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» Computing persistent homology
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TVCG
2010
162views more  TVCG 2010»
13 years 9 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»
14 years 2 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
13 years 2 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
13 years 2 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
13 years 9 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...