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Binary Image 2D Shape Learning and Recognition Based on Lattice-Computing (LC) Techniques

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Abstract

This work introduces a Type-II fuzzy lattice reasoning (FLRtypeII) scheme for learning/generalizing novel 2D shape representations. A 2D shape is represented as an element—induced from populations of three different shape descriptors—in the product lattice (F 3,⪯), where (F,⪯) denotes the lattice of Type-I intervals’ numbers (INs). Learning is carried out by inducing Type-II INs, i.e. intervals in (F,⪯). Our proposed techniques compare well with alternative classification methods from the literature in three benchmark classification problems. Competitive advantages include an accommodation of granular data as well as a visual representation of a class. We discuss extensions to gray/color images, etc.

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References

  1. Amanatiadis, A., Kaburlasos, V.G., Gasteratos, A., Papadakis, S.E.: Evaluation of shape descriptors for shape-based image retrieval. IET Image Process. (2011, in press)

  2. Andreu, G., Crespo, A., Valiente, J.M.: Selecting the toroidal self-organizing feature maps (TSOFM) best organized to object recognition. In: Proceedings of the International Conference on Neural Networks, vol. 2, pp. 1341–1346 (1997)

    Google Scholar 

  3. Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)

    Article  Google Scholar 

  4. Berretti, S., Del Bimbo, A., Pala, P.: Retrieval by shape similarity with perceptual distance and effective indexing. IEEE Trans. Multimed. 2(4), 225–239 (2000)

    Article  Google Scholar 

  5. Biasotti, S., Cerri, A., Frosini, P., Giorgi, D., Landi, C.: Multidimensional size functions for shape comparison. J. Math. Imaging Vis. 32(2), 161–179 (2008)

    Article  MathSciNet  Google Scholar 

  6. Birkhoff, G.: Lattice Theory. Colloquium Publications, vol. 25. Am. Math. Soc., Providence (1967)

    MATH  Google Scholar 

  7. Bloch, I.: Spatial reasoning under imprecision using fuzzy set theory, formal logics and mathematical morphology. Int. J. Approx. Reason. 41(2), 77–95 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bloch, I.: Lattices of fuzzy sets and bipolar fuzzy sets and mathematical morphology. Inf. Sci. 181(10), 2002–2015 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bloch, I., Maitre, H.: Fuzzy mathematical morphologies: a comparative study. Pattern Recognit. 28(9), 1341–1387 (1995)

    Article  MathSciNet  Google Scholar 

  10. Bober, M.: MPEG-7 visual shape descriptors. IEEE Trans. Circuits Syst. Video Technol. 11(6), 716–719 (2001)

    Article  Google Scholar 

  11. Braga-Neto, U., Goutsias, J.: A theoretical tour of connectivity in image processing and analysis. J. Math. Imaging Vis. 19(1), 5–31 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Daliri, M.R., Torre, V.: Shape recognition based on kernel-edit distance. Comput. Vis. Image Underst. 114(10), 1097–1103 (2010)

    Article  Google Scholar 

  13. Deng, T.-Q., Heijmans, H.J.A.M.: Grey-scale morphology based on fuzzy logic. J. Math. Imaging Vis. 16(2), 155–171 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Flusser, J., Suk, T.: Pattern recognition by affine moment invariants. Pattern Recognit. 26(1), 167–174 (1993)

    Article  MathSciNet  Google Scholar 

  15. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  16. Graña, M.: Lattice computing and natural computing—guest editorial. Neurocomputing 72(10–12), 2065–2066 (2009)

    Article  Google Scholar 

  17. Graña, M., Villaverde, I., Maldonado, J.O., Hernandez, C.: Two lattice computing approaches for the unsupervised segmentation of hyperspectral images. Neurocomputing 72(10–12), 2111–2120 (2009)

    Article  Google Scholar 

  18. Graña, M., Savio, A.M., García-Sebastián, M., Fernandez, E.: A lattice computing approach for on-line fMRI analysis. Image Vis. Comput. 28(7), 1155–1161 (2010)

    Article  Google Scholar 

  19. Graña, M., Chyzhyk, D., García-Sebastián, M., Hernández, C.: Lattice independent component analysis for functional magnetic resonance imaging. Inf. Sci. 181(10), 1910–1928 (2011)

    Article  Google Scholar 

  20. Heijmans, H.J.A.M.: Morphological Image Operators. Academic Press, New York (1994)

    MATH  Google Scholar 

  21. Jammeh, E.A., Fleury, M., Wagner, C., Hagras, H., Ghanbari, M.: Interval type-2 fuzzy logic congestion control for video streaming across IP networks. IEEE Trans. Fuzzy Syst. 17(5), 1123–1142 (2009)

    Article  Google Scholar 

  22. Kaburlasos, V.G.: Towards a Unified Modeling and Knowledge-Representation Based on Lattice Theory. Studies in Computational Intelligence, vol. 27. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  23. Kaburlasos, V.G.: Information engineering applications based on lattices—guest editorial. Inf. Sci. 181(10), 1771–1773 (2011)

    Article  MathSciNet  Google Scholar 

  24. Kaburlasos, V.G., Kehagias, A.: Novel fuzzy inference system (FIS) analysis and design based on lattice theory. IEEE Trans. Fuzzy Syst. 15(2), 243–260 (2007)

    Article  Google Scholar 

  25. Kaburlasos, V.G., Pachidis, T.: A lattice-computing ensemble for reasoning based on formal fusion of disparate data types, and an industrial dispensing application. Inf. Fusion (2011, in press)

  26. Kaburlasos, V.G., Papadakis, S.E.: Granular self-organizing map (grSOM) for structure identification. Neural Netw. 19(5), 623–643 (2006)

    Article  MATH  Google Scholar 

  27. Kaburlasos, V.G., Papadakis, S.E.: Fuzzy lattice reasoning (FLR) implies a granular enhancement of the fuzzy-ARTMAP classifier. In: Proceedings of JCIS, Salt Lake City, Utah, pp. 1610–1616 (2007)

    Google Scholar 

  28. Kaburlasos, V.G., Papadakis, S.E.: A granular extension of the fuzzy-ARTMAP (FAM) neural classifier based on fuzzy lattice reasoning (FLR). Neurocomputing 72(10–12), 2067–2078 (2009)

    Article  Google Scholar 

  29. Kaburlasos, V.G., Petridis, V.: Fuzzy lattice neurocomputing (FLN) models. Neural Netw. 13(10), 1145–1169 (2000)

    Article  Google Scholar 

  30. Kaburlasos, V.G., Athanasiadis, I.N., Mitkas, P.A.: Fuzzy lattice reasoning (FLR) classifier and its application for ambient ozone estimation. Int. J. Approx. Reason. 45(1), 152–188 (2007)

    Article  MATH  Google Scholar 

  31. Kaburlasos, V.G., Moussiades, L., Vakali, A.: Fuzzy lattice reasoning (FLR) type neural computation for weighted graph partitioning. Neurocomputing 72(10–12), 2121–2133 (2009)

    Article  Google Scholar 

  32. Kaburlasos, V.G., Amanatiadis, A., Papadakis, S.E.: 2-D shape representation and recognition by lattice computing techniques. In: Corchado, E., Graña, M., Savio, A.M. (eds.) Proc. Int. Conf. HAIS, San Sebastián, Spain, 2010. LNAI, vol. 6077, pp. 391–398. Springer, Berlin (2010)

    Google Scholar 

  33. Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132(1–4), 195–220 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  34. Kauppinen, H., Seppänen, T., Pietikäinen, M.: An experimental comparison of autoregressive and Fourier-based descriptors in 2D shape classification. IEEE Trans. Pattern Anal. Mach. Intell. 17(2), 201–207 (1995)

    Article  Google Scholar 

  35. Kim, J.-G., Noble, J.A., Brady, J.M.: Probabilistic models for shapes as continuous curves. J. Math. Imaging Vis. 33(1), 39–65 (2009)

    Article  MathSciNet  Google Scholar 

  36. Liao, S.X., Pawlak, M.: On the accuracy of Zernike moments for image analysis. IEEE Trans. Pattern Anal. Mach. Intell. 20(12), 1358–1364 (1998)

    Article  Google Scholar 

  37. Ling, H., Jacobs, D.W.: Shape classification using the inner-distance. IEEE Trans. Pattern Anal. Mach. Intell. 29(2), 286–299 (2007)

    Article  Google Scholar 

  38. Liu, H., Xiong, S., Fang, Z.: FL-GrCCA: a granular computing classification algorithm based on fuzzy lattices. Comput. Math. Appl. 61(1), 138–147 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  39. Maragos, P.: Lattice image processing: a unification of morphological and fuzzy algebraic systems. J. Math. Imaging Vis. 22(2–3), 333–353 (2005)

    Article  MathSciNet  Google Scholar 

  40. Mélange, T., Nachtegael, M., Sussner, P., Kerre, E.E.: On the decomposition of interval-valued fuzzy morphological operators. J. Math. Imaging Vis. 36(3), 270–290 (2010)

    Article  Google Scholar 

  41. Mendel, J.M.: Type-2 fuzzy sets and systems: an overview. IEEE Comput. Intell. Mag. 2(1), 20–29 (2007)

    Article  MathSciNet  Google Scholar 

  42. Mendel, J.M., John, R.I.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)

    Article  Google Scholar 

  43. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)

    Article  Google Scholar 

  44. Nachtegael, M., Sussner, P., Mélange, T., Kerre, E.E.: On the role of complete lattices in mathematical morphology: from tool to uncertainty model. Inf. Sci. 181(10), 1971–1988 (2011)

    Article  MATH  Google Scholar 

  45. Papadakis, S.E., Kaburlasos, V.G.: Piecewise-linear approximation of nonlinear models based on probabilistically/possibilistically interpreted intervals’ numbers (INs). Inf. Sci. 180(24), 5060–5076 (2010)

    Article  MATH  Google Scholar 

  46. Papadakis, S.E., Tzionas, P., Kaburlasos, V.G., Theocharis, J.B.: A genetic based approach to the Type I structure identification problem. Informatica 16(3), 365–382 (2005)

    MathSciNet  MATH  Google Scholar 

  47. Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley, Chichester (2008)

    Google Scholar 

  48. Ronse, C.: Why mathematical morphology needs complete lattices. Signal Process. 21(2), 129–154 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  49. Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing their shock graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 550–571 (2004)

    Article  Google Scholar 

  50. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)

    MATH  Google Scholar 

  51. Serra, J.: Image Analysis and Mathematical Morphology. Theoretical Advances, vol. 2. Academic Press, New York (1988)

    Google Scholar 

  52. Sugeno, M., Kang, G.T.: Structure identification of fuzzy model. Fuzzy Sets Syst. 28(1), 15–33 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  53. Sussner, P.: Generalizing operations of binary autoassociative morphological memories using fuzzy set theory. J. Math. Imaging Vis. 19(2), 81–93 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  54. Sussner, P., Esmi, E.L.: Morphological perceptrons with competitive learning: lattice-theoretical framework and constructive learning algorithm. Inf. Sci. 181(10), 1929–1950 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  55. Sussner, P., Valle, M.E.: Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality. J. Math. Imaging Vis. 32(2), 139–159 (2008)

    Article  MathSciNet  Google Scholar 

  56. Sussner, P., Nachtegael, M., Mélange, T.: L-fuzzy mathematical morphology: an extension of interval-valued and intuitionistic fuzzy mathematical morphology. In: Proceedings of the 28th NAFIPS, Cincinnati, OH, pp. 1–6 (2009)

    Google Scholar 

  57. Tanaka, K., Sano, M., Watanabe, H.: Modeling and control of carbon monoxide concentration using a neuro-fuzzy technique. IEEE Trans. Fuzzy Syst. 3(3), 271–279 (1995)

    Article  Google Scholar 

  58. Thakoor, N., Gao, J., Jung, S.: Hidden Markov model-based weighted likelihood discriminant for 2-D shape classification. IEEE Trans. Image Process. 16(11), 2707–2719 (2007)

    Article  MathSciNet  Google Scholar 

  59. Tzafestas, C.S., Maragos, P.: Shape connectivity: multiscale analysis and application to generalized granulometries. J. Math. Imaging Vis. 17(2), 109–129 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  60. Valle, M.E., Sussner, P.: A general framework for fuzzy morphological associative memories. Fuzzy Sets Syst. 159(7), 747–768 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  61. Valle, M.E., Sussner, P.: Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning. Neural Netw. 24(1), 75–90 (2011)

    Article  MATH  Google Scholar 

  62. Wagner, C., Hagras, H.: Toward general type-2 fuzzy logic systems based on zSlices. IEEE Trans. Fuzzy Syst. 18(4), 637–660 (2010)

    Article  Google Scholar 

  63. Wang, B., Shen, W., Liu, W.-Y., You, X.-G., Bai, X.: Shape classification using tree-unions. In: Proceedings of the IEEE 2010 20th International Conference on Pattern Recognition (ICPR), pp. 983–986 (2010)

    Chapter  Google Scholar 

  64. Xu, Y., Ruan, D., Qin, K., Liu, J.: Lattice-Valued Logic. Studies in Fuzziness and Soft Computing, vol. 132. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  65. Yang, M.-S., Lin, D.-C.: On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput. Math. Appl. 57(6), 896–907 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  66. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  67. Zadeh, L.A.: From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circuits Syst.—I, Fundam. Theory Appl. 45(1), 105–119 (1999)

    Article  MathSciNet  Google Scholar 

  68. Zhang, D., Lu, G.: Review of shape representation and description techniques. Pattern Recognit. 37(1), 1–19 (2004)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Human-Machines-Interaction (HMI) Laboratory, Department of Industrial Informatics, Technological Educational Institution of Kavala, Kavala, 65404, Greece

    Vassilis G. Kaburlasos, S. E. Papadakis & Angelos Amanatiadis

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  1. Vassilis G. Kaburlasos
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  2. S. E. Papadakis
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  3. Angelos Amanatiadis
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Correspondence to Vassilis G. Kaburlasos.

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Kaburlasos, V.G., Papadakis, S.E. & Amanatiadis, A. Binary Image 2D Shape Learning and Recognition Based on Lattice-Computing (LC) Techniques. J Math Imaging Vis 42, 118–133 (2012). https://doi.org/10.1007/s10851-011-0301-3

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