Abstract
To avoid the destruction of the colour topology of image and the loss of details caused by the existing morphological operators, new colour morphological operators are proposed based on formal concept analysis (FCA). The main idea is to define a set of structuring elements (SEs) for morphological operators, one for each pixel of the image, which can be adapted to the image content. FCA tools, which have good performance in structuring information, are used to find similar pixels that can form SEs. Then, the new operators are defined and applied to different colour spaces. Experimental results show that the proposed operators outperform other kind of operators in preserving detail information and the structures within colour images, which improve the precision of image processing.
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Salazar-Colores, S., Ramos-Arreguín, J.-M., Echeverri, C.J.O., Cabal-Yepez, E., Pedraza-Ortega, J.-C., Rodriguez-Resendiz, J.: Image dehazing using morphological opening, dilation and gaussian filtering. Signal Image Video Process. 12(7), 1329–1335 (2018)
Moser, G., Zerubia, J.: Mathematical Models for Remote Sensing Image Processing. Springer, Berlin (2018)
Baug, A., Choudhury, N.R., Ghosh, R., Dalai, S., Chatterjee, B.: Identification of single and multiple partial discharge sources by optical method using mathematical morphology aided sparse representation classifier. IEEE Trans. Dielectr. Electr. Insul. 24(6), 3703–3712 (2017)
Wang, P., Yao, Y.: Ce3: a three-way clustering method based on mathematical morphology. Knowl. Based Syst. 155, 54–65 (2018)
Aptoula, E., Lefèvre, S.: On lexicographical ordering in multivariate mathematical morphology. Pattern Recognit. Lett. 29(2), 109–118 (2008)
Angulo, J.: Morphological colour operators in totally ordered lattices based on distances: application to image filtering, enhancement and analysis. Comput. Vis. Image Underst. 107(1–2), 56–73 (2007)
Aptoula, E., Lefèvre, S.: A comparative study on multivariate mathematical morphology. Pattern Recognit. 40(11), 2914–2929 (2007)
Ya-ning, G.Y.L., Jun-ping, W.: Color vector morphological operators on graph space. Acta Electron. Sin. 43(3), 0372–2112 (2015)
Bouchet, A., Alonso, P., Pastore, J.I., Montes, S., Díaz, I.: Fuzzy mathematical morphology for color images defined by fuzzy preference relations. Pattern Recognit. 60, 720–733 (2016)
González-Castro, V., Debayle, J., Pinoli, J.-C.: Color adaptive neighborhood mathematical morphology and its application to pixel-level classification. Pattern Recognit. Lett. 47, 50–62 (2014)
Pinoli, J.-C., Debayle, J.: General adaptive neighborhood mathematical morphology. In: 2009 16th IEEE International Conference on Image Processing (ICIP), pp. 2249–2252. IEEE (2009)
Bibiloni, P., Gonzalez-Hidalgo, M., Massanet, S.: Soft color morphology. In: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–6. IEEE (2017)
Bibiloni, P., González-Hidalgo, M., Massanet, S.: Soft color morphology: a fuzzy approach for multivariate images. J. Math. Imaging Vis. 61(3), 394–410 (2019)
Subramanian, C.M., Cherukuri, A.K., Chelliah, C.: Role based access control design using three-way formal concept analysis. Int. J. Mach. Learn. Cybern. 9(11), 1807–1837 (2018)
Zhao, M., Zhang, S., Li, W., Chen, G.: Matching biomedical ontologies based on formal concept analysis. J. Biomed. Semant. 9(1), 11 (2018)
Couso, I., Borgelt, C., Hullermeier, E., Kruse, R.: Fuzzy sets in data analysis: from statistical foundations to machine learning. IEEE Comput. Intell. Mag. 14(1), 31–44 (2019)
Bloch, I.: Mathematical morphology, lattices, and formal concept analysis. In: 8th International Conference on Concept Lattices and Their Applications (CLA 2011)-Invited Conference, p. 1. Citeseer (2011)
Atif, J., Bloch, I., Hudelot, C.: Some relationships between fuzzy sets, mathematical morphology, rough sets, F-transforms, and formal concept analysis. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 24(Suppl 2), 1–32 (2016)
Bloch, I.: Morphological links between formal concepts and hypergraphs. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds.) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science, vol. 10225. Springer, Cham (2017)
Yoneda, Y., Sugiyama, M., Washio, T.: Learning graph representation via formal concept analysis. arXiv:1812.03395 (2018)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (2012)
Huynh-Thu, Q., Ghanbari, M.: Scope of validity of PSNR in image/video quality assessment. Electron. Lett. 44(13), 800–801 (2008)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P., et al.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
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This work was supported by the National Natural Science Foundation of China (No. 61872433).
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Zhao, L., Wang, J. & Li, Y. Colour morphological operators based on formal concept analysis. SIViP 14, 151–158 (2020). https://doi.org/10.1007/s11760-019-01536-y
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DOI: https://doi.org/10.1007/s11760-019-01536-y