**8. References**


The problem of image processing and edge detection under fuzziness and uncertainty has been considered. The role of fuzzy logic in representing and managing the uncertainties in these tasks was explained. Various fuzzy set theoretic tools for measuring information on grayness ambiguity and spatial ambiguity in an image were discussed along with their characteristics. Some examples of edge detection, whose outputs are responsible for the overall performance of a recognition (vision) system, were considered in order to demonstrate the effectiveness of these tools in providing both soft and hard decisions. Gray information is expensive and informative. Once it is thrown away, there is no way to get it back. Therefore one should try to retain this information as long as possible throughout the decision making tasks for its full use. When it is required to make a crisp decision at the highest level one can always throw away or ignore this information. The significance of retaining the gray information in the form of class membership for soft decision is evident. Uncertainty in determining a membership function in this regard and the tools for its management were also stated. Finally a few real life applications of these methodologies are

The proposed technique used fuzzy if then rules are a sophisticated bridge between human knowledge on the one side and the numerical framework of the computers on the other side, simple and easy to understand. To achieve a higher level of image quality considering the

 The proposed technique is able to overcome the draw backs of spatial domain methods like thresholding and frequency domain methods like Gaussian low pass filter. The

The proposed technique is tested on different type of images, like degraded, low

 In this chapter we introduce the Type-2 FIS to detect edges. Type-2 FIS edge detector includes appropriately defined membership function using expert knowledge and decides about pixel classification as edge or non edge. Experimental results shown that, the proposed method extract more integrity of edges and avoid more noise than *prewitt* 

[1] Boskovitz, V.; and Guterman, H., "An Adaptive Neuro-Fuzzy System for Automatic

[2] Celeux G.; and Govaert G.. "Gaussian parsimonious clustering models" *International* 

[3] Edelsbrunner, H.; Kirkpatrik, D.G.; and Seidel, R., "On the Shape of a Set of Points in the Plane", *IEEE Transaction on Information Theory*, vol. 29, no. 4, July 1983, pp.551-559. [4] Hanmandlu,M.;See,J.;Vasikarla,S.;"Fuzzy edge detector using entropy optimization". In

[5] Jain A. K., "Fundamentals of digital image processing", Prentice-Hall, Inc., New Jersy,

*journal on Pattern Recognition*, vol.28, no. 5, May1995,pp.781-793.

and Computing,ITCC,vol.1 April 2004, pp 665–670.

image segmentation and edge detection", *IEEE Transactions on fuzzy systems*, vol.

Proceedings of the International Conference on InformationTechnology: Coding

subjective perception and opinion of the human observers.

proposed technique is able to improve the contrast of the image.

**7. Conclusion** 

described.

contrasted images.

**8. References** 

1986.

operator and Type-2 FIS.

10, no. 2, April 2002, pp. 247–262.


www.owlnet.rice.edu/~elec539/Proyects97/morphjrks/moredge.html


http://www.doc.ic.ac.uk/~nd/surprise\_96/journal/vol2/jp6/article2.html


**14** 

Wei-Yen Hsu

*Taiwan* 

**Neuro-Fuzzy Prediction for Brain-Computer** 

The brain-computer interface (BCI) work is to provide humans an alternative channel that allows direct transmission of messages from the brain by analyzing the brain's mental activities [1–7]. The brain activity is recorded by means of multi-electrode electroencephalographic (EEG) signals that are either invasive or noninvasive. Noninvasive recording is convenient and popular in BCI applications so it is commonly used. According to the definition suggested at the first international meeting for BCI technology, the term BCI is reserved for a system that must not depend on the brain's normal output pathways of peripheral nerves and muscles [2]. It has become popular for BCI systems on motor imagery (MI) EEG signals in the last decade [8]. It reveals that there are special characteristics of event-related desynchronization (ERD) and synchronization (ERS) in mu and beta rhythms over the sensorimotor cortex during MI tasks by discriminating EEG signals between left and right MIs [9, 10]. ERD/ERS is the task-related or event-related change in the amplitude of the oscillatory behavior of specific cortical areas within various frequency bands. An amplitude (or power) increase is defined as event-related synchronization while an amplitude (or power) decrease is defined as event-related desynchronization. As other event-related potentials, ERD/ERS patterns are associated with sensory processing and motor behavior [2]. The principal objective of this study is to propose a BCI system, which combines neuro-fuzzy prediction and multiresolution fractal feature vectors (MFFVs) with

A model is used for time series prediction to forecast future events based on known past events [11]. A variety of methods have been presented in time series prediction, such as linear regression, Kalman filtering [12], neural network (NN) [13], and fuzzy inference system (FIS) [14]. Linear regression is simple and common, but it has less adaptation. Kalman filtering is an adaptive method, but intrinsically linear. The NN can approximate any nonlinear functions, but it demands a great deal of training data and is hard to interpret. On contrary, FIS has good capability of interpretation, but its adaptability is relative low. FISs are fuzzy predictions that can learn fuzzy "if-then" rules to predict data. They are readable, extensible, and universally approximate [14]. Adaptive neuro-fuzzy inference system (ANFIS) [15] integrates the advantage of both NN and fuzzy system. That is, ANFIS not only has good learning capability, but can be also interpreted easily. In addition, the training of ANFIS is fast and it can usually converge only depending on a small data set.

**1. Introduction** 

support vector machine, for MI classification.

*Graduate Institute of Biomedical Informatics, Taipei Medical University* 

**Interface Applications** 

[24] Webpage8, Michael D. Heath, (Florida, Mayo de 1996), "A Robustal Visual Method for Assessing the Relative Performance of Edge Detection Algorithms", Available: http://marathon.csee.usf.edu/edge/edge\_detection.html

[26] Webpage8,. http://www.hafsamx.org/his/index.htm
