Vitaliy Kurlin
A fast and robust algorithm to count topologically persistent holes in noisy clouds
Kurlin, Vitaliy
Authors
Abstract
Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in noisy clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary contours when the cloud is analyzed at all possible scales. We design the algorithm to count holes that are most persistent in the filtration of offsets (neighborhoods) around given points. The input is a cloud of n points in the plane without any user-defined parameters. The algorithm has a near linear time and a linear space O(n). The output is the array (number of holes, relative persistence in the filtration). We prove theoretical guarantees when the algorithm finds the correct number of holes (components in the complement) of an unknown shape approximated by a cloud.
Citation
Kurlin, V. (2014). A fast and robust algorithm to count topologically persistent holes in noisy clouds.
Conference Name | CVPR : Computer Vision and Pattern Recognition |
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Conference Location | Columbus, Ohio, USA |
Start Date | Jun 24, 2023 |
Publication Date | 2014 |
Deposit Date | May 14, 2014 |
Publicly Available Date | Mar 28, 2024 |
Series Title | Proceedings of IEEE Conference CVPR |
Publisher URL | http://www.cv-foundation.org/openaccess/CVPR2014.py |
Files
Accepted Conference Proceeding
(1.5 Mb)
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