Pao-Ta Yu

Weighted fuzzy mean filters for image processing

Copyright (c) 1997 Elsevier Science B.V. All rights reserved. A new fuzzy filter for the removal of heavy additive impulse noise, called the weighted fuzzy mean (WFM) filter, is proposed and analyzed in this paper. The WFM-filtered output signal is the mean value of the corrupted signals in a sample matrix, and these signals are weighted by a membership grade of an associated fuzzy set stored in a knowledge base. The knowledge base contains a number of fuzzy sets decided by experts or derived from the histogram of a reference image. When noise probability exceeds 0.3, WFM gives very superior performance compared with conventional filters when evaluated by mean absolute error (MAE), mean square error (MSE), peak signal-to-noise-rate (PSNR) and subjective evaluation criteria. For dedicated hardware implementation, WFM is also much simpler than the conventional median filter.

FORECASTING FUZZY TIME SERIES ON A HEURISTIC HIGH-ORDER MODEL

ABSTRACT Chen first proposed the high-order fuzzy-time series model to overcome the drawback of existing fuzzy first-order forecasting models. His model involved easy calculations and forecasted more accurately than the other models. This study proposes an enhanced fuzzy-time series model, called heuristic high-order fuzzy time series model, to deal with forecasting problems. The proposed model aims to overcome the deficiency of Chens model, which depends strongly on the highest-order fuzzy-time series to eliminate ambiguities at forecasting and requires a vast memory for data storage. The empirical analysis reveals that the proposed model yields more accurate forecasts.

Partition fuzzy median filter based on fuzzy rules for image restoration

In this paper, a novel adaptive median-based filter, called the partition fuzzy median (PFM) filter, is proposed for improving the median-based filter to preserve image details while effectively suppressing impulsive noises. The proposed filter achieves its effect through a summation of the weighted output of the median filter and the related weighted input signal. The weights are set in accordance with the fuzzy rules. In order to design this weight function, a method to partition of the observation vector space and a learning approach are proposed so that the mean square error of the filter output can be minimum. Based on the constrained least mean square algorithm, an iterative learning procedure is derived and its convergence property is investigated. As for the noise suppressing on both fixed- and random-valued impulses without degrading the quality of fine details, extensive experimental results demonstrate that the proposed filter outperforms the other median-based filters in the literature. The new filter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples.

Convergence behavior and N-roots of stack filters

The convergence behavior of two types of stack filters is investigated. Both types are shown to possess the convergence property and to exhibit nontrivial behavior. The first type of stack filter has the erosive property; it erodes any input signal to a root after a sufficient number of passes. The second type of stack filter has the dilative property; it dilates any input signal to a root after a sufficient number of passes. For each type of stack filter, an algorithm is presented which can determine a filter that has any specific signal or set of signals as roots. These two algorithms are efficient in that their execution time is a linear function of the length of the input signal, the width of the filter window, and the number of signals to be preserved. Since some stack filters have the phenomenon of oscillations when they filter some input signals successively, a partial ordering is defined over the set of stack filters which makes it possible to determine upper and lower bounds for these oscillations. >

On the optimal design of fuzzy neural networks with robust learning for function approximation

A novel robust learning algorithm for optimizing fuzzy neural networks is proposed to address two important issues: how to reduce the outlier effects and how to optimize fuzzy neural networks, in the function approximation. This algorithm is able to reduce the outlier effects by cooperating with a conventional robust approach, and then to optimize fuzzy neural networks by determining the optimal learning rates which can minimize the next-step mean error at each iteration of our algorithm.

Convergence behavior and root signal sets of stack filters

The four different types of stack filters, type-0 through type-3, are determined by four different shapes of the on-set of the positive Boolean function from which the stack filter is constructed.Under all three appending strategies commonly considered in the literature-first and last value carry-on strategy, constant value carry-on strategy, and the circular approach-stack filters of type-0 through type-2 possess the convergence property, while type-3 stack filters do not all share this property. Examples of cyclic behavior in type-3 stack filters are given. Conditions under which certain operations on stack filters which possess the convergence property produce other filters with this property are provided.In perhaps the most important result in this paper, it is shown that the root signal set of any type-3 stack filter is the intersection of the root sets of the type-1 and type-2 stack filters from which the type-3 filter is constructed. This should simplify the task of finding the set of roots of type-3 stack filters.The rates of convergence for stack filters of type-1 and type-2 are determined for each appending approach. The convergence behavior and rates of convergence of stack filters of type-1 and type-2 are then generalized to include type-1 and type-2 filters with indexi.

Adaptive fuzzy hybrid multichannel filters for removal of impulsive noise from color images

Abstract On the design of multichannel filters, especially in color image restoration, it is not easy to simultaneously achieve three objectives: noise attenuation, chromaticity retention, and edges or details preservation. In this paper, we propose a new class of multichannel filters called adaptive fuzzy hybrid multichannel (AFHM) filters to achieve these three objectives simultaneously. Our novel approach is mainly based on human concept (heuristic rules) and provides a significant framework to take the merits of filtering behavior of three filters: a vector median (VM) filter, a vector directional (VD) filter, and an identity filter. On the design of an AFHM filter, our approach is a powerful and flexible scheme to achieve these three objectives because human concept can be efficiently expressed by fuzzy implicative rules for improving the filtering performance. The AFHM filters are able to effectively inherit the merits of filtering behaviors of these three filters in color image restoration applications. This is the first paper to include human concept to design multichannel filters. Moreover, a faster convergence property of the learning algorithm is investigated to reduce the time complexity of the AFHM filters. Extensive simulation results illustrate that AFHM filters not only achieve these three objectives but also possess the robust and adaptive capabilities, and demonstrate that the performance of AFHM filters outperforms that of other proposed filtering techniques.

Genetic-based fuzzy hybrid multichannel filters for color image restoration

Abstract On the design of multichannel filters, especially in color image restoration, it is not easy to simultaneously achieve three objectives: noise attenuation, chromaticity retention, and edges or details preservation. In this paper we propose a new class of multichannel filters, called genetic-based fuzzy hybrid multichannel (GFHM) filters, to reach these three objectives simultaneously. The design of GFHM filters is mainly based on human concept (heuristic rules) and genetic algorithms. Because the human concept can be readily and efficiently expressed by fuzzy implicative rules, GFHM filters can take the useful characteristics of filtering behavior of three filters: a vector median, a vector directional, and an identity filter. Since genetic algorithms possess the global-searching capability for an optimal solution, they are able to effectively optimize GFHM filters to improve the filtering performance. In color image restoration applications, extensive simulation results illustrate that GFHM filters not only achieve these three objectives but also possess the robust and the adaptive capability; moreover, these simulation results also demonstrate that the performance of GFHM filters outperforms that of other proposed filtering techniques.

Fuzzy stack filters-their definitions, fundamental properties, and application in image processing

A new fuzzy filter, called fuzzy stack filter (FSF), is proposed to extend the filtering capability of conventional stack filter (SF), which is based on the positive Boolean function (PBF) as its window operator. We fuzzify the onset and off-set of a given PBF to obtain two types of fuzzy PBFs. Then, we adopt the architecture of threshold decomposition to develop this new fuzzy filter with a fuzzy PBF as its window operator. Each fuzzy PBF is associated with a set of control parameters. Therefore, the original PBF can be estimated from above and below by two fuzzy PBFs with appropriate control parameters. Furthermore, we can apply the fuzzy modifiers to modify the fuzzy PBFs such that the PBFs can be completely estimated by the fuzzy PBFs. Hence, the stack filter is a special case of fuzzy stack filter. Since some control parameters are added in this new filter, the neural learning algorithms can be easily developed under the flexibility of the given control parameters. We first propose the fuzzy (m,n) rank-order filter to test our proposed learning algorithm. In this simple learning algorithm, we can remove the noise-corrupted images very well in contrast to the filtering behavior of rank-order filters. We believe that the results presented will lead to more fruitful research on more advanced and powerful learning algorithms dedicated to the appropriate applications.

Thresholding noise-free ordered mean filter based on Dempster-Shafer theory for image restoration

This work proposes a new decision-based filter, the thresholding noise-free ordered mean (TNOM) filter based on the Dempster-Shafer (D-S) evidence theory, to preserve more details of images than can other decision-based filters, while effectively suppressing impulse noise. The new filter mechanism is composed of an efficient D-S impulse detector and a noise filter that works by estimating the central noise-free ordered mean (CNOM) value. The D-S evidence theory provides a way to deal with the uncertainty in the evidence and information fusion. Pieces of evidence are extracted, and the mass functions defined using the local information in the filter window. Then, the decision rule is applied to determine whether noise exists, according to the final combined belief value. If a pixel is detected to be a corrupted pixel, then the proposed filter will be triggered to replace it. Otherwise, the pixel is kept unchanged. With respect to the noise suppression of noise on both fixed-valued and random-valued impulses without smearing the fine details in the image, extensive simulation results reveal that the proposed scheme significantly outperforms other decision-based filters.