Context-free attentional operators: the generalized symmetry transform
International Journal of Computer Vision - Special issue on qualitative vision
A hough transform technique for the detection of reflectional symmetry and skew-symmetry
Pattern Recognition Letters
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting, localizing and grouping repeated scene elements from an image
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Symmetry Detection by Random Sampling and Voting Process
ICIAP '99 Proceedings of the 10th International Conference on Image Analysis and Processing
A Reflective Symmetry Descriptor for 3D Models
Algorithmica
Symmetry descriptors and 3D shape matching
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A Spectral Technique for Correspondence Problems Using Pairwise Constraints
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Augmented planar reflective symmetry transform
The Visual Computer: International Journal of Computer Graphics
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Partial Similarity of Objects, or How to Compare a Centaur to a Horse
International Journal of Computer Vision
Partial intrinsic reflectional symmetry of 3D shapes
ACM SIGGRAPH Asia 2009 papers
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
Segmenting periodic reliefs on triangle meshes
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constructing regularity feature trees for solid models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Discovering texture regularity as a higher-order correspondence problem
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
A graph-based approach to symmetry detection
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
Characterizing structural relationships in scenes using graph kernels
ACM SIGGRAPH 2011 papers
Exploring collections of 3D models using fuzzy correspondences
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Computer Graphics Forum
The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
ACM SIGGRAPH 2012 Courses
Microtiles: Extracting Building Blocks from Correspondences
Computer Graphics Forum
Multi-scale partial intrinsic symmetry detection
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Skeleton-based intrinsic symmetry detection on point clouds
Graphical Models
Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry
ACM Transactions on Graphics (TOG)
Shape matching via quotient spaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Weak convex decomposition by lines-of-sight
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We introduce the Symmetry Factored Embedding (SFE) and the Symmetry Factored Distance (SFD) as new tools to analyze and represent symmetries in a point set. The SFE provides new coordinates in which symmetry is "factored out," and the SFD is the Euclidean distance in that space. These constructions characterize the space of symmetric correspondences between points -- i.e., orbits. A key observation is that a set of points in the same orbit appears as a clique in a correspondence graph induced by pairwise similarities. As a result, the problem of finding approximate and partial symmetries in a point set reduces to the problem of measuring connectedness in the correspondence graph, a well-studied problem for which spectral methods provide a robust solution. We provide methods for computing the SFE and SFD for extrinsic global symmetries and then extend them to consider partial extrinsic and intrinsic cases. During experiments with difficult examples, we find that the proposed methods can characterize symmetries in inputs with noise, missing data, non-rigid deformations, and complex symmetries, without a priori knowledge of the symmetry group. As such, we believe that it provides a useful tool for automatic shape analysis in applications such as segmentation and stationary point detection.