**1. Introduction**

270 Fuzzy Inference System – Theory and Applications

Xia, Y.; Leung, H. & Bossè, E.(2002). Neural data fusion algorithms based on a linearly

Zadeh, L.A. (1965) Fuzzy sets. *Information and Control,* Vol. 8, pp.338-353, 1965.

329, Mar 2002.

constrained least square method. *IEEE Trans on Neural Networks,* Vol. 13, pp.320-

The process of detecting outlines of an object and boundaries between objects and the background in the image is known as edge detection. It is an important tool used in many applications: such as image processing, computer vision and pattern recognition [1].

Linear time-invariant (LTI) filter is the most common method to the edge detection. On the condition of rst-order filter, an edge is considered as an abrupt variation in gray level between two neighbor pixels. Then the aim is to find out the points in the image which the first-order derivative of the gray level is of high magnitude. The root mean square value (RMS) is often used as the threshold value to the input image [2].

Second order operators are used sometimes. LoG (Laplacian-of-Gaussian) [3] filter is the most commonly used. There are three drawbacks with this operator. Firstly, it produces the greater computational complexity. Secondly, it generates a continuous line to represent all edges in the input image, and is also not adequate to describe more general structures.

Fuzzy logic represents a powerful approach to decision making. Since the concept of fuzzy logic was formulated in 1965 by Zadeh, many researches have been carried out its applications in the various areas of digital image processing: such as image assessment, edge detection, image segmentation, etc [4]. Bezdek et al, trained a neural net to give the same fuzzy output as a normalized Sobel operator [5]. The advantage of the new method over the traditional edge detector is very apparent. In the system described in [6, 7], all inputs to the fuzzy inference systems (FIS) system are obtained by applying to the original image a high-pass filter, a first-order edge detector filter (Sobel operator) and a low-pass (mean) filter. The adopted fuzzy rules and the fuzzy membership functions are specified according to the kind of filtering to be executed.
