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109
A planarreflective symmetry transform for 3d shapes
 ACM Transactions on Graphics (Proc. Siggraph
, 2006
"... Copyright © 2006 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and ..."
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Cited by 104 (8 self)
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Copyright © 2006 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.
A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each Ndimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there ar ..."
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Cited by 89 (18 self)
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We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each Ndimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are seven frieze groups describing monochrome patterns that repeat along one direction and 17 wallpaper groups for patterns that repeat along two linearly independent directions to tile the plane. We develop a set of computer algorithms that "understand" a given periodic pattern by automatically finding its underlying lattice, identifying its symmetry group, and extracting its representative motifs. We also extend this computational model for nearperiodic patterns using geometric AIC. Applications of such a computational model include pattern indexing, texture synthesis, image compression, and gait analysis.
3D Symmetry Detection Using The Extended Gaussian Image
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Symmetry detection is important in the area of computer vision. A 3D symmetry detection algorithm is presented in this correspondence. The symmetry detection problem is converted to the correlation of the Gaussian image. Once the Gaussian image of the object has been obtained, the algorithm is inde ..."
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Cited by 77 (0 self)
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Symmetry detection is important in the area of computer vision. A 3D symmetry detection algorithm is presented in this correspondence. The symmetry detection problem is converted to the correlation of the Gaussian image. Once the Gaussian image of the object has been obtained, the algorithm is independent of the input format. The algorithm can handle different kinds of images or objects. Simulated and real images have been tested in a variety of formats, and the results show that the symmetry can be determined using the Gaussian image.
A Reflective Symmetry Descriptor for 3D Models
 ALGORITHMICA
, 2004
"... Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represent ..."
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Cited by 71 (8 self)
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Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm that computes the symmetry descriptor in O(N 4 log N) time for an N × N × N voxel grid and computes a multiresolution approximation in O(N 3 log N) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.
Detecting symmetry and symmetric constellations of features
 In ECCV
, 2006
"... Abstract. A novel and efficient method is presented for grouping feature points on the basis of their underlying symmetry and characterising the symmetries present in an image. We show how symmetric pairs of features can be efficiently detected, how the symmetry bonding each pair is extracted and ev ..."
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Cited by 65 (3 self)
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Abstract. A novel and efficient method is presented for grouping feature points on the basis of their underlying symmetry and characterising the symmetries present in an image. We show how symmetric pairs of features can be efficiently detected, how the symmetry bonding each pair is extracted and evaluated, and how these can be grouped into symmetric constellations that specify the dominant symmetries present in the image. Symmetries over all orientations and radii are considered simultaneously, and the method is able to detect local or global symmetries, locate symmetric figures in complex backgrounds, detect bilateral or rotational symmetry, and detect multiple incidences of symmetry. 1
Gait Sequence Analysis using Frieze Patterns
 Proc. of European Conf. on Computer Vision
, 2002
"... We analyze walking people using a gait sequence representation that bypasses the need for frametoframe tracking of body parts. ..."
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Cited by 65 (2 self)
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We analyze walking people using a gait sequence representation that bypasses the need for frametoframe tracking of body parts.
Shape from Symmetry
, 2005
"... We describe a technique for reconstructing probable occluded surfaces from 3D range images. The technique exploits the fact that many objects possess shape symmetries that can be recognized even from partial 3D views. Our approach identifies probable symmetries and uses them to extend the partial ..."
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Cited by 50 (0 self)
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We describe a technique for reconstructing probable occluded surfaces from 3D range images. The technique exploits the fact that many objects possess shape symmetries that can be recognized even from partial 3D views. Our approach identifies probable symmetries and uses them to extend the partial 3D shape model into the occluded space. To accommodate objects consisting of multiple parts, we describe a technique for segmenting objects into parts characterized by different symmetries. Results are provided for a realworld database of 3D range images of common objects, acquired through an active stereo rig.
Full and Partial Symmetries of NonRigid Shapes
 INTERNATIONAL JOURNAL OF COMPUTER VISION
"... Symmetry and selfsimilarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection ..."
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Cited by 43 (10 self)
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Symmetry and selfsimilarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for nonrigid ones: extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we present a generalization of symmetries for nonrigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification.
A Reflective Symmetry Descriptor
 European Conference on Computer Vision (ECCV
, 2002
"... Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. ..."
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Cited by 42 (7 self)
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Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists.
Detecting Symmetry in Grey Level Images: The Global Optimization Approach
 In Proceedings of the 13th International Conference on Pattern Recognition, volume I
, 1996
"... The detection of significant local reflectional symmetry in grey level images is considered. Prior segmentation is not assumed, and it is intended that the results could be used for guiding visual attention and for providing side information to segmentation algorithms. A local measure of reflectio ..."
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Cited by 31 (2 self)
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The detection of significant local reflectional symmetry in grey level images is considered. Prior segmentation is not assumed, and it is intended that the results could be used for guiding visual attention and for providing side information to segmentation algorithms. A local measure of reflectional symmetry that transforms the symmetry detection problem to a global optimization problem is defined. Reflectional symmetry detection becomes equivalent to finding the global maximum of a complicated multimodal function parameterized by the location of the center of the supporting region, its size, and the orientation of the symmetry axis. Unlike previous approaches, time consuming exhaustive search is avoided. A global optimization algorithm for solving the problem is presented. It is related to genetic algorithms and to adaptive random search techniques. The efficiency of the suggested algorithm is experimentally demonstrated. Just one thousand evaluations of the local symmetry measure are typically needed in order to locate the dominant symmetry in natural test images.