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» Computing persistent homology
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TVCG
2010
162views more  TVCG 2010»
15 years 4 months ago
Computing Robustness and Persistence for Images
—We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to a continuous function, we study the robustness of homology c...
Paul Bendich, Herbert Edelsbrunner, Michael Kerber
CAIP
2007
Springer
170views Image Analysis» more  CAIP 2007»
15 years 10 months ago
Image Segmentation Using Topological Persistence
Abstract. This paper presents a new hybrid split-and-merge image segmentation method based on computational geometry and topology using persistent homology. The algorithm uses edge...
David Letscher, Jason Fritts
COMPGEOM
2011
ACM
14 years 10 months ago
An output-sensitive algorithm for persistent homology
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homo...
Chao Chen, Michael Kerber
COMPGEOM
2011
ACM
14 years 10 months ago
Zigzag persistent homology in matrix multiplication time
We present a new algorithm for computing zigzag persistent homology, an algebraic structure which encodes changes to homology groups of a simplicial complex over a sequence of sim...
Nikola Milosavljevic, Dmitriy Morozov, Primoz Skra...
MFCS
2010
Springer
15 years 4 months ago
Persistent Homology under Non-uniform Error
Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classe...
Paul Bendich, Herbert Edelsbrunner, Michael Kerber...