Triangulating a simple polygon in linear time
Discrete & Computational Geometry
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
Folding flat silhouettes and wrapping polyhedral packages: new results in computational origami
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Linear-time triangulation of a simple polygon made easier via randomization
Proceedings of the sixteenth annual symposium on Computational geometry
Convex Decomposition of Simple Polygons
ACM Transactions on Graphics (TOG)
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Bounds on the Length of Convex Partitions of Polygons
Proceedings of the Fourth Conference on Foundations of Software Technology and Theoretical Computer Science
Polygon decomposition based on the straight line skeleton
Proceedings of the nineteenth annual symposium on Computational geometry
Decomposing a polygon into its convex parts
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Approximate convex decomposition
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
IEEE Transactions on Computers
Measuring Concavity on a Rectangular Mosaic
IEEE Transactions on Computers
An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge
IEEE Transactions on Computers
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Shape partitioning by convexity
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Convex Partitions with 2-Edge Connected Dual Graphs
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Hierarchical convex approximation of 3D shapes for fast region selection
SGP '08 Proceedings of the Symposium on Geometry Processing
A system to detect rooms in architectural floor plan images
DAS '10 Proceedings of the 9th IAPR International Workshop on Document Analysis Systems
Articulation-invariant representation of non-planar shapes
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
ACCORD: with approximate covering of convex orthogonal decomposition
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Convex partitions with 2-edge connected dual graphs
Journal of Combinatorial Optimization
Automatic generation of suboptimal navmeshes
MIG'11 Proceedings of the 4th international conference on Motion in Games
SMI 2012: Full α-Decomposition of polygons
Computers and Graphics
A clustering-based ensemble technique for shape decomposition
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Real-Time markerless hand gesture recognition with depth camera
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
Approximate partitioning of 2D objects into orthogonally convex components
Computer Vision and Image Understanding
Perceptually friendly shape decomposition by resolving segmentation points with minimum cost
Journal of Visual Communication and Image Representation
Real time dynamic fracture with volumetric approximate convex decompositions
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ε-Isometry based shape approximation for image content representation
Signal Processing
Real-time Hand Gesture Recognition from Depth Images Using Convex Shape Decomposition Method
Journal of Signal Processing Systems
Weak convex decomposition by lines-of-sight
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Hi-index | 0.00 |
We propose a strategy to decompose a polygon, containing zero or more holes, into ''approximately convex'' pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignore less significant artifacts such as wrinkles and surface texture. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant non-convex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of 'increasingly convex' decompositions. A user specified tolerance determines the degree of concavity that will be allowed in the lowest level of the hierarchy. Our algorithm computes an ACD of a simple polygon with n vertices and r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard or, if the polygon has no holes, takes O(nr^2) time. Models and movies can be found on our web-pages at: http://parasol.tamu.edu/groups/amatogroup/.