Discrete & Computational Geometry
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Topology guaranteeing manifold reconstruction using distance function to noisy data
Proceedings of the twenty-second annual symposium on Computational geometry
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Stability of Persistence Diagrams
Discrete & Computational Geometry
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Optimal homologous cycles, total unimodularity, and linear programming
Proceedings of the forty-second ACM symposium on Theory of computing
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tracking a generator by persistence
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
SIAM Journal on Computing
Annotating simplices with a homology basis and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications. In this paper we present an algorithm to compute a set of loops from a point data that presumably sample a smooth manifold M ⊂ Rd. These loops approximate a shortest basis of the one dimensional homology group H1(M) over coefficients in finite field Z2. Previous results addressed the issue of computing the rank of the homology groups from point data, but there is no result on approximating the shortest basis of a manifold from its point sample. In arriving our result, we also present a polynomial time algorithm for computing a shortest basis of H1 (Κ) for any finite simplicial complex Κ whose edges have non-negative weights.