Introduction to Algorithms
Multiresolution feature extraction for unstructured meshes
Proceedings of the conference on Visualization '01
Polygon decomposition based on the straight line skeleton
Proceedings of the nineteenth annual symposium on Computational geometry
Convex decompositions of polyhedra
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Simultaneous shape decomposition and skeletonization
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Variational, meaningful shape decomposition
ACM SIGGRAPH 2006 Sketches
Approximate convex decomposition of polyhedra
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Example-based skeleton extraction
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Convex hull covering of polygonal scenes for accurate collision detection in games
GI '08 Proceedings of graphics interface 2008
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Randomized cuts for 3D mesh analysis
ACM SIGGRAPH Asia 2008 papers
Approximate convex decomposition of polyhedra and its applications
Computer Aided Geometric Design
Approximate convex decomposition and its applications
Approximate convex decomposition and its applications
A benchmark for 3D mesh segmentation
ACM SIGGRAPH 2009 papers
Combinatorial shape decomposition
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
Meaningful 3D shape partitioning using Morse functions
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Object Decomposition Via Curvilinear Skeleton Partition
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
Minimum near-convex decomposition for robust shape representation
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Proceedings of the 26th annual ACM symposium on User interface software and technology
SMI 2013: Towards building smart self-folding structures
Computers and Graphics
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Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n"c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n"c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31].