry decreases in a rather unremarkable way when it is presented away from the centre of the visual field. Here we show that symmetrical targets are vulnerable to the same interference as other stimuli when surrounded by non-target elements. These results provide further evidence that symmetry is not special to the early visual system, and reinforce the notion that our fascination with symmetry is more likely attributable to cognitive and aesthetic factors than to specialized, low level mechanisms in the visual system. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
Open AccessArticle Reduction of Image Complexity Explains Aesthetic Preference for Symmetry
Symmetry 2011, 3(3), 443-456; doi:10.3390/sym3030443
Received: 11 April 2011 / Revised: 2 June 2011 / Accepted: 29 June 2011 / Published: 11 July 2011
Cited by 4 | PDF Full-text (228 KB)
Abstract
Symmetric patterns are more appealing to human observers than asymmetric ones. Here, we investigate the visual information processing mechanisms underlying this aesthetic preference. All stimuli were derived from phase scrambled versions of forty face or nature images. In addition to the scrambled images,
[...] Read more.
Symmetric patterns are more appealing to human observers than asymmetric ones. Here, we investigate the visual information processing mechanisms underlying this aesthetic preference. All stimuli were derived from phase scrambled versions of forty face or nature images. In addition to the scrambled images, there were four other types of test image: symmetric, in which one part of the image was a reflection of another around an axis; repetitive, in which one part of the image was a copy of the other; anti-symmetric, similar to symmetric but with the contrast of one side reversed; and interleaved patterns, in which half of the symmetric pattern was replaced by a scrambled image. The number of axes ranged from 1 to 16 for all image types. The task of our 20 observers was to give a preference rating to each image on a 6-point Lickert scale. The preference rating increased with the number of axes for all stimulus types. The observers showed a similar preference for symmetric and repetitive patterns and slightly less preference for anti-symmetric patterns. The preference for interleaved patterns was much less than for other types of stimuli. Preference for an image cannot be explained by either the ecological significance of its content or the slope of its amplitude spectrum. Instead, preference can be accounted for by the complexity of the image. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
Open AccessArticle Any Pair of 2D Curves Is Consistent with a 3D Symmetric Interpretation
Symmetry 2011, 3(2), 365-388; doi:10.3390/sym3020365
Received: 10 February 2011 / Revised: 27 May 2011 / Accepted: 30 May 2011 / Published: 10 June 2011
Cited by 4 | PDF Full-text (473 KB) | Supplementary Files
Abstract
Symmetry has been shown to be a very effective a priori constraint in solving a 3D shape recovery problem. Symmetry is useful in 3D recovery because it is a form of redundancy. There are, however, some fundamental limits to the effectiveness of symmetry.
[...] Read more.
Symmetry has been shown to be a very effective a priori constraint in solving a 3D shape recovery problem. Symmetry is useful in 3D recovery because it is a form of redundancy. There are, however, some fundamental limits to the effectiveness of symmetry. Specifically, given two arbitrary curves in a single 2D image, one can always find a 3D mirror-symmetric interpretation of these curves under quite general assumptions. The symmetric interpretation is unique under a perspective projection and there is a one parameter family of symmetric interpretations under an orthographic projection. We formally state and prove this observation for the case of one-to-one and many-to-many point correspondences. We conclude by discussing the role of degenerate views, higher-order features in determining the point correspondences, as well as the role of the planarity constraint. When the correspondence of features is known and/or curves can be assumed to be planar, 3D symmetry becomes non-accidental in the sense that a 2D image of a 3D asymmetric shape obtained from a random viewing direction will not allow for 3D symmetric interpretations. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
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Open AccessArticle Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity
Symmetry 2011, 3(2), 246-264; doi:10.3390/sym3020246
Received: 1 March 2011 / Revised: 15 April 2011 / Accepted: 19 May 2011 / Published: 25 May 2011
Cited by 6 | PDF Full-text (6643 KB)
Abstract
Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classified into one of 17 different Wallpaper groups, and while computational models have been developed which can extract an
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Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classified into one of 17 different Wallpaper groups, and while computational models have been developed which can extract an image's symmetry group, very little work has been done on how humans perceive these patterns. This study presents the results from a grouping experiment using stimuli from the different wallpaper groups. We find that while different images from the same wallpaper group are perceived as similar to one another, not all groups have the same degree of self-similarity. The similarity relationships between wallpaper groups appear to be dominated by rotations. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
Open AccessArticle Visual Discrimination of the 17 Plane Symmetry Groups
Symmetry 2011, 3(2), 207-219; doi:10.3390/sym3020207
Received: 1 April 2011 / Revised: 25 April 2011 / Accepted: 4 May 2011 / Published: 11 May 2011
PDF Full-text (1097 KB)
Abstract
Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification.
[...] Read more.
Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of experiments and the discussion of methodological problems is preceded by a brief overview of the role which symmetry has played in the visual arts. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)

Review

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Open AccessReview The First Appearance of Symmetry in the Human Lineage: Where Perception Meets Art
Symmetry 2011, 3(1), 37-53; doi:10.3390/sym3010037
Received: 17 January 2011 / Revised: 23 February 2011 / Accepted: 23 February 2011 / Published: 1 March 2011
Cited by 11 | PDF Full-text (596 KB)
Abstract
Although symmetry may be important for understanding the selection of form in art over the historical period, this preference may have originally stemmed from certain basic perceptual mechanism that initially arose during prehistory. The first signs of an awareness to symmetry can be
[...] Read more.
Although symmetry may be important for understanding the selection of form in art over the historical period, this preference may have originally stemmed from certain basic perceptual mechanism that initially arose during prehistory. The first signs of an awareness to symmetry can be found in the archaeological record with the arrival of Acheulean handaxes, especially those dating from 500,000 years ago onwards, which are typified by a prodigious bilateral symmetry. As handaxes represent the earliest material record of an interest in symmetry by the human lineage, they provide a privileged means of understanding why this kind of form came to be valued by later human groups, particularly in relation to “art”. Although still controversial, the preference for symmetry at such an early date has been linked to various aspects of perception relating to enduring evolutionary factors. In this regard, it will be demonstrated how the preference for symmetrical Acheulean tools arose out of long standing perceptual correlates relating to ecological factors that predated the arrival of hominins. Full article
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
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