Humans, animals and insects have an innate ability to perceive and take advantage of symmetry, which is a pervasive phenomenon presenting itself in all forms and scales in natural and man-made environments. Although our understanding of repeated patterns is generalized by the mathematical concept of symmetries and group theory, perception and recognition of symmetry has yet to be fully explored in machine intelligence and computer vision, and few effective computational methods are available today.

In response to a resurging interest in computational symmetry with the vision community, this timely and unique workshop/tutorial/competition is organized to investigate this potentially powerful intermediate level tool.

The event has three main parts: (1) a multidisciplinary perspective on the importance and lasting impact of symmetry, presented by a worldwide group of distinguished speakers;

(2) a detailed summary of the mathematical theory, state of the art algorithms and a diverse set of applications (successes and failures); and

(3) the algorithms and the outcome of the symmetry detection competition, presented by the top three performers on the benchmarked symmetry detection algorithm competition.

Active participations by computer vision researchers, especially graduate students, in this event are expected, leading to broadened understanding and appreciation of symmetry in all participants, as well as an acute and lasting impact to their research and their use of computational symmetry tools. A website with the content of the workshop/tutorial, the competition process and final results is set up before and augmented after the workshop, for public access.

Project Report

Symmetry is a pervasive phenomenon presenting itself in all forms and scales in natural and man-made environments, from galaxies to biological structures as well as in the arts. Much of our understanding of the world is based on the perception and recognition of repeated patterns that are generalized by the mathematical concept of symmetries. Humans and animals have an innate ability to perceive and take advantage of symmetry in everyday life, but harnessing this powerful insight for machine intelligence remains an elusive goal for computer science. Though the term Computational Symmetry was formally defined by the PI in 2000, referring to algorithmic treatments of symmetries, seeking symmetries (primarily reflection symmetry) automatically by programs from digital data has been attempted for over four decades without - a common image database - a set of annotated training data - a set of publicly available baseline algorithms to be compared against - a benchmark study - a set of evaluation standards to gauge the progress in the field of automatic symmetry detection from real images Thus the goal of this project was set to fulfill these gaps through a sequence of activities supported this NSF grant including organizing - a full-day tutorial on "Computational Symmetry: Past, Present, and Future" ( during European Conference on Computer Vision (ECCV) 2010 - a full-day competition/workshop on "Symmetry Detection from Real World Images" ( during IEEE Computer Vision and Pattern Recognition Conference 2011 This is the first ever competition for symmetry detection algorithms. Though the scale was relatively small (ten submissions worldwide), the impact is huge. For the first time, the publicly available image datasets are categorized and annotated into reflection, rotation and translation symmetries respectively (, which has already been used in several published papers in computer vision. The submitted algorithms are evaluated objectively and quantitatively. Evaluation standards are also made publicly available as well as the detailed outcomes ( Since symmetry is a common concept in human perception which is relevant in many different scientific fields as well as in ones daily lives, the PI and her team have reached out to the general public for their voluntary contributions of photos with real world symmetries. A call for photo submission was set up on Flickr ( 144 photos have been collected so far and some of them are used for the competition. The number of photos on this site continues to grow to this day. Major findings: Symmetry detection from real world images is a very difficult problem in computer vision. This competition has collected state of the art algorithms for three types of symmetries: reflection, rotation and translation. However, the outcome of the competition 2011 is disappointing in that all the submitted algorithms perform no better than the baseline algorithms (both of the baseline algorithms are publicly available). The baseline algorithms are, for rotation and reflection symmetry detection – Loy,G. and Eklundh,J. (2006), Detecting symmetry and symmetric constellations of features, ECCV. and for translation symmetry detection in 2D (distorted wallpaper patterns) -- M. Park, K. Brocklehurst, R. T. Collins, and Y. Liu (2009), Deformed Lattice Detection in Real-World Images using Mean-Shift Belief Propagation, IEEE Transaction on Pattern Analysis and Machine Intelligence (TPAMI). Vol. 31, No. 10. Nevertheless, the outcome of this project has fulfilled a long lasting gap in computer vision as expected – a benchmarked image database, a set of baseline algorithms and a set of evaluation standards for reflection, rotation and translation symmetry detection algorithms respectively. Researchers beyond computer vision community can use these data sets and algorithms to facilitate pattern discovery in their respective fields. A detailed summary of the first symmetry detection competition supported by US NSF can be found in: Ingmar Rauschert, Kyle Brocklehurst , Somesh Kashyap, Jingchen Liu and Yanxi Liu, "First Symmetry Detection Competition: Summary and Results", (2011). Tech Report, Published Bibliography: CSE Dept Technical Report No. CSE11-012, Penn State University The first paper on quantitative evaluation of symmetry detection algorithm performance: 'Performance Evaluation of State-of-the-Art Discrete Symmetry Detection Algorithms' by Park, Lee, Chen, Kashyap, Butt and Liu (CVPR'08) Besides the generous support of NSF, this sequence of activities has been carried out under the strong support and the watching eyes of this advisory committee: Jacob Feldman (Rutgers) Richard Hartley (ANU) Takeo Kanade (CMU) Jitendra Malik (U.C. Berkeley) Doris Schattschneider (Moravian College) Marjorie Senechal (Smith College) Christopher Tyler (SKBIC) Luc Van Gool (ETH Zurich & University of Leuven) Laurent Younes (Johns Hopkins University) Alan Yuille (UCLA) Andrew Zisserman (Oxford)

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Pennsylvania State University
University Park
United States
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