Edge‐preserving smoothing using the fuzzy control technique

Abstract

When a random noise is superposed on a signal with an abrupt change (i.e., edge), as in the case of the image signal, there is a large overlap of the frequency component between the abrupt changes (edge) of the signal and the noise. Then it is impossible to realize both the noise elimination and the edge preservation sufficiently by the conventional linear filter, such as the mean filter. Thus, a nonlinear technique is required in order to eliminate the noise and preserve details of the original signal where the coefficient of the smoothing filter is determined according to the properties of the data in the window. There can be more than one observed value in the filter window that can be used to specify the properties of the data. It is difficult, however, to represent precisely the properties of the image signal using a single observed value. In addition, the observed values contain ambiguities since they are calculated from the local image data with superposed noise. In other words, it is required to determine the filter coefficients based on multiple obseved values containing ambiguities. For such a problem, the fuzzy control rule, which is utilized effectively in control problems, can be applied to calculate the control variable (i.e., filter coefficient) adequately by the nonlinear technique from the multiple observed values containing ambiguities. In this paper, the nonlinear filtering technique based on the fuzzy control rule is presented and the usefulness of the filter in the noise elimination from the image signal is demonstrated.

Edge-preserving fuzzy filters based on differences between pixels

“…The a, b, c, d, e, and f in Table 5 indicate the results obtained with no processing, the proposed method, a median filter having a cross mask, a mean filter having a 3 ´ 3 mask, an e filter having a cross mask, and the method with cross mask proposed in Ref. 6, respectively. In Table 3, the results obtained using the median filter having the cross mask, the e filter having the cross mask, and the method with cross mask proposed in Ref.…”

“…For comparison, the image processed by a DWMTM filter, an e filter with cross mask, and the method with cross mask proposed in Ref. 6 are shown in Figs. 9, 10, and 11, respectively.…”

“…Actually, fine MSEs were obtained in the range of a from 230 to 280, when the relationship between a and MSE was examined for some values of b and g. Furthermore, for the condition where the value of a was fixed, when the values of b and g were adjusted by a method similar to that used in Ref. 6, it was determined that the suitable parameters were a = 245, b = 0.0, and g = 0.4. The following simulation was carried out using these parameters.…”

“…For example, Arakawa and coworkers proposed fuzzy median filters [4] using fuzzy clustering and have extended their approach to median filters using fuzzy rules [5]. Takashima and others also proposed fuzzy filters suitable for the reduction of mixed noise based on fuzzy control [6] and have extended this method to a fuzzy filter whose fuzzy rules can be optimized for white Gaussian noise [7]. In this filter, fuzzy control laws are described by using the difference between the original signal and the output of the median filter to detect impulsive noise, and difference and position information to detect white Gaussian noises.…”

“…For this reason median filters are required for the reduction of mixed noise in Ref. 6. However, since these features can be extracted by considering the difference between all pairs of points, the proposed method can reduce impulsive and white Gaussian noise without the use of median filters.…”