Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Computation of the Smith normal form of polynomial matrices
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
On computing greatest common divisors with polynomials given by black boxes for their evaluations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
European Journal of Combinatorics - In memoriam François Jaeger
Discrete & Computational Geometry
Interface surfaces for protein-protein complexes
Journal of the ACM (JACM)
Persistence Diagrams of Cortical Surface Data
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Image segmentation using topological persistence
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
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In this paper techniques from persistent homology are generalized to homotopy groups and to algebraic invariants from knot theory. We define the persistent Alexander module, which can be used to detect knotting in a complex and determine when the knotting changes when viewed from different scales. Algorithms that use the persistent Alexander module are also presented and applied to examples including protein structures. While the basic definition of persistent homotopy is known, this is the first work to use it successfully for computations.