We address the problem of computing these representative cycles, termed as persistent 1-cycles, for H1-persistent homology with Z2 coefficients. We propose an alternative set of meaningful persistent 1-cycles that can be computed with an efficient polynomial time algorithm. We also inspect the stability issues of the optimal persistent 1-cycles and the persistent 1-cycles computed by our algorithm with the observation that the perturbations of both cannot be properly bounded. We design a software, presented in this webpage which applies our algorithm to various datasets. Experiments on 3D point clouds, mineral structures, and images show the effectiveness of our algorithm in practice.
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Copyright: Jyamiti group at the Ohio State University. No commercial use of the software is permitted without proper license.