Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Salient geometric features for partial shape matching and similarity
ACM Transactions on Graphics (TOG)
Hierarchical mesh segmentation based on fitting primitives
The Visual Computer: International Journal of Computer Graphics
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Shape Classification Using the Inner-Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Folding meshes: hierarchical mesh segmentation based on planar symmetry
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Randomized cuts for 3D mesh analysis
ACM SIGGRAPH Asia 2008 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
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
Symmetry factored embedding and distance
ACM SIGGRAPH 2010 papers
Skeleton-based intrinsic symmetry detection on point clouds
Graphical Models
Structure-aware shape processing
SIGGRAPH Asia 2013 Courses
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We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape. Since different point pairs can share a common point, shape regions covered by points in different scale clusters can overlap. We introduce the symmetry scale matrix (SSM), where each entry estimates the likelihood two point pairs belong to symmetries at the same scale. The pair-to-pair symmetry affinity is computed based on a pair signature which encodes scales. We perform spectral clustering using the SSM to obtain the scale clusters. Then for all points belonging to the same scale cluster, we perform the second-level spectral clustering, based on a novel point-to-point symmetry affinity measure, to extract partial symmetries at that scale. We demonstrate our algorithm on complex shapes possessing rich symmetries at multiple scales.