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Topological persistence on a Jordan curve

Publication ,  Journal Article
Zheng, Y; Gu, S; Tomasi, C
Published in: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
October 23, 2012

Topological persistence measures the resilience of extrema of a function to perturbations, and has received increasing attention in computer graphics, visualization and computer vision. While the notion of topological persistence for piece-wise linear functions defined on a simplicial complex has been well studied, the time complexity of all the known algorithms are super-linear (e.g. O(n log n)) in the size n of the complex. We give an O(n) algorithm to compute topological persistence for a function defined on a Jordan curve. To the best of our knowledge, our algorithm is the first to attain linear asymptotic complexity, and is asymptotically optimal. We demonstrate the usefulness of persistence in shape abstraction and compression. © 2012 IEEE.

Duke Scholars

Published In

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

DOI

ISSN

1520-6149

Publication Date

October 23, 2012

Start / End Page

3693 / 3696
 

Citation

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Zheng, Y., Gu, S., & Tomasi, C. (2012). Topological persistence on a Jordan curve. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 3693–3696. https://doi.org/10.1109/ICASSP.2012.6288718
Zheng, Y., S. Gu, and C. Tomasi. “Topological persistence on a Jordan curve.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, October 23, 2012, 3693–96. https://doi.org/10.1109/ICASSP.2012.6288718.
Zheng Y, Gu S, Tomasi C. Topological persistence on a Jordan curve. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012 Oct 23;3693–6.
Zheng, Y., et al. “Topological persistence on a Jordan curve.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Oct. 2012, pp. 3693–96. Scopus, doi:10.1109/ICASSP.2012.6288718.
Zheng Y, Gu S, Tomasi C. Topological persistence on a Jordan curve. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012 Oct 23;3693–3696.

Published In

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

DOI

ISSN

1520-6149

Publication Date

October 23, 2012

Start / End Page

3693 / 3696