Abstract
The extension of the Hit-or-Miss transform (HMT) to grey-level images is difficult due to the problem of defining the complement of an image in this context. Thus, several extensions have been proposed in the literature avoiding the use of the complement. However, in the fuzzy framework, the complement is well-established by means of a fuzzy negation and the binary HMT can be extended preserving its geometrical interpretation. In this paper, we extend the binary HMT to a fuzzy HMT (FHMT) using the mathematical morphology based on t-norms. Some properties of this operator are studied and some initial experimental results are presented proving the potential of the FHMT in shape recognition and pattern matching.
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References
Al-Omari, M., Qahwaji, R., Colak, T., Ipson, S.: Morphological-based filtering of noise: Practical study on solar images. In: IEEE International Conference on Signal Processing and Communications, ICSPC 2007, pp. 1075–1078 (2007)
Aptoula, E., Lefèvre, S., Ronse, C.: A hit-or-miss transform for multivariate images. Pattern Recogn. Lett. 30(8), 760–764 (2009), http://dx.doi.org/10.1016/j.patrec.2009.02.007 , doi:10.1016/j.patrec.2009.02.007
Baczyński, M., Jayaram, B. (eds.): Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008)
Barat, C., Ducottet, C., Jourlin, M.: Pattern matching using morphological probing. In: Proc. of Int. Conf. on Image Processing, ICIP 2003, vol. 1, pp. 369–372 (2003), doi:10.1109/ICIP.2003.1246975
Beliakov, G., Pradera, A., Calvo, T. (eds.): Aggregation Functions: A Guide for Practitioners. STUDFUZZ, vol. 221. Springer, Heidelberg (2007)
Bloch, I., Maître, H.: Fuzzy mathematical morphologies: a comparative study. Pattern Recognition 28, 1341–1387 (1995)
Bloomberg, D.S., Maragos, P.: Generalized hit-miss operators. Proc SPIE 1350, Image Algebra and Morphological Image Processing 116, 116–128 (1990), http://dx.doi.org/10.1117/12.23580 , doi:10.1117/12.23580
Bouraoui, B., Ronse, C., Baruthio, J., Passat, N., Germain, P.: 3D segmentation of coronary arteries based on advanced mathematical morphology techniques. Computerized Medical Imaging and Graphics 34(5), 377–387 (2010), http://www.sciencedirect.com/science/article/pii/S0895611110000121 , doi:10.1016/j.compmedimag.2010.01.001
De Baets, B.: Fuzzy morphology: A logical approach. In: Ayyub, B.M., Gupta, M.M. (eds.) Uncertainty Analysis in Engineering and Science: Fuzzy Logic, Statistics, and Neural Network Approach, pp. 53–68. Kluwer Academic Publishers, Norwell (1997)
Deng, T.Q.: Fuzzy logic and mathematical morphology. Tech. rep., Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands (2000)
Dimitrova, D., Popov, A.: Finding face features in color images using fuzzy hit-or-miss transform. In: Proceedings of the 9th WSEAS International Conference on Fuzzy Systems, FS 2008, pp. 79–84. World Scientific and Engineering Academy and Society (WSEAS), Stevens Point (2008), http://dl.acm.org/citation.cfm?id=1416056.1416069
González, M., Ruiz-Aguilera, D., Torrens, J.: Algebraic properties of fuzzy morphological operators based on uninorms. In: Artificial Intelligence Research and Development. Frontiers in Artificial Intelligence and Applications, vol. 100, pp. 27–38. IOS Press, Amsterdam (2003)
González-Hidalgo, M., Mir-Torres, A., Ruiz-Aguilera, D., Torrens, J.: Fuzzy morphology based on uninorms: Image edge-detection. opening and closing. In: Tavares, J., Jorge, N. (eds.) Computational Vision and Medical Image Processing, pp. 127–133. Taylor & Francis Group, London (2008)
González-Hidalgo, M., Massanet, S., Torrens, J.: Discrete t-norms in a fuzzy mathematical morphology: Algebraic properties and experimental results. In: Proceedings of WCCI-FUZZ-IEEE, Barcelona, Spain, pp. 1194–1201 (2010)
Heijmaans, H.: Morphological Image Operators. Academic Press, Boston (1994)
Intajag, S., Paithoonwatanakij, K.: Automated boundary extraction by gradient fuzzy gray-scale hit-or-miss transformation. In: The 2000 IEEE Asia-Pacific Conference on Circuits and Systems, IEEE APCCAS 2000, pp. 465–468 (2000), doi:10.1109/APCCAS.2000.913537
Intajag, S., Paithoonwatanakij, K., Cracknell, A.: Iterative satellite image segmentation by fuzzy hit-or-miss and homogeneity index. IEEE Proceedings on Vision, Image and Signal Processing 153(2), 206–214 (2006), doi:10.1049/ip-vis:20045211
Jin, X., Davis, C.: Vector-guided vehicle detection from high-resolution satellite imagery. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2004, vol. 2, pp. 1095–1098 (2004), doi:10.1109/IGARSS.2004.1368603
Khosravi, M., Schafer, R.W.: Template matching based on a grayscale hit-or-miss transform. IEEE Trans. Image Processing 5(6), 1060–1066 (1996)
Klement, E., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)
Lefèvre, S., Weber, J.: Automatic building extraction in VHR images using advanced morphological operators. In: Urban Remote Sensing Joint Event, pp. 1–5 (2007), 10.1109/URS.2007.371825
Mansoor, A.B., Mian, A.S., Khan, A., Khan, S.A.: Fuzzy morphology for edge detection and segmentation. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part II. LNCS, vol. 4842, pp. 811–821. Springer, Heidelberg (2007), http://dl.acm.org/citation.cfm?id=1779090.1779177
Matheron, G.: Random Sets and Integral Geometry. Wiley (1975)
Murray, P., Marshall, S.: A new design tool for feature extraction in noisy images based on grayscale hit-or-miss transforms. IEEE T. Image Process. 20(7), 1938–1948 (2011), doi:10.1109/TIP.2010.2103952
Nachtegael, M., Kerre, E.E.: Classical and fuzzy approaches towards mathematical morphology. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing. STUDFUZZ, vol. 52, ch. 1, Physica-Verlag, New York (2000)
Naegel, B., Passat, N., Ronse, C.: a) Grey-level hit-or-miss transforms-Part I: Unified theory. Pattern Recognition 40, 635–647 (2007)
Naegel, B., Passat, N., Ronse, C.: b) Grey-level hit-or-miss transforms-Part II: Application to angiographic image processing. Pattern Recognition 40, 648–658 (2007)
Ouyang, Y.: On fuzzy implications determined by aggregation operators. Inform. Sci. 193, 153–162 (2012)
Perret, B., Lefèvre, S., Collet, C.: A robust hit-or-miss transform for template matching applied to very noisy astronomical images. Pattern Recognition 42, 2470–2480 (2009)
Popov, A.T.: General approach for fuzzy mathematical morphology. In: Proc. of 8th International Symposium on Mathematical Morphology (ISMM), pp. 39–48 (2007)
Raducanu, B., Graña, M.: A grayscale hit-or-miss transform based on level sets. In: Proc. IEEE Intl. Conf. Image Processing, Vancouver, BC, Canada, pp. 931–933 (2000)
Raducanu, B., Graña, M., Albizuri, X., d’Anjou, A.: A probabilistic hit-and-miss transform for face localization. Pattern Anal. Appl. 7(2), 117–127 (2004), http://dx.doi.org/10.1007/s10044-004-0207-4 , doi:10.1007/s10044-004-0207-4
Ronse, C.: A lattice-theoretical morphological view on template extraction in images. Journal of Visual Communication and Image Representation 7(3), 273–295 (1996), http://www.sciencedirect.com/science/article/pii/S1047320396900243 , doi:10.1006/jvci.1996.0024
Schaefer, R., Casasent, D.: Nonlinear optical hit—miss transform for detection. Appl. Opt. 34(20), 3869–3882 (1995), http://ao.osa.org/abstract.cfm?URI=ao-34-20-3869 , doi:10.1364/AO.34.003869
Serra, J.: Image analysis and mathematical morphology, vol. 1. Academic Press, London (1982)
Sinha, D., Sinha, P., Douherty, E., Batman, S.: Design and analysis of fuzzy morphological algorithms for image processing. IEEE Trans on Fuzzy Systems 5(4) (1997)
Soille, P.: Morphological Image Analysis, 2nd edn. Springer, Heidelberg (2003)
Stankov, K., He, D.C.: Building detection in very high spatial resolution multispectral images using the hit-or-miss transform. IEEE Geosci. Remote S. 10(1), 86–90 (2013)
Velasco-Forero, S., Angulo, J.: Hit-or-miss transform in multivariate images. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010, Part I. LNCS, vol. 6474, pp. 452–463. Springer, Heidelberg (2010), http://dx.doi.org/10.1007/978-3-642-17688-342
Wang, M., Leung, Y., Zhou, C., Pei, T., Luo, J.: A mathematical morphology based scale space method for the mining of linear features in geographic data. Data Min. Knowl. Disc. 12, 97–118 (2006), http://dx.doi.org/10.1007/s10618-005-0021-7 , doi:10.1007/s10618-005-0021-7
Weber, J., Lefèvre, S.: Spatial and spectral morphological template matching. Image and Vision Computing 30, 934–945 (2012)
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González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D. (2013). Fuzzy Hit-or-Miss Transform Using the Fuzzy Mathematical Morphology Based on T-norms. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_38
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DOI: https://doi.org/10.1007/978-3-642-39165-1_38
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