Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Symmetry as a Continuous Feature
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Computational Model for Periodic Pattern Perception Based on Frieze and Wallpaper Groups
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry descriptors and 3D shape matching
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Deformation Invariant Image Matching
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Accurate detection of symmetries in 3D shapes
ACM Transactions on Graphics (TOG)
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Combining Cues: Shape from Shading and Texture
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
ACM SIGGRAPH 2007 papers
Folding meshes: hierarchical mesh segmentation based on planar symmetry
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Deformed Lattice Discovery Via Efficient Mean-Shift Belief Propagation
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Symmetry Detection for Multi-object Using Local Polar Coordinate
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
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
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
RepFinder: finding approximately repeated scene elements for image editing
ACM SIGGRAPH 2010 papers
Detecting symmetry and symmetric constellations of features
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Structure-preserving retargeting of irregular 3D architecture
Proceedings of the 2011 SIGGRAPH Asia Conference
Shape palindromes: analysis of intrinsic symmetries in 2d articulated shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Microtiles: Extracting Building Blocks from Correspondences
Computer Graphics Forum
Skeleton-based intrinsic symmetry detection on point clouds
Graphical Models
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Automatic detection of symmetries, regularity, and repetitive structures in 3D geometry is a fundamental problem in shape analysis and pattern recognition with applications in computer vision and graphics. Especially challenging is to detect intrinsic regularity, where the repetitions are on an intrinsic grid, without any apparent Euclidean pattern to describe the shape, but rising out of (near) isometric deformation of the underlying surface. In this paper, we employ multidimensional scaling to reduce the problem of intrinsic structure detection to a simpler problem of 2D grid detection. Potential 2D grids are then identified using an autocorrelation analysis, refined using local fitting, validated, and finally projected back to the spatial domain. We test the detection algorithm on a variety of scanned plaster models in presence of imperfections like missing data, noise and outliers. We also present a range of applications including scan completion, shape editing, super-resolution, and structural correspondence.