Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological methods in image and signal processing
Morphological methods in image and signal processing
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Digital image processing
Digital Image Restoration
Digital Picture Processing
Probability and Statistics in the Engineering and Computing Sciences
Probability and Statistics in the Engineering and Computing Sciences
A new algorithm for image noise reduction using mathematical morphology
IEEE Transactions on Image Processing
Generalized deterministic annealing
IEEE Transactions on Neural Networks
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Nonlinear regression analysis with respect to fuzzy characteristicsets, or fuzzy nonlinear regression, is a potentiallyuseful and previously unexplored digital signal processing tool. Here, thefuzzy regression model is used in the image enhancement problem. Given anoisy image, the noise is eliminated by computing a regression—the“closest” image to the input image that has membership in thecharacteristic set. The known properties of the original, uncorruptedimagery (e.g., smoothness) are used to define membership in thecharacteristic set. With conventional crisp characteristic sets that enforcethe characteristic property in a global sense, the local image structure maybe sacrificed. In this paper, a method to compute fuzzy nonlinearregressions for the piecewise constant characteristic property is given.Solutions are produced by minimizing an energy functional that penalizesdeviation from the sensed (corrupted) image and deviation from piecewiseconstancy. The construction of the energy functional, the analyticalselection of the functional parameters, the minimization technique used(generalized deterministic annealing), and the fuzzy membership function aredetailed. Finally, image enhancement examples are provided for remotelysensed imagery.