Incremental-decremental algorithm for computing AT-models and persistent homology

Authors:
Rocio Gonzalez-Diaz;Adrian Ion;Maria Jose Jimenez;Regina Poyatos
Affiliations:
Applied Math Dep. (I), School of Computer Engineering, University of Seville;Pattern Recognition and Image Processing Group, Vienna University of Technology and Institute of Science and Technology, Austria;Applied Math Dep. (I), School of Computer Engineering, University of Seville;Applied Math Dep. (I), School of Computer Engineering, University of Seville
Venue:
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Year:
2011

Citing 13
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Abstract

In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one for computing persistent homology [6,14,15]. We also present a decremental algorithm for computing AT-models that allows to extend the persistence computation to a wider setting. Finally, we show how to combine incremental and decremental techniques for persistent homology computation.