In this paper, we present a novel approach to the restoration of noise-corrupted image, which is particularly effective at removing highly impulsive noise while preserving image details. This is accomplished through a fuzzy smoothing filter constructed from a set of fuzzy membership functions for which the initial parameters are derived in accordance with input histogram. A principle of conservation in histogram potential is incorporated with input statistics to adjust the initial parameters so as to minimize the discrepancy between a reference intensity and the output of defuzzification process. Similar to median filters (MF), the proposed filter has the benefits that it is simple and it assumes no a priori knowledge of specific input image, yet it shows superior performance over conventional filters (including MF) for the full range of impulsive noise probability. Unlike in many neuro-fuzzy or fuzzy-neuro filters where random strategy is employed to choose initial membership functions for subsequent lengthy training, the proposed filter can achieve satisfactory performance without any training.

This paper presents a two-stage approach that is effective for performing fast clustering. First, a competitive neural network (CNN) that can harmonize mean squared error and information entropy criteria is employed to exploit the substructure in the input data by identifying the local density centers. A Gravitation neural network (GNN) then takes the locations of these centers as initial weight vectors and undergoes an unsupervised update process to group the centers into clusters. Each node (called gravi-node) in the GNN is associated with a finite attraction radius and would be attracted to a nearby centroid simultaneously during the update process, creating the Gravitation-like behavior without incurring complicated computations. This update process iterates until convergence and the converged centroid corresponds to a cluster. Compared to other clustering methods, the proposed clustering scheme is free of initialization problem and does not need to pre-specify the number of clusters. The two-stage approach is computationally efficient and has great flexibility in implementation. A fully parallel hardware implementation is very possible.