Wavelet theory and its application to pattern recognition (Q2703391)

This book is devoted to a challenging research topic that is related to both areas of wavelet theory and pattern recognition. Wavelet theory has been employed in many fields and applications, such as signal and image processing, theoretical mathematics, control system, and all. This book focuses on this research topic.NEWLINENEWLINENEWLINEThis book is organized into two parts, namely, Chapters 1-4 extend wavelet theory, while Chapter 5-9 deal with the application of the wavelet theory to pattern recognition, which is the main part of this book.NEWLINENEWLINENEWLINEInitially, in Chapter 1, a brief description of wavelet theory is introduced, and a comparison between the wavelet and Fourier transforms is discussed. This chapter reviews established applications of the wavelet theory in pattern recognition.NEWLINENEWLINENEWLINEIn Chapter 2, the general theory of the continuous wavelet transform is addressed, and its major properties are investigated including the characterization of Lipschitz regularity of signals by the wavelet transform and the filtering properties of the wavelet transform.NEWLINENEWLINENEWLINEChapter 3 considers multiresolution analysis and wavelet bases, where the basic concepts of the both are presented as well as the construction of them. As an important algorithm for implementing the discrete wavelet transform, Mallat algorithm is introduced.NEWLINENEWLINENEWLINEAfter these chapters, some typical wavelet bases including the orthonormal and nonorthonormal bases are provided in Chapter 4.NEWLINENEWLINENEWLINEBy formulating the wavelet theory and the general applications with wavelet theory, the second part of this book demonstrates more detailed applications. All of these applications were made by the authors' research group. Chapter 5 develops a novel method to identify different structures of the edges and design an algorithm to detect the step-structure edges. This technique can be employed to contour extraction and 2-D object recognition.NEWLINENEWLINENEWLINEChapter 6 presents a new approach to feature extraction. In this way, the wavelet decomposition was used to produce wavelet sub-patterns, and thereafter, the fractal divider dimension were utilized to find the numerical features from these sub-patterns. Chapter 7 applies 2-D multiresolution analysis and Mallat algorithm to form document analysis.NEWLINENEWLINENEWLINEIn Chapter 8 several algorithms for Chinese character processing are studied, based on cubic B-spline wavelet transform, namely (1) compression of Chinese characters, (2) enlargement of the Chinese character, (3) generation of type style of Chinese fonts.NEWLINENEWLINENEWLINEChapter 9 deals with the classification of patterns with wavelet theory. In this way, the orthogonal wavelet series are used for the probability density estimation in the classifier design.