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Symmetry
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Symmetry: Theory and Applications in Vision
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Symmetry: Theory and Applications in Vision

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

Deadline for manuscript submissions: closed (1 February 2015) | Viewed by 33507

Special Issue Editors

Dr. Christopher W. Tyler

E-Mail Website
Guest Editor
Smith-Kettlewell Brain Imaging Center, Smith-Kettlewell Eye Research Institute, 2318 Fillmore Street, San Francisco, CA 94115, USA
Interests: human symmetry perception; mathematical systems analysis; complexity theory; texture analysis; self-referential systems; symmetry in art; consciousness
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Zygmunt Pizlo

E-Mail Website
Guest Editor
Department of Psychological Sciences, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-2081, USA
Prof. Dr. Manish Singh

E-Mail Website
Guest Editor
Department of Psychology & Center for Cognitive Science, Rutgers University, New Brunswick, NJ 08854, USA

Special Issue Information

Dear Colleagues,

Symmetry has a solid foundation in mathematics where it refers to invariance with respect to a group of transformations. When viewed from an information-theoretic standpoint, symmetry is thus a form of redundancy. For years, symmetry has played a central role in art, esthetics, architecture, physics, and computer science. It has recently started playing a similar role in human and computer vision as well. Symmetry is widely prevalent in the natural environment; and symmetric structures are inherently simpler. For both reasons, symmetry can serve as a powerful “prior” that perceptual systems can use to infer invariant 3D structure from 2D images. Moreover various forms of symmetry can be used to represent the shape of complex objects in a compact manner. This special issue is devoted to various types of symmetry and their role in human and computer vision.

Prof. Dr. Christopher W. Tyler
Prof. Dr. Zygmunt Pizlo
Prof. Dr. Manish Singh
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • symmetry
  • structure
  • visual
  • spatial
  • art
  • perception
  • cognition

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Published Papers (5 papers)

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Research

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823 KiB  
Article
Reduction by Lie Group Symmetries in Diffeomorphic Image Registration and Deformation Modelling
by Stefan Sommer and Henry O. Jacobs
Symmetry 2015, 7(2), 599-624; https://doi.org/10.3390/sym7020599 - 7 May 2015
Cited by 1 | Viewed by 6004
Abstract
We survey the role of reduction by symmetry in the large deformation diffeomorphic metric mapping framework for registration of a variety of data types (landmarks, curves, surfaces, images and higher-order derivative data). Particle relabelling symmetry allows the equations of motion to be reduced [...] Read more.
We survey the role of reduction by symmetry in the large deformation diffeomorphic metric mapping framework for registration of a variety of data types (landmarks, curves, surfaces, images and higher-order derivative data). Particle relabelling symmetry allows the equations of motion to be reduced to the Lie algebra allowing the equations to be written purely in terms of the Eulerian velocity field. As a second use of symmetry, the infinite dimensional problem of finding correspondences between objects can be reduced for a range of concrete data types, resulting in compact representations of shape and spatial structure. Using reduction by symmetry, we describe these models in a common theoretical framework that draws on links between the registration problem and geometric mechanics. We outline these constructions and further cases where reduction by symmetry promises new approaches to the registration of complex data types. Full article
(This article belongs to the Special Issue Symmetry: Theory and Applications in Vision)
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34144 KiB  
Article
Unsupervised Object Modeling and Segmentation with Symmetry Detection for Human Activity Recognition
by Jui-Yuan Su, Shyi-Chyi Cheng and De-Kai Huang
Symmetry 2015, 7(2), 427-449; https://doi.org/10.3390/sym7020427 - 23 Apr 2015
Cited by 6 | Viewed by 7125
Abstract
In this paper we present a novel unsupervised approach to detecting and segmenting objects as well as their constituent symmetric parts in an image. Traditional unsupervised image segmentation is limited by two obvious deficiencies: the object detection accuracy degrades with the misaligned boundaries [...] Read more.
In this paper we present a novel unsupervised approach to detecting and segmenting objects as well as their constituent symmetric parts in an image. Traditional unsupervised image segmentation is limited by two obvious deficiencies: the object detection accuracy degrades with the misaligned boundaries between the segmented regions and the target, and pre-learned models are required to group regions into meaningful objects. To tackle these difficulties, the proposed approach aims at incorporating the pair-wise detection of symmetric patches to achieve the goal of segmenting images into symmetric parts. The skeletons of these symmetric parts then provide estimates of the bounding boxes to locate the target objects. Finally, for each detected object, the graphcut-based segmentation algorithm is applied to find its contour. The proposed approach has significant advantages: no a priori object models are used, and multiple objects are detected. To verify the effectiveness of the approach based on the cues that a face part contains an oval shape and skin colors, human objects are extracted from among the detected objects. The detected human objects and their parts are finally tracked across video frames to capture the object part movements for learning the human activity models from video clips. Experimental results show that the proposed method gives good performance on publicly available datasets. Full article
(This article belongs to the Special Issue Symmetry: Theory and Applications in Vision)
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443 KiB  
Article
The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation
by Bart Farell
Symmetry 2015, 7(2), 336-353; https://doi.org/10.3390/sym7020336 - 3 Apr 2015
Cited by 4 | Viewed by 6412
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry: Theory and Applications in Vision)
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741 KiB  
Article
Evidence for Obliqueness of Angles as a Cue to Planar Surface Slant Found in Extremely Simple Symmetrical Shapes
by Casper J. Erkelens
Symmetry 2015, 7(1), 241-254; https://doi.org/10.3390/sym7010241 - 9 Mar 2015
Cited by 6 | Viewed by 6593
Abstract
The Necker cube is a striking example for perceptual dominance of 3D over 2D. Object symmetry and obliqueness of angles are co-varying cues that may underlie the perceived slant of Necker cubes. To investigate the power of the oblique-angle cue, slants were judged [...] Read more.
The Necker cube is a striking example for perceptual dominance of 3D over 2D. Object symmetry and obliqueness of angles are co-varying cues that may underlie the perceived slant of Necker cubes. To investigate the power of the oblique-angle cue, slants were judged of extremely simple symmetrical shapes. Slant computations based on an assumption of orthogonality were made for two abutting lines as a function of vertex angle and the slant of the screen. Computed slants were compared with slants judged by six subjects under binocular viewing conditions. Judged slant was highly correlated with slant specified by the oblique angles under an assumption of orthogonality. The contributions of screen cues, including binocular disparity, were negligible. The consistency of the judgments across subjects indicates the assumption of orthogonality as one of the principles underlying slant perception. Necker cubes illustrate that the visual system can disengage unambiguous cues in favor of ambiguous object-symmetry and oblique-angle cues, if the latter indicate very different slants. Selective disengagement of cues may be the mechanism that underlies the success of 2D images in ancient, as well as modern civilizations. Full article
(This article belongs to the Special Issue Symmetry: Theory and Applications in Vision)
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Review

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5373 KiB  
Review
A Framework for Symmetric Part Detection in Cluttered Scenes
by Tom Lee, Sanja Fidler, Alex Levinshtein, Cristian Sminchisescu and Sven Dickinson
Symmetry 2015, 7(3), 1333-1351; https://doi.org/10.3390/sym7031333 - 20 Jul 2015
Cited by 5 | Viewed by 6749
Abstract
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance [...] Read more.
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today’s recognition systems are faced with cluttered scenes and the assumption that a closed contour exists, i.e., that figure-ground segmentation has been solved, rendering much of the medial axis community’s work inapplicable. In this article, we review a computational framework, previously reported in [1–3], that bridges the representation power of the medial axis and the need to recover and group an object’s parts in a cluttered scene. Our framework is rooted in the idea that a maximally-inscribed disc, the building block of a medial axis, can be modelled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes. Full article
(This article belongs to the Special Issue Symmetry: Theory and Applications in Vision)
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