Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
An upper bound on the sum of squares of degrees in a graph
Discrete Mathematics
Enumerating all connected maximal common subgraphs in two graphs
Theoretical Computer Science
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
The boost graph library: user guide and reference manual
The boost graph library: user guide and reference manual
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Discrete & Computational Geometry
Discrete Mathematics and Its Applications: And Its Applications
Discrete Mathematics and Its Applications: And Its Applications
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Communications of the ACM - 50th anniversary issue: 1958 - 2008
Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension
Proceedings of the twenty-fifth annual symposium on Computational geometry
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
A barcode shape descriptor for curve point cloud data
Computers and Graphics
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Algorithms and theory of computation handbook
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Technical Section: Efficient construction of the Čech complex
Computers and Graphics
Computational topology in text mining
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
Computational Geometry: Theory and Applications
Geometry in the space of persistence modules
Proceedings of the twenty-ninth annual symposium on Computational geometry
Towards topological analysis of high-dimensional feature spaces
Computer Vision and Image Understanding
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The Vietoris-Rips complex characterizes the topology of a point set. This complex is popular in topological data analysis as its construction extends easily to higher dimensions. We formulate a two-phase approach for its construction that separates geometry from topology. We survey methods for the first phase, give three algorithms for the second phase, implement all algorithms, and present experimental results. Our software can be used also for constructing any clique complex, such as the weak witness complex.