**1. Introduction**

278 Fuzzy Inference System – Theory and Applications

[5] Kuo, R. J. (1997). A robotic die polishing system through fuzzy neural networks,

[6] Tizhoosh H.R.(2002). Fast fuzzy edge detection, *Proceedings of Fuzzy Information* 

[7] Lin, C. T., Lee, S. G.(1994). Reinforcement structure/parameter learning for neural

[8] Shahana B., Prasad B., E D Nagendra Prasad T. (2011). A New Approach for Edge Detection Using First Order Techniques. *IJCSt* , Volume 2, Number 1, pp. 78-82. [9] Abdallah A. Alshennawy, and Ayman A. Aly. (2009). Edge Detection in Digital Images

[10] Cristiano Jacques Miosso1, Adolfo Bauchspiess. (2001). Fuzzy Inference System Applied

[13] Aborisade, D. O. (2010). Fuzzy Logic Based Digital Image Edge Detection. *Global Journal of Computer Science and Technology*, Volume 10, Number 14, pp. 78-83.

[11] Yujing Zhang. (2008). *Image Treatment and Analysis Technology.* Beijing, pp. 189-193. [12] Wafa B., Fardin A. T., Om-Kolsoom S. (2009). Fuzzy Edge Detection Based on Pixel's

network based fuzzy logic systems, *IEEE Trans. Fuzzy Systems ,* Volume 2, Number

Using Fuzzy Logic Technique. World Academy of Science, Engineering and

to Edge Detection in Digital Images. *Proceedings of the V Brazilian Conference on Neural Networks - V Congresso Brasileiro de Redes Neurais*. April 2–5, - PUC, Rio de

Gradient and Standard Deviation Values. *PROCEEDINGS OF THE IMCSIT*.

*Computer Industry,* Volume 32, Number 3, pp. 273–280.

*Processing Society*, pp. 239-242.

Technology 51, pp. 178-186.

Janeiro - RJ - Brazil, pp. 481-486.

Volume 4, pp. 7-10.

1 , pp. 46–63.

Image processing is characterized by a procedure of information processing for which both the input and output are images, such as photographs or frames of video [Jain'86]. Most image processing techniques involve treating the image as a two-dimensional signal and applying standard signal processing techniques to it.[webpage1] Fuzzy Image Processing (FIP) is a collection of different fuzzy approaches to image processing. Nevertheless, the following definition can be regarded as an attempt to determine the boundaries. Fuzzy image processing includes all approaches that understand, represent and process the images, their segments and features as fuzzy sets. [webpage2]The representation and processing of the images depend on the selected fuzzy technique and on the problem to be solved [Jang'95]. Here is a list of general observations about fuzzy logic:

*Fuzzy logic is conceptually easy to understand.* 

The mathematical concepts behind fuzzy reasoning are very simple. Fuzzy logic is a more intuitive approach without the far-reaching complexity. Fuzzy logic is flexible. With any given system, it is easy to layer on more functionality without Starting again from scratch.

*Fuzzy logic is tolerant to imprecise data.* 

In real world everything is imprecise if you look closely enough, but more than that, most of the data which appear to be precise are imprecise after careful inspection. Fuzzy reasoning builds this understanding for the system rather than tackling it onto the end (precise).

*Fuzzy logic can be built on top of the experience of experts.* 

Fuzzy logic relies upon the experience of experts who already have familiarity and understanding about the functionality of systems.

*Fuzzy logic can model nonlinear functions of arbitrary complexity.* 

A fuzzy system can be created to match any set of input-output data. This process is made particularly easy by adaptive techniques like Adaptive Neuro-Fuzzy Inference Systems (ANFIS), which are available in Fuzzy Logic Toolbox.

Type-2 Fuzzy Logic for Edge Detection of Gray Scale Images 281

This chapter spread over seven sections. Section 2 briefly describes uncertainties in recognition system. Brief description of Type-2 FIS is given in Section 3, while Section 4 deals with image pre-processing. Edge detection methods are elaborated in Section 5. Section 6 present experimentation and simulation results. Finally, conclusions are relegated

Diagnosis

Treatment planning

3. Face recognition 4. Fingerprint recognition

6. Machine vision

to Section 7.

Study of anatomical structures

5. Automatic traffic controlling systems

2. Locate objects in satellite images (roads, forests, etc.)

Fig. 1. Uncertainty/imperfect knowledge in image processing.

**2. Uncertainties in a recognition system and relevance of fuzzy set theory** 

A gray scale image possesses some ambiguity within the pixels due to the possible multivalued levels of brightness. This pattern uncertainty is due to inherent vagueness rather than randomness. The conventional approach to image analysis and recognition consists of segmenting (hard partitioning) the image space into meaningful regions, extracting its different features (e.g. edges, skeletons, centroid of an object), computing the various properties of and relationships among the regions, and interpreting and/or classifying the image. Since the regions in an image are not always clearly defined, uncertainty can arise at every phase of the job. Any decision taken at a particular level will have an impact on all higher level activities. In defining image regions, its features and relations in a recognition system (or vision system) should have sufficient provision for representing the uncertainties

*Fuzzy logic can be blended with conventional control techniques.* 

Fuzzy systems don't necessarily replace conventional control methods. In many cases fuzzy systems augment them and simplify their implementation. Fuzzy logic is based on natural language. The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic. Because fuzzy logic is built on the structures of qualitative description used in everyday language, fuzzy logic is easy to use. Natural language, which is used by ordinary people on a daily basis, has been shaped by thousands of years of human history to be convenient and efficient. Sentences written in ordinary language represent a triumph of efficient communication [Webpage3].

The most important reasons for FIP are as follows:


In many image-processing applications, expert knowledge is used to overcome the difficulties in object recognition, scene analysis, etc. Fuzzy set theory and fuzzy logic offer us powerful tools to represent and process human knowledge in the form of fuzzy IF-THEN rules. On the other side, many difficulties in image processing arise because of the uncertain nature of the data, tasks, and results. This uncertainty, however, is not always due to the randomness but to the ambiguity and vagueness. Beside randomness which can be managed by probability theory, FIP can distinguish between three other kinds of imperfection in the image processing.


These problems are fuzzy in the nature. The question whether a pixel should become darker or brighter after processing than it is before? Where is the boundary between two image segments? What is a tree in a scene analysis problem? All of these and other similar questions are examples for situations that a fuzzy approach can be applied in a more suitable way to manage the imperfection.

FIP is an amalgamation of different areas of fuzzy set theory, fuzzy logic and fuzzy measure theory. The most important theoretical components of fuzzy image processing:


Applications of Edge Detection: Some of the practical applications of edge detection are:-


Diagnosis

280 Fuzzy Inference System – Theory and Applications

Fuzzy systems don't necessarily replace conventional control methods. In many cases fuzzy systems augment them and simplify their implementation. Fuzzy logic is based on natural language. The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic. Because fuzzy logic is built on the structures of qualitative description used in everyday language, fuzzy logic is easy to use. Natural language, which is used by ordinary people on a daily basis, has been shaped by thousands of years of human history to be convenient and efficient. Sentences written in

ordinary language represent a triumph of efficient communication [Webpage3].

2. Fuzzy techniques can manage the vagueness and ambiguity efficiently

1. Fuzzy techniques are powerful tools for knowledge representation and processing

In many image-processing applications, expert knowledge is used to overcome the difficulties in object recognition, scene analysis, etc. Fuzzy set theory and fuzzy logic offer us powerful tools to represent and process human knowledge in the form of fuzzy IF-THEN rules. On the other side, many difficulties in image processing arise because of the uncertain nature of the data, tasks, and results. This uncertainty, however, is not always due to the randomness but to the ambiguity and vagueness. Beside randomness which can be managed by probability theory, FIP can distinguish between three other kinds of

These problems are fuzzy in the nature. The question whether a pixel should become darker or brighter after processing than it is before? Where is the boundary between two image segments? What is a tree in a scene analysis problem? All of these and other similar questions are examples for situations that a fuzzy approach can be applied in a more

FIP is an amalgamation of different areas of fuzzy set theory, fuzzy logic and fuzzy measure

Measures of Fuzziness and Image Information (entropy, correlation, divergence,

Fuzzy Inference Systems (FIS) (image fuzzification, inference, image defuzzification)

Applications of Edge Detection: Some of the practical applications of edge detection are:-

theory. The most important theoretical components of fuzzy image processing:

*Fuzzy logic can be blended with conventional control techniques.* 

The most important reasons for FIP are as follows:

imperfection in the image processing.

Vague (complex/ill-defined) knowledge

suitable way to manage the imperfection.

Fuzzy Geometry (Metric, topology,)

Locate tumors and other pathologies

Fuzzy Clustering (Fuzzy c-means, possibility c-means,)

Fuzzy Mathematical Morphology (Fuzzy erosion, fuzzy dilation,)

expected values,)

1. Medical Imaging

 Measure tissue volumes Computer guided surgery

 Grayness ambiguity Geometrical fuzziness


This chapter spread over seven sections. Section 2 briefly describes uncertainties in recognition system. Brief description of Type-2 FIS is given in Section 3, while Section 4 deals with image pre-processing. Edge detection methods are elaborated in Section 5. Section 6 present experimentation and simulation results. Finally, conclusions are relegated to Section 7.

Fig. 1. Uncertainty/imperfect knowledge in image processing.
