Possibility-based perception: A reflection on recognizing the pattern of shapes

Author

Abstract

Within the past years, probability and possibility have both been elaborated as two key concepts in formulating the issue of uncertainty in various domains of decision making like pattern recognition. Possibility pays attention to the existing structure of a pattern (or a situation), while the main concern of probability is to emphasize on the problems experienced in the past. When we talk about "structure" the question is how the meaningful components in a pattern (or a situation) may come into existence based on specific models. Accordingly the perception based on possibility takes us to the paint where a set of possibilities with regard to these meaningful components come together to figure out the class identity of the related pattern based on the possibility of the presence of these specific models.
In this paper, we try to show how the possibility of a pattern class can be assessed on the ground of the information belonging to its meaningful components which are supposed to come into existence based on specific models.
To give a clear image of the proposed approach, recognition of shape patterns that are structural in nature, is taken into consideration.

Keywords


[1] Lodwick, W.A. (2021). Fuzzy, Possibility, Probability, and Generalized Uncertainty Theory in Mathematical Analysis. Journal of Mahani Mathematical Research, Vol.10, Issue 2, pp.73-101.

[2] Zadeh, L.A. (1999). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, Vol. 100, Supplement 1, pp. 9-34.

[3] Dubois D., Prade H. (1998). Possibility Theory: Qualitative and Quantitative Aspects. In: Smets P. (eds) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 1, Springer, Dordrecht.

[4] Pyt’ev Y.P. and Zhivotnikov G. S. (2004). On the methods of possibility theory for morphological image analysis. Pattern Recognition, Image Analysis, 14 (1), pp.60–71.

[5] Dubois, D., Prade, H. (2012). Possibility theory: an approach to computerized processing of uncertainty. Springer Science Business Media.

[6] Knill, D. C., Richards, W. (Eds.). (1996). Perception as Bayesian inference. Cambridge University Press.
 
[7] Stroock, D. W. (2000). Probability Theory: An Analytic View. Cambridge: Cambridge University Press.

[8] Jaynes E.T. and Bretthorst G. L. (2003). Probability Theory: The Logic of Science. Cambridge University Press.

[9] Devroye L., Györfi L., Lugosi G. (2013). A Probabilistic Theory of Pattern Recognition. Springer; Softcover reprint of the original 1st ed. 1996 edition (November 22, 2013).

[10] Medasani, S., Kim, J., Krishnapuram, R. (1998). An overview of membership function generation techniques for pattern recognition. International Journal of approximate reasoning, 19(3-4), 391-417.

[11] Bezdek, J. C., Keller, J., Krisnapuram, R., Pal, N. (1999). Fuzzy models and algorithms for pattern recognition and image processing (Vol. 4). Springer Science Business Media.

[12] Bezdek, J. C. (2013). Pattern recognition with fuzzy objective function algorithms. Springer Science Business Media.

[13] Fukunaga, K., Hostetler, L. (1975). The estimation of the gradient of a density function, with applications in pattern recognition. IEEE Transactions on information theory, 21(1), 32-40.

[14] Bishop, C. M. (1995). Neural networks for pattern recognition. Oxford university press.

[15] Jain, A. K. (1987). Advances in statistical pattern recognition. In Pattern recognition theory and applications (pp. 1-19). Springer, Berlin, Heidelberg.

[16] Cha, S. H. (2007). Comprehensive survey on distance/similarity measures between probability density functions. City, 1(2), 1.
 
[17] Kohonen, T. (1990). Statistical pattern recognition revisited. In Advanced neural computers (pp. 137-144). North-Holland.

[18] Pau, L. F. (1982). Fusion of multisensor data in pattern recognition. In Pattern recognition theory and applications (pp. 189-201). Springer, Dordrecht.

[19] Repp, B. H., Milburn, C., Ashkenas, J. (1983). Duplex perception: Confirmation of fusion. Perception Psychophysics, 33(4), 333-337.

[20] Della Riccia, G., Lenz, H. J., Kruse, R. (Eds.). (2001). Data fusion and perception. Springer.

[21] Sun, Q. S., Zeng, S. G., Liu, Y., Heng, P. A., Xia, D. S. (2005). A new method of feature fusion and its application in image recognition. Pattern Recognition, 38(12), 2437-2448.

[22] Schwenker, F., Dietrich, C., Thiel, C., Palm, G. (2006). Learning of decision fusion mappings for pattern recognition. International Journal on Artificial Intelligence and Machine Learning (AIML), 6, 17-21.

[23] Hak, T., Dul, J. (2009). Pattern matching.

[24] Hoffmann, C. M., O’Donnell, M. J. (1982). Pattern matching in trees. Journal of the ACM (JACM), 29(1), 68-95.

[25] Dubois, D., Prade, H., Testemale, C. (1988). Weighted fuzzy pattern matching. Fuzzy sets and systems, 28(3), 313-331.

[26] Cayrol, M., Farreny, H., Prade, H. (1982). Fuzzy pattern matching. Kybernetes.