Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Parts of Visual Form: Computational Aspects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Analyzing nonconvex 2D and 3D patterns
Computer Vision and Image Understanding
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Polygon decomposition based on the straight line skeleton
Proceedings of the nineteenth annual symposium on Computational geometry
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
IEEE Transactions on Computers
Approximate convex decomposition of polyhedra and its applications
Computer Aided Geometric Design
Approximate convex decomposition of polygons
Computational Geometry: Theory and Applications
Segmenting animated objects into near-rigid components
The Visual Computer: International Journal of Computer Graphics
Hierarchical convex approximation of 3D shapes for fast region selection
SGP '08 Proceedings of the Symposium on Geometry Processing
Combinatorial shape decomposition
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
Fast hierarchical animated object decomposition using approximately invariant signature
The Visual Computer: International Journal of Computer Graphics
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Minimum near-convex decomposition for robust shape representation
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Dynamic Minkowski sums under scaling
Computer-Aided Design
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Decomposing a shape into visually meaningful parts comes naturally to humans, but recreating this fundamental operation in computers has been shown to be difficult. Similar challenges have puzzled researchers in shape reconstruction for decades. In this paper, we recognize the strong connection between shape reconstruction and shape decomposition at a fundamental level and propose a method called @a-decomposition. The @a-decomposition generates a space of decompositions parameterized by @a, the diameter of a circle convolved with the input polygon. As we vary the value of @a, some structural features appear and disappear quickly while others persist. Therefore, by analyzing the persistence of the features, we can determine better decompositions that are more robust to both geometrical and topological noises.