Abstract
In this paper we provide an algorithm to decide (or, to help the decision about) whether some repeatedly occurring pattern in a digital image can be considered to have periodical nature or not. Our approach extracts specific image components and represent them by single pixels. To decide upon the gridness nature of the resulting point set we use lattice theory and the LLL algorithm to fit lattices to the point set, and an efficient lattice point counting method of Barvinok. With this work we complete some of our corresponding former results, where the fitting of the lattice ignored possible holes inside the point set. Namely, now after some appropriate transformations we consider the convex hull of the point set which way we can detect and punish such fitted lattice points that fall in holes of the original point set, or equivalently image pattern. As a practical demonstration of our method we present how it can be applied to recognize segmentation errors of atypical/typical pigmented networks in skin lesion images.
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Acknowledgements
Research was supported in part by the project EFOP-3.6.2-16-2017-00015 supported by the European Union and the State of Hungary, co-financed by the European Social Fund, and by the NKFIH grants K115479 and K128088.
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Hajdu, L., Harangi, B., Tiba, A., Hajdu, A. (2019). Detecting Periodicity in Digital Images by the LLL Algorithm. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_78
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DOI: https://doi.org/10.1007/978-3-030-27550-1_78
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