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An Finite-Automata and Discrete Wavelet Transform to the Representation of Fractal Images

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 توفيق عبد الخالق عباس الاسدي 5/10/2011 11:14:27 AM
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An Finite-Automata and Discrete Wavelet Transform to the Representation of Fractal Images
 

Tawfiq A. Abaas, Ahmed K. ObaedUniversity of Babylon, college of science
 

  ABSTRACT :
 
 In this paper, we propose a new approach to represent the features of image objects in order to recognize it. The proposed approach consists of three stages. The first stage includes a segmentation  of an image into regions, and then DWT is applied to each of these regions for extracting the statistical properties such as the energy and standard deviation. In the final stage, the FA is constructed to represent the extracted features. The performance of the proposed approach is demonstrated in the domain of fractal images.  
 
 
INTRODUCTION:
 

 Fractal are a geometric patterns that are self similar and can be zoomed infinitely. They are used especially in computer modeling of irregular patterns and structures in nature(Saranathan). The representation of objects in fractal images is necessary for recognizing them, where it refers to significant parts (regions, edges) of which the image is composed. Thus representation requires segmenting the image into such parts, and then to extract and compare the object features in it. There are various kinds of object features: shapes, distribution (of brightness, color,…), texture, etc. (Tomiya and Ageishi 2003). Among them, the shape information must be the most robust and the most effective for the fractal images. All information on the shape of an object is, for example, contained in its boundary pixels. Generally, the edge-detection is applied to get the pixels of the boundaries that form the shape features. In recent years, wavelet transform(WT) has attracted significant attention in scientific research and engineering applications since it is very powerful for analyzing transient signals/images for its capability of multiresolution analysis with localization in both time and frequency domains. The wavelet-based multiresolution analysis is very efficient in pattern recognition, image compression, and other domains.  In fractal images where the regions or objects are composed of parts arranged in particular ways, and the parts themselves are arrangement of subparts, and so on. There is analogy between this type of representation and the use of finite automata (FA) to define language. Mindek (2004) describes the method to represent the images by finite automata and application in image recognition. In his method, the image is partitioned into blocks with the same size and give code for each block, then describe this codes by finite automata. This paper present a method to represent the fractal images using FA.The remainder of the paper  is organized as follows. In section 2. and section 3. we introduce edge-detection and wavelet transform respectively. Section 4. present FA. In the next section, we describe the proposed approach. Finally, the experimental results and conclusions will be generated. Fractal are a geometric patterns that are self similar and can be zoomed infinitely. They are used especially in computer modeling of irregular patterns and structures in nature(Saranathan). The representation of objects in fractal images is necessary for recognizing them, where it refers to significant parts (regions, edges) of which the image is composed. Thus representation requires segmenting the image into such parts, and then to extract and compare the object features in it. There are various kinds of object features: shapes, distribution (of brightness, color,…), texture, etc. (Tomiya and Ageishi 2003). Among them, the shape information must be the most robust and the most effective for the fractal images. All information on the shape of an object is, for example, contained in its boundary pixels. Generally, the edge-detection is applied to get the pixels of the boundaries that form the shape features. In recent years, wavelet transform(WT) has attracted significant attention in scientific research and engineering applications since it is very powerful for analyzing transient signals/images for its capability of multiresolution analysis with localization in both time and frequency domains. The wavelet-based multiresolution analysis is very efficient in pattern recognition, image compression, and other domains.  In fractal images where the regions or objects are composed of parts arranged in particular ways, and the parts themselves are arrangement of subparts, and so on. There is analogy between this type of representation and the use of finite automata (FA) to define language. Mindek (2004) describes the method to represent the images by finite automata and application in image recognition. In his method, the image is partitioned into blocks with the same size and give code for each block, then describe this codes by finite automata. This paper present a method to represent the fractal images using FA.The remainder of the paper  is organized as follows. In section 2. and section 3. we introduce edge-detection and wavelet transform respectively. Section 4. present FA. In the next section, we describe the proposed approach. Finally, the experimental results and conclusions will be generated.  


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