Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate convex decomposition of polyhedra
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Model Composition from Interchangeable Components
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Upright orientation of man-made objects
ACM SIGGRAPH 2008 papers
Randomized cuts for 3D mesh analysis
ACM SIGGRAPH Asia 2008 papers
Curve skeleton extraction from incomplete point cloud
ACM SIGGRAPH 2009 papers
Approximate convex decomposition of polygons
Computational Geometry: Theory and Applications
Hierarchical convex approximation of 3D shapes for fast region selection
SGP '08 Proceedings of the Symposium on Geometry Processing
Illustrating how mechanical assemblies work
ACM SIGGRAPH 2010 papers
Learning 3D mesh segmentation and labeling
ACM SIGGRAPH 2010 papers
Symmetry factored embedding and distance
ACM SIGGRAPH 2010 papers
A Measure of Non-convexity in the Plane and the Minkowski Sum
Discrete & Computational Geometry
Joint shape segmentation with linear programming
Proceedings of the 2011 SIGGRAPH Asia Conference
Variational mesh decomposition
ACM Transactions on Graphics (TOG)
Minimum near-convex decomposition for robust shape representation
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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We define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly convex regions. The decomposition is applied without explicitly measuring the convexity rank. The method merely amounts to a spectral clustering of a matrix representing the all-pairs line of sight. Our method can be directly applied on an oriented point cloud and does not require any topological information, nor explicit concavity or convexity measures. We demonstrate the efficiency of our algorithm on a large number of examples and compare them qualitatively with competitive approaches.