@article{geiger_kogan_2021, title={Non-congruent non-degenerate curves with identical signatures}, volume={63}, ISSN={["1573-7683"]}, url={https://doi.org/10.1007/s10851-020-01015-x}, DOI={10.1007/s10851-020-01015-x}, abstractNote={While the equality of differential signatures (Calabi et al, Int. J. Comput. Vis. 26: 107-135, 1998) is known to be a necessary condition for congruence, it is not sufficient (Musso and Nicolodi, J. Math Imaging Vis. 35: 68-85, 2009). Hickman (J. Math Imaging Vis. 43: 206-213, 2012, Theorem 2) claimed that for non-degenerate planar curves, equality of Euclidean signatures implies congruence. We prove that while Hickman's claim holds for simple, closed curves with simple signatures, it fails for curves with non-simple signatures. In the later case, we associate a directed graph with the signature and show how various paths along the graph give rise to a family of non-congruent, non-degenerate curves with identical signatures. Using this additional structure, we formulate congruence criteria for non-degenerate, closed, simple curves and show how the paths reflect the global and local symmetries of the corresponding curve.}, number={5}, journal={JOURNAL OF MATHEMATICAL IMAGING AND VISION}, publisher={Springer Science and Business Media LLC}, author={Geiger, Eric and Kogan, Irina A.}, year={2021}, month={Jun}, pages={601–625} }
 @article{geiger_kogan_2021, title={Non-congruent non-degenerate curves with identical signatures (Feb, 1007/s10851-020-01015-x, 2021)}, volume={63}, ISBN={1573-7683}, url={https://doi.org/10.1007/s10851-021-01028-0}, DOI={10.1007/s10851-021-01028-0}, abstractNote={A correction to this paper has been published: https://doi.org/10.1007/s10851-021-01028-0}, number={6}, journal={JOURNAL OF MATHEMATICAL IMAGING AND VISION}, publisher={Springer Science and Business Media LLC}, author={Geiger, Eric and Kogan, Irina A.}, year={2021}, pages={776–776} }