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On Fuzzy Nonlinear Regression for Image Enhancement

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Abstract

Nonlinear regression analysis with respect to fuzzy characteristic sets, or fuzzy nonlinear regression, is a potentially useful and previously unexplored digital signal processing tool. Here, the fuzzy regression model is used in the image enhancement problem. Given a noisy image, the noise is eliminated by computing a regression—the “closest” image to the input image that has membership in the characteristic set. The known properties of the original, uncorrupted imagery (e.g., smoothness) are used to define membership in the characteristic set. With conventional crisp characteristic sets that enforce the characteristic property in a global sense, the local image structure may be sacrificed. In this paper, a method to compute fuzzy nonlinear regressions for the piecewise constant characteristic property is given. Solutions are produced by minimizing an energy functional that penalizes deviation from the sensed (corrupted) image and deviation from piecewise constancy. The construction of the energy functional, the analytical selection of the functional parameters, the minimization technique used (generalized deterministic annealing), and the fuzzy membership function are detailed. Finally, image enhancement examples are provided for remotely sensed imagery.

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Authors and Affiliations

  1. School of Electrical & Computer Engineering, Oklahoma State University, 202 Engineering South, Stillwater, Oklahoma, 74078

    Scott T. Acton

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Acton, S.T. On Fuzzy Nonlinear Regression for Image Enhancement. Journal of Mathematical Imaging and Vision 8, 239–253 (1998). https://doi.org/10.1023/A:1008222617999

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