<title>Image interpolation, approximation, and classification using fuzzy neural nets</title>

Abstract

Interpolation and classification are widely used in image processing and pattern recognition, including remote sensed image processing. In fact, interpolation and classification can be considered as problems of optimization, i.e., finding an optimal mapping from the value space of variables to the value space of the function, or from the feature space to the class space. Different methods are sued, some are based on known numerical data, and the others, on expert rules. In general, they have difficulty to integrate both the knowledge of experts and that implied in known numerical training samples. In the present paper, we propose to use neural fuzzy systems with asymmetric (pi) membership functions. A new global criterion to optimize and the corresponding learning algorithm are proposed also. To test the performance of the system proposed, we apply it to interpolation and classification problems. The comparison with other methods shows better behavior of such systems. The neural fuzzy system using asymmetric (pi) membership functions has the following advantages: (1) Asymmetric (pi) membership function gives a more general model of fuzzy rules, improving the precision of neural fuzzy system and assuring a good convergence in learning: (2) The neural fuzzy system can integrate both kinds of knowledge. (3) The neural fuzzy system allows a refinement of the expert knowledge, and the new fuzzy rulers found are easy to interpret.