分子類神經網路於數位影像處理的應用

國 立 交 通 大 學

電機與控制工程學系

博 士 論 文

分子類神經網路於數位影像處理的應用

Applications of Cellular Neural Networks in

digital image processing

研 究 生：壽 宇 文

指導教授：林 進 燈

分子類神經網路於影像處理的應用

Applications of Cellular Neural Networks in

digital image processing

研 究 生：壽宇文 Student：Yu-Wen Shou

指導教授：林進燈 博士 Advisor：Dr. Chin-Teng Lin

國 立 交 通 大 學

電 機 與 控 制 工 程 學 系

博 士 論 文

A Dissertation

Submitted to Department of Electrical and Control Engineering

College of Electrical Engineering and Computer Science

National Chiao Tung University

in partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

in

Electrical and Control Engineering

June 2006

Hsinchu, Taiwan, Republic of China

分子類神經網路於數位影像處理

的應用

研究生： 壽宇文 指導教授： 林進燈 博士

國立交通大學電機與控制工程學系(研究所)博士班

摘 要

在這篇論文裡，我們將分子類神經網路(Cellular Neural Networks)應用於複雜 且具有代表性地數位影像處理；分子類神經網路一直在學術界有著其特殊且不可 取代的地位，其原因主要在於其具備了完整的理論基礎以及在實用時穩定性 (stability)和堅固性(robustness)的易於操控，當然最吸引人地莫過於分子類神經網 路可硬體實現化的優勢，不過由於硬體實現可能性的考量，分子類神經網路中樣 版(template)的設計往往是愈單純愈容易達到硬體實現的目的，但此一設計限制 卻和一般數位影像處理演算法的需求大異其逕，也因此使得在過去的文獻裡分子 類神經網路只侷限於應用在一些簡單的影像處理技術，為了突破此一瓶頸，我們 所提出的這篇論文不但清楚詳細地討論分子類神經網路於高階影像處裡的可能 應用演算法更提出實際案例來證明分子類神經網路應用的可能性，所以我們所提 出的方法不僅可以解決過去一些高階影像處理的問題，同時也為未來種種數位影 像處理於硬體實現的可能提供了一個完整及實際的實現策略。 這篇論文主要可以分為三大部分：在第一部份裡，我們會詳細地說明並討論 在過去到現在大部分將分子類神經網路應用於影像處理的相關文獻及未來所有 可能的發展和技術，另外也將分子類神經網路作一完整的介紹，除此之外，我們 也會特別著重於分子類神經網路在影像處理相關應用理論的討論以及其硬體實 現化的考量；在第二部分裡，我們提出了一個將分子類神經網路應用於影像辨識 處理的基礎分析—紋路分析(Texture Analysis)，這是由於紋路分析的複雜性和普 遍性會使得分子類神經網路於高階影像處理的應用不會只侷限在單一的影像處 理技術，其中我們也提出了一個相當有用的空間特徵(spatial feature)，此一特徵 不但可以使複雜地高階影像處理能夠應用分子類神經網路，也為影像辨識技術提 供了一個很好的辨識機制；在最後一部分裡，我們也將文件影像分析做了一個完 整的剖析，並以文件影像的去網點為例來說明在實際情況下的分子類神經網路的 應用，如此演算法的開發也為文件影像處理提供了更多實際的應用，更考量了文 件影像處理若以軟體實現時的計算量負荷，而對未來高階數位影像處理能夠以硬 體實現來提高處理速度提供了無限的可能。

Applications of Cellular Neural Networks

in digital image processing

Student: Yu-Wen Shou Advisor: Dr. Chin-Teng Lin

Department of Electrical and Control Engineering

National Chiao-Tung University

Abstract

This dissertation tackles the all-time challenging research field of digital image processing by using Cellular Neural Network as means of its application. As we all know, Cellular Neural Network has been critically acclaimed by the academia for its impeccable theoretical structure and the stability and robustness its applications speak for. Aside from these advantages it presents, Cellular Neural Network appears to be compelling in that it can be practically realized for hardware compilation. However, this does not mean Cellular Neural Network is without limitations. When it comes to hardware compilation of Cellular Neural Network, decent and satisfactory results only come with easy and simple template design, which on the contrary contradicts the algorithmic expectations we have for image processing. This explains why, for years, among all those respectable academic papers and researches, Cellular Neural Network has been applied only for simple, low-level image processing technology. In this dissertation, I will not only dig into the possible algorithms of applications of Cellular Neural Network in higher-level image processing, but use practical case study to justify how these applications may turn out with unexpectedly outstanding performance. In such doing, this dissertation serves as a step stone for papers of its counterparts to come, and, more importantly, it proposes a strategic alternative to the

realization of models for image processing.

This dissertation consists of three major parts. In the first part, detailed discussions and delicate analyses of academic papers on Cellular Neural Network will be provided in the hope of helping us see the potentiality of Cellular Neural Network in the applications of image processing. I will focus on the aforementioned limitations on hardware compilation as well. In the second part, I will put forth “texture analysis” as one basic model of analysis when we apply Cellular Neural Network to image processing. In this so-called texture analysis, a useful “spatial feature” is especially drawn to help us overcome possible problems of more complicated Cellular Neural Network applications in image processing. “Spatial feature” also serves as a well-functioning mechanism for technology of image identification. In the last part of this thesis, I will look into a case study, where Cellular Neural Network is applied to help de-screen document image. Using it as an example, we will see how algorithms of Cellular Neural Network may be of marvelous use in applications in document image processing, since it would reduce a great deal of calculation and computation when applied to software compilation, yet opens up unlimited possibilities for higher-speed hardware compilation of high-level image processing.

Acknowledgment

Contents

1.2.1 Cellular Neural Networks ...2

1.2.2 Texture Analysis...4

1.2.3 Genetic Algorithms ...6

1.2.4 Image Documentation...8

1.2.5 Genetic Algorithm based Cellular Neural Network...10

1.3 Contributions...12

1.4 Concluding Remarks...16

2. Fundamentals of Cellular Neural Network and Genetic Algorithm ...18

2.1 The Fundamental Architecture of CNN ...18

2.1.1 Basic CNN formula...20

2.1.2 General CNN model ...21

2.2 CNN Templates for Digital Image Processing...22

2.2.1 Edge Detection CNN Template...23

2.2.2 Color Inverse CNN Template ...24

2.2.3 Image Thresholding CNN Template ...25

2.2.4 Low-pass Filtering CNN Template ...26

2.2.5 Laplacian CNN Template...27

2.2.6 Half-toning CNN Template...28

2.3 CNN Justifications ...29

2.4 Concluding Remarks of CNN...31

2.5 Genetic Algorithm (GA) ...32

2.6 Essentials in GA...34

2.7 Discussions of GA ...38

2.7.1 Parameter settings ...38

2.7.2 Global optimization ...39

2.8 Concluding Remarks of GA...42

3. Image Descreening based on GA-CNN Texture Classification...43

3.1 Introduction...43

3.2 The Proposed System Architecture...44

3.3 Screening Texture Classification ...47

3.3.1 Screening-Texture Patterns ...48

3.3.2 Smooth Indices for Screening-Texture Block Detection ...50

3.4 Design of CNN Templates for Screening Texture Classification by GA ...52

3.4.1 The Settings of CNN Templates ...53

3.4.2 Parameter Adjustments in GA ...54

3.4.3 CNN Template Design by GA ...55

3.5 Selection of Descreening Filters ...61

3.6 Adaptive Determination of Arguments in the Chosen Descreening Filter ...63

3.7 Experimental Results ...65

3.7.1 The Training Phase ...65

3.7.2 The Testing (Descreening) Phase...68

3.8 Concluding Remarks...73

4. Texture Discrimination based on GA-CNN proliferation structure ...75

4.1 Introduction...75

4.2 The Proposed System Architecture ...76

4.3 Transition Bit String (TBS)...79

4.4 The Characteristics of Texture Patterns from CNN’s ...84

4.4.1 The Settings of CNN Templates ...85

4.4.2 The Overview of Texture Patterns Based on CNN’s ...86

4.5 Design of Characteristic Templates Optimized by Genetic Algorithms (GA’s)...89

4.5.1 The Design Rules on GA by TBS ...89

4.6 Texture Classification Mechanism...96

4.7 Experimental Results ...98

4.8 Concluding Remarks...106

5. Conclusions and Perspectives ...108

List of Figures

Fig. 2.1_1 Expression of an isolated cell...20

Fig. 2.2.1_1 Edge detection example by some specified template for (a) the binary image (b) the gray-level image (Left: the original image, Right: the processed image) ...24

Fig. 2.2.2_1 Inverse operation example by some specified template for (a) the binary image (b) the gray-level image (Left: the original image, Right: the processed image) ...25

Fig. 2.2.3_1 Thresholding example by some specified template (Left: the original image, Right: the processed image) ...26

Fig. 2.2.4_1 Low-pass filtering example by some specified template (Left: the original image, Right: the processed image)...27

Fig. 2.2.5_1 Laplacian operation example by some specified template for (a) the binary image (b) the gray-level image (Left: the original image, Right: the processed image) ...28

Fig. 2.2.6_1 Image half-toning by some specified template for (a) the natural gray-level image (b) the human gray-level image (Left: the original image, Right: the processed image) ...29

Fig. 2.4_1 Flow chart of the systematical GA structure ...34

Fig. 2.5_1 Illustrating figure for one-point crossover ...36

Fig. 2.5_2 Illustrating figure for two-point crossover...37

Fig. 2.5_3 Illustrating figure for masking crossover...37

Fig. 2.6.3_1 Illustrating figure for linear scaling...41

Fig. 3.2_1. Flowchart of the training phase of the proposed GA-CNN-based texture classification scheme. ...45

Fig. 3.2_2. Flowchart of the proposed image descreening technique. ...46

Fig. 3.3.1_1 Three example screened images. Images (a) – (c) contain different types of screening patterns. ...49

Fig. 3.3.1_2 Screening Example 1 ...50

Fig. 3.3.1_3 Screening Example 2 ...50

Fig. 3.3.2_1 Partition in the screening pattern for calculating the smooth indices ...51

Fig. 3.4.3_1 Mapping function from the cost function g(.) to the fitness function f(.)...56

Fig. 3.4.3_2 The encoding process of chromosomes in the GA-CNN training phase...58 Fig. 3.4.3_3 The GA designed CNN’s templates for screening textures

classification...60 Fig. 3.4.3_4 (a) The variation of the fitness values during the evolutions of GAs by 200, 400, and 500 generations, respectively. (From left to right) (b) The testing screening pattern for texture classification in gray scales and its binary desired output. (c) The simulated results after texture classification during the evolutions of GAs by 100, 200, 300, 400, and 500 generations, respectively. (From left to right)...61 Fig. 3.4.3_5 The convergence curve for mean squared errors of the fitness function. ...61 Fig. 3.6_1 An x projection function of the screening pattern ...64 Fig. 3.7.1_1 One defined screening type. (a) The original screening pattern. (b) The screening pattern in gray scales. (c) The desired classification result. (d) Our experimental classification result. ...67 Fig. 3.7.1_2 The other defined screening type. (a) The original screening pattern. (b) The screening pattern in gray scales. (c) The desired classification result. (d) Our experimental classification result. ...67 Fig. 3.7.1_3 The mixed screening type. (a) The original screening pattern. (b) The screening pattern in gray scales. (c) The desired classification result. (d) Our experimental classification result. ...67 Fig. 3.7.1_4 An illustrative image for the extraction of screening patterns by smooth indices. ...68 Fig. 3.7.2_1 A testing image for descreening using the Gaussian filter. (a) The original image. (b) The descreened image. ...70 Fig. 3.7.2_2 A testing image for descreening using the Gaussian filter. (a) The original image. (b) The descreened image. ...71 Fig. 3.7.2_3 A testing image for descreening using the median filter. (a) The original image. (b) The descreened image. ...71 Fig. 3.7.2_4 The comparison to other famous methods. (a) The descreened images by our approach. (b) The descreened images by wavelet filtering method. (c) The descreened images by Gaussian filtering method. (d) The descreened images by Medium filtering method. (The images in each row represent various processed images in our database) ...73 Fig. 4.2_1 The GA-CNN based proliferating system (a) Feature extraction phase (b) The recognition phase ...79 Fig. 4.3_1 Illustrations for TBS plots (a) The ideal texture patterns in various frequencies and orientations (b) The corresponding TBS plots orderly arranged from left to right, and top to bottom (corresponding to (a.1) ~ (a.6)). ...83 Fig. 4.4.2_1 Illustration Figure for Feature Mapping based on CNN’s by (a)

Non-overlapping condition and (b) Overlapping condition...88 Fig. 4.4.2_2 Illustration Figure for the distribution in features projected from different CNN templates...88 Fig. 4.5.1_1 Optimized CNN template set for all sixteen texture patterns ...94 Fig. 4.5.1_2 GA training process for our defined CNN template (a) The misclassified texture patterns in the first run (b) The evolved feature maps during the training phase by GA (c) The corresponding fitness function for the best, average, and poorest populations after 50, 100, and 200 generations accordingly...95 Fig. 4.5.1_3 The convergence curve by GA trainings ...95 Fig. 4.7_1 Texture representation for four texture case (a) the original texture patterns (b) feature maps (c) TBS. ...102 Fig. 4.7_2 Texture representation for eight texture case (a) the original texture patterns (b) feature maps (c) TBS. ...103 Fig. 4.7_3 Texture representation for eight texture case based on another CNN template illustrated by (a) feature maps (b) TBS in the horizontal direction (c) TBS in the vertical direction. ...103 Fig. 4.7_4 The convergence condition by GA for (a) The general CNN template (19 optimized parameters) (b) Our predefined CNN template...104

List of Tables

Table 3.7.1_1 Comparison of the smooth indices with respect to three screening patterns in distinct smoothness, (a), (b), and (c) accordingly. ...68 Table 3.7.1_2 Comparison of the classification error for screening patterns by ROB, TE (or gray level average), and our introduced parameters (one determinative index and two screening estimates) in terms of different output formats (Binary/Gray scale)...68 Table 3.7.2_1 Comparison of descreening performance and screening extent in human’s observation by credits and discredits halved in 5 (normally we have three different ranges: low for degree 1-3, medium for degree 4-7, high for degree 8-10)...73 Table 4.7_1 Numerical Comparison for texture discrimination ability based on Fig.4.7_2 and 4.7_3...104 Table 4.7_2 Comparison in the classification outcome based on various features ...105 Table 4.7_3 Experimental results for different rotations of texture patterns...105 Table 4.7_4 Experimental results for different sizes of texture patterns ...105 Table 4.7_5 Experimental results for different TBS (vertical and horizontal)...105 Table 4.7_6 Experimental results for tenfold cross-validation testing model...106 Table 4.7_7 Experimental results for the case when the number of clusters is not known ...106

1. Introduction

In this chapter, we will introduce the related surveys in the applications based on Cellular Neural Networks (CNN’s), the applied image processing techniques in particular. We mainly propose the methodology based on CNN’s for some image processing techniques in this thesis. In this section, we shall begin with what motivated this thesis, and then introduce state-of-the-art in the related areas of the main content of this thesis. In addition, we explicitly define our contributions of the proposed methodology at the end of this section, which might enhance the readability of this thesis.

1.1 Motivation

In the past studies, CNN’s have been well-known for its hardware implementability and the well-connected interactions between the corresponding cells. The basic theory and foundation of CNN’s is not the only issue for most researchers, but how to apply CNN to any industrial or academic areas is yet more interesting and significant. Therefore, the characteristics of CNN’s in hardware implementations and digital image processing motivate us to produce the works related to the discussions in high-order image processing techniques. As we know, the applications of CNN’s are always restricted since we have to take into consideration the hardware implementations and chip design in the development of our algorithms for more complicated applications. In this way, the design of CNN structure has to be as simple as possible. That is the reason that the current status of CNN’s focuses on the chip design for simpler image files like binary ones. It is obvious that most problems in image processing are difficult and unpredictable. In order to avoid using CNN’s too theoretically, we have been dedicated to searching for more possibilities in many image processing applications by CNN’s. Besides, we need to find more solutions for

enhancing the image processing performance and speeding up the algorithms in more complicated images and issues, image documentation in particular. We thus try to carry out all the above requirements and inspire more ideas for readers by this thesis.

1.2 Related Works

1.2.1 Cellular Neural Networks

We shall introduce the interesting topics and various applied fields of CNN’s in this section. In the beginning of developing CNN structure, the studies of the basic theory and the distinguished characteristics in CNN’s are the most important issues in its related research areas. It is surely that most works related to CNN’s cannot simulate its reactions without regarding the stability and robustness of CNN’s [1] ~ [2]. However, the equivalent accounts will be beyond the scope of this thesis. We do not need to highly stress on this issue simply because the problems of hardware implementations can be overcome if the CNN template can be optimized in the restricted range. In addition, the discussions of the steady and transient responses attract the attention of most researchers. When it comes to the applications of CNN’s, the transient response especially matters since it can reflect the connected relationship of corresponding cells of the specific location in the input signal. As for the related applications of CNN, how to determine a better CNN template is quite a critical topic. Apparently the intuitive design and the learning process both lead to the technical approach for deciding a specific CNN template. We have broadly two kinds of approaches in search of CNN templates in the past literature, including analytical and learning methods. The analytical approaches should be composed of a set of local rules which characterize the dynamics of a cell, depending on its neighboring cells. And the operating templates can be obtained correctly by an affine set of inequalities from the transformed local rules [3] ~ [4]. According to different ways of training, the

learning approaches can be classified as local and global learning algorithms. The local learning algorithms [5] ~ [6] take advantage of the neural-based training process like neural networks in back propagation while the global ones [7] ~ [8] optimize CNN templates in a stochastic form like genetic algorithms or simulated annealing approaches.

The difficulty of CNN template design lies in the fulfillment of a given task with implementable templates. As what we mentioned above, the analytical approaches indeed provide a systematical way to look for a better template more simply and directly [9] ~ [10]. Nevertheless, a simpler approach must not give a satisfactory performance or results for complex tasks. There also exist some useful learning approaches such as genetic algorithms [11] or combined strategy for finding robust and stable CNN templates. For the hybrid methods, they combined stochastic optimization schemes with hill climbing algorithms [12]. The combined strategy can solve some specified problems as long as its design fits the requirements of a given issue in advance, but the design would be sometimes more complicated and result in the betray of CNN kernel concept. Thus and so, we need to find not only a systematical and standard approach but also a flexible algorithm for determining CNN templates in an easier fashion. That is the reason that we would adopt genetic algorithms to optimize a better template for any given task. No doubt, this kind of learning methods like genetic algorithms have been studied in the past researches, which makes the related material more sufficient and the researching timing more mutual.

CNN templates can be regarded as coupled or uncoupled by the center element of the control template. In fact, the uncoupled template has ensured the center cell to be free from the surrounding influence. Hence most techniques based on CNN’s for digital image processing would be defined in the CNN template library by this right

kind of template form. Take the applications in shadow projection, global connectivity detection, and connected component scanning for instance, the form of the relative CNN template would be distributed more regularly [13]. As the counterpart, the distribution of template would be irregular if the defined local rules cannot describe the dynamic behavior of input signals. Since the form of template cannot be indicated by its regularity, we would rather simulate our required CNN template by the learning algorithms in this thesis.

1.2.2 Texture Analysis

In this section, we will survey the related material in texture analysis. For texture characterization and classification, statistical approaches have the major impact on the advanced studies of texture analysis. Texture classification has long been one of the most difficult problems to tackle in image processing in terms of the characteristics of various texture patterns, say, uniformity, regularity, coarseness, just to name a few of it. Therefore, many different approaches have been put forth to solve the problems of texture classifications. To carry out a better performance and more comprehensive results in classifying different textures, a great amount of solutions to the analyses of texture patterns are proposed to in the hope of revealing some inherent natures of these patterns and being proven useful for further applications to the higher level processing. There totally exist eight kinds of analytical approaches, inclusive of optical and digital transforms, high-frequency-component analysis, autocorrelation functions, structural elements, co-occurrence probabilities and run length measurement by spatial gray toning, and autoregressive models [14]. Among these approaches, some of them directly or indirectly estimate the spatial frequency of image textures and some of them make use of the structural methods. This is because texture patterns in the different uniformity could be sensitive to different ranges of spatial frequency band. The structural approaches introduced in [15] ~ [16] generally

take the matching procedure to detect the spatial regularity of shapes called structural elements in a binary image, and the descriptions of auto–correlated textures could be carried out by more complicated texture patterns. The co-occurrence probabilities of textures can be described by spatial gray toning, and this approach utilizes various changes of distances between different textures. Also, the approach by measuring run lengths in different gray scales can characterize coarser or finer textures as more or less dominant pixels in a fixed gray toning run length. As to the autoregressive model, it estimates the gray toning proportion of any given pixel in the predefined neighborhood for the representative texture patterns. It can be easily observed that the distribution of coefficients has a very large variation for different image textures. These approaches naturally have different pros and cons and can be made up for each other. For the details of related comparison, [17] concludes that spatial frequency approaches generally have worse performance than the other approaches, and the structural approaches can only apply to the binary images. Besides, the co-occurrence approach can describe the spatial within-relationship of textural patterns by gray toning and can be less influential by monotonic gray toning transformations. The defection of this approach is the inability of describing the shape aspects for tonal primitives, which makes it hard to work well in texture patterns composed of large-area primitives. Finally, the auto-regression model by a given linear estimator can synthesize texture patterns more correctly, so it is more representative for macro-textures. On the other hand, this approach will complicate the analyzed texture patterns by micro-textured segments.

As the popular models and approaches which we have stressed on, it is not an easy task for researchers to find an absolute solution for texture classification and discrimination. And it is uneasy to develop a set of useful features for texture representation. This thesis hence strives itself for finding an analyzing feature set for

texture analysis in addition to working on the practical applications based on CNN’s. As the matter of fact, texture analysis can be seen as the fundamental research to any other image processing techniques. That is to say not only the structure presented in texture analysis can motivate the methodology of other issuing problems but also the developed features for texture representation may be applied to the proper processing approaches of related academic fields. We here try our best to look for more applications based on CNN’s for future possibilities in hardware, and in pursuit of solving these significant problems more useful tools and corresponding features have to be developed to fit the requirements of them.

1.2.3 Genetic Algorithms

In the past, genetic algorithms (GAs) could be characterized by the practical applications, robust optimization and search methods. Many researchers applied this learning algorithm to various areas such as genetic synthesis, chip design, strategy planning, machine learning, image and speech processing. The search methods by GA come from the mechanism of evolution and the combination of natural genetics [18]. The evolution of GA began from the heuristic search approach to simulated annealing algorithm. Simulated annealing algorithm takes thermodynamics into consideration and annealing here can be used as the optimization process for mathematical simulation [19] ~ [20]. Actually, simulated annealing and genetic algorithms are similar in the sense that they use the probabilities for searching the maximum or minimum of functions. However, genetic algorithms would be much different and superior for generating a sequence of populations by using selection, crossover and mutation. For extending the nature of GA, only the individuals with proper chromosomes can be well adapted to competition and survive, so adapting to a changing environment is essential for the survival of each species. The characteristics of genes can be dominated by the respective genetic content if the survival capability

is characterized by the features of corresponding individuals. In some defined case, the observed features can be controlled by a bottom unit like the role of a gene, and the set of genes dominates the features observed from the chromosomes. The evolution process though manifests itself as a succession of changes in sensing the variation of features, and its driving force causes the joint reaction of genetic reproduction mainly coming from the recombination of each other and the appropriate selection. As to the principle regulations of GA, only the fittest individuals can survive and reproduce, and this kind of natural phenomenon can be described as “the survival of the fittest” which truly reflects how GA can be related to the way of genetic combination. As a result, the genes of the fittest survive while the weaker ones fade away. Natural selection implies the survival of the fittest genes, and simultaneously the reproduction process generates diverse choices in the gene pool. The first step of evolution usually combines the chromosomes from the parent generation for reproduction, and then a new combination of genes as well as a new gene pool will be generated. For the combined genes with a worse representative power, the exchange of genetic chromosomes called crossover provides a better combination of genes. Finally, the iterative selection and crossover keep on the evolution process of this gene pool and the generation of competitive individuals will make the learning process terminate properly. Hence, GA can be applied to some problems like optimization or local max/min searching since solving these analytical problems is equivalent to finding the best numerical solution by GA. The reference [21] illustrates the standard form of GA which represents a binary alphabet as the strings of bits in the encoding process and provides the necessary driving power for better solutions to survive in the selection process. The evolved genetic chromosomes should be associated with the higher fitness value, and then could be compared with other reproduced generation. The higher the fitness values of the produced population,

the higher chances of survival for the competitive genes. Also, the crossover operation exchanges the proportion of transferred bits between strings to enhance the performance of reproduction. The mutation operation in GA causes sporadic and random alteration of the bits of strings, and it also implies a direct connection with outer world. Mutation hence at times helps to look for the better combination of chromosomes especially in the difficulty of getting the optimized solution.

We have introduced the related studies and the fundamental concept of GA in this section. As what we described above, GA is not only an adaptive learning algorithm but also a deterministic approach for global optimization. In this thesis, we use GA as the training tool for looking for the related parameters in CNN settings. GA here plays an important role in the design of templates when no a-priori information can be given in advance. The nature of GA makes the processed results from the optimized template approach the desirable ones of our applications. Therefore, GA indeed provides a better solution for us to optimize an arbitrary CNN template in the specific field of applications.

1.2.4 Image Documentation

Image documentation can be regarded as one significant step of image preprocessing before dealing with any complicated applications. As we know, there are many key topics in this field such as noisy background removal, image descreening, image deskewing, auto-cropping, and so forth. Each of them has some crucial influence on some issues in the related research fields. We take image descreening for example to illustrate how we can handle this difficult problem by hardware orientated CNN’s. More complex issues in image documentation can also be solved by the generalized approach. In fact, image descreening takes an important part in the analysis of document images. It could make much easier the following

processes of document images such as texture or graphic separation. The existence of screening signals will make it harder to handle and analyze the document images, and the specific kind of problems in dealing with document images are the general ones for photo preprocessing or image enhancement.

There exist many methods for image documentation such as wavelet transforms, thresholding techniques, and the statistical analysis methods, etc. Wavelet transforms use the decomposition analysis of different levels to remove these undesirable screening signals. Its key point lies on the choice of basis functions. From the papers [22] ~ [24], we could find the applications restricted by using wavelet transforms with common basis functions such like Haar function and Daubetch spline function. In addition, the quality of documental images may suffer degradation during transformation from a scanned halftoned image to electronic formats through the introduction of artifacts such as morie patterns [25] ~ [27]. Numerous inverse halftoning or descreening methods have been used to eliminate these artifacts regardless of the causes for generation of screening noisy patterns [27] ~ [29]. In most studies, (inverse) halftoning techniques can be generally classified into two categories: frequency [30] and spatial [31] domain approaches. As a matter of fact, frequency domain approaches could keep more textured information in the screened images; whereas spatial domain approaches retain more properties for the spread of locations of screenings. That is also the reason that most papers tend to use such frequency domain methods like FFT, wavelet, or even Gabor filtering methods. Unfortunately, their descreening results are still restricted even if complex filters are used through time consuming procedures. This mainly results from that no fixed filter could be successfully employed in every kind of screened images. Thus, in chapter 3, we introduce a unique mechanism including two parts: the classification of screening

textures and the descreening procedure by the selected adaptive lowpass filter based on the classified screening textures. We hence propose a new strategy for image descreening in image documentation based on an innovative analyzing model in this thesis. It consists of the design of CNN structure and studies of characteristics in document images. Due to the different intensity of screening signals in different images, the screenings can be detected and processed by the proper solutions. And also, our proposed scheme for an optimal selection of filters can remove the screening signals more efficiently. We demonstrate our experimental results with a large number of various document images to show the robustness and stability of the proposed method. In the chapter 3, we will give the details of our proposed methods in the design of CNN structure for the representative topic in image documentation – image descreening.

1.2.5 Genetic Algorithm based Cellular Neural Network

In this section, we would like to survey the related applications of CNN by GA. Especially, we would focus on the topics introduced in this thesis, texture analysis and image descreening. Like neural networks [32] ~ [35], CNN is a large-scale nonlinear analog circuit, which processes signals in real time. CNN is made of a massive aggregate of regularly spaced circuit clones, called cells, which communicate each other directly only through its nearest neighbors [13]. To avoid the results from being confined and thus leading to an unsatisfactory outcome as shown in [36], [37], GA is therefore preferred to solve the problems of stability and adaptation in CNN’s for two reasons. First, GA here carries with itself a dual function in deciding template elements for CNN: it serves to minimize the objective function, the optimization while avoiding the occurrence of oscillation and chaos when testing the pros and cons of working templates for CNN, that is, adaptation. Second, the design of template elements for CNN based on GA is no longer subject to the types of objective

functions and minima, i.e., differentiability of the cost function and the existence of local, global, separate, multiple minima, etc. Another advantage is the fact that GA not only applies itself to single layer CNN, but also can be used for the parametric design of multilayer CNN. Like what is mentioned in [38], the template design of multilayer CNN is necessary at times for complex problems that cannot be solved or realized in the easier manner of single layer CNN particularly. Selecting CNN templates by GA, therefore, has been widely adopted in every field of applications, regardless of single- or multilayer CNN, and shown to be powerful and robust in theory and practice [38] ~ [41]. Stochastic learning approaches, GA in particular, have become a crucial alternative to deterministic ones, which replace the classical methods by using the independent properties of initial conditions and the domain of applications combined with the implicit parallelism [39]. And the detailed descriptions about GA for choosing template elements of multilayer CNN have been given in reference [42] where only the global responses to the input images of the system would be available. The multilayer CNN design is certainly employed in the near future if the texture patterns were much more complicated than those we expected or no a prior information about the structure of the system had been given, or the separate operation of every layer had been in need. In [43], three different CNN templates trained by GA were proposed and carried out to give us a comparative index for performance of the system in different combinations of evolutional ways among generations, i.e. the average, inverse, and time-interpolated templates. Also, a modified assumption of parameters in GA like crossover or mutation rate in [43] made it practical to push the responses out of the way giving rise to the difficulty of convergence. Beside of the changes of fitness functions in GA, GA could be amended in other evaluation forms like the penalty functions mentioned in [39], [42] to give a punishment assessment between layers of CNN if the structure of multilayer CNN is

required. Now that the precise adjustment of parameters in our CNN template design based on GA is not necessary for our screening pattern classification in the descreening process, some slight changes about GA like the adaptation of fitness functions, how to set the parameters in the evolutional flows, etc. would be very useful and applicable to the issue of image descreening addressed in the chapter 3. Besides, the advanced studies on GA based CNN will be given in chapter 4 in more details.

1.3 Contributions

We will organize this thesis by giving our contributed parts and the whole constructed structure of our strategic approach in this section. This thesis contributes to applying CNN’s in digital image processing. CNN’s have been only used in the simple and direct operations of image processing techniques. In this thesis, we try to see CNN’s in various realized simulations for image analysis. More clearly, this thesis deals with image processing problems by a separate mechanism which makes use of CNN architecture and original information extracted from image data. At this place, CNN plays an important role in image analysis – feature extraction. CNN is not only distinguished in its hardware implementability but also reveals some information of digital images in some sense by placing different CNN templates. To be more systematically, we shall firstly introduce our structure of CNN and our significant contributions in two aspects.

A. Image analysis

CNN has been used in many areas including digital image processing. Since using CNN is subject to the relationship between the original image files and CNN parameters, the image processing techniques by CNN should be simple and the convolved results from CNN should be reflected directly. This thesis pursues using

CNN to analyze the information of image data. Later in the chapter 3 of this thesis, we demonstrated how to use CNN in some high-level image processing like image documentation. CNN here is a classifier for specific predefined patterns to determine the following strategy after classification where we have referred the CNN structure as one part of the whole software simulations and algorithm development. Simultaneously, CNN is used to decide the related arguments that could reflect the linking relationship between image data and CNN parameter setting. This thesis thus introduces a complete strategic approach to understand the image natures for image analysis. We then explicitly list the main contributions in this identified category which have been made by our proposed structure as follows.

A.1 Image preprocessing

CNN used to handle some simple image applications, so many studies only focused on the preprocessing steps of digital image processing. In this thesis, we have clearly defined the range of space that CNN could be applied to and the corresponding adjustments and critical points in CNN parameter setting. That is, our applications in image processing by CNN would focus on algorithm development rather than hardware implementation only because the lack of CNN applications makes it hard to use the advantages of CNN structure well.

A.2 Image documentation

We applied CNN to image documentation since this field is a very important one in various researching fields of image processing. Also many problems in image documentation have been challenging and difficult even in software engineering and simulations. Therefore, we prove that CNN could not only be valid for simple operations of image analysis but also useful for more complicated applications. This thesis makes use of CNN structure to discuss the natures of image data for understanding the characteristics of documental images. In this way, CNN is like an

analytical tool for illustrating image data rather than a specific tool for some specific application. This thesis successfully uses CNN in image processing in a different point of view. For the other significant contribution proposed by this thesis, we have the following category.

B. Feature extraction

Unlike the traditional approaches using CNN’s in the literature, this thesis does not focus on finding a specific CNN template for some specific image applications. CNN is taken as an analytical tool for digital image processing, in which CNN could be regarded as a transformation mapping like FFT, wavelet transform, and so forth in software engineering. The previous researches by CNN put a higher stress on hardware construction than being applied to more complicated applications and understanding the nature of images. This thesis hence tries to work on applying CNN to more complicated image applications and associating CNN templates with the characteristics of image files. Therefore, we have proposed a new approach in feature extraction by using CNN’s and provided a transformation process to project the original image information into another feature space in this thesis. And this mainly focuses on the following subparts.

B.1 A pre-classified mechanism for different screening images

In the past, the performance of image descreening has been restricted only because the same strategy has to be applied to for many kinds of images. We thus in this thesis proposed a very different structure – the pre-classified mechanism for different screening images. This mechanism makes it easier to deal with various screening images and made a great improvement in image descreening performance. It implies that the CNN structure can also combine with any motivated mechanism from software-oriented status.

Our proposed approach in this thesis illustrates the simple CNN outputs in a very different way and also associates the image natures with every adjusted arguments of CNN cell. For image analysis and texture discrimination, the illustrative way of CNN outputs makes the applications by CNN more prevailing and flexible.

B.3 A proliferated structure of CNN templates

The optimization of CNN templates was difficult and insufficient. Thus, we try to propose a proliferated structure to determine CNN templates more adaptively and efficiently. In our proposed structure, CNN templates could be flexibly proliferated for any set of texture patterns. The number of CNN templates that we have to optimize for any prepared texture patterns could be effectively reduced and the optimization process would be shortened in the predefinition of CNN templates. B.4 A new feature series for texture analysis – Transition Bit String (TBS)

The most significant matters in the difficulty of applying CNN to the higher-level image processing lie in the lack of image information extracted from CNN. Because of this, we proposed the one-dimensional feature curve as well as its feature series in this thesis to provide more chances of using CNN for more applications of image processing. Our proposed feature curves help to understand the natures of textured image patterns and also offer an evaluation index to determine whether the texture patterns that we have to classify in our database are discriminated enough and to decide the number of CNN templates and the corresponding parameters in the optimized templates. As above, we have roughly introduced in this thesis how we could apply CNN in complicated applications of image processing and what kind of relative CNN arguments we have to predefine and determine in advance. To sum up, we have introduced in here the main contributions before getting in the kernel part of this thesis. We did this to make the organization of this thesis more clear and definite.

1.4 Concluding Remarks

In this chapter, we have introduced the related surveys and state-of-the-art of each essential item presented in this thesis. Also, we illustrate the main contributions of this thesis. The structure of CNN’s in the past was only applied to some simple and intuitive applications of image processing. Hence we develop more algorithms based on CNN’s in order to increase the future applications for hardware implementation. In this whole framework, we need to look for an efficient method to optimize the related parameters which have to be determined in CNN structure. The detailed information of GA has been given in this section and the prominent features of using GA in the design of arguments have also been introduced. As long as an effective approach to deciding CNN parameters can be determined, the key solutions for our chosen applications by CNN’s would depend on understanding the characteristics of digital images. In this way, more applications based on CNN’s could be brought in the CNN field much easier. In addition, we also work on image documentation, image descreening in particular, since this kind of issues have been the most difficult problems that need to be dealt with by CNN’s. So we try to get to know more about the internal characteristics of document images and associate this relationship with CNN’s. It is natural for us to design the related arguments in image descreening when implemented by CNN’s. In fact, image descreening can be regarded as one of high-order image applications because we cannot handle this problem by a simple strategy for all cases. We firstly give the survey of image documentation in this chapter and later in chapter 3 and 4 we will show the systematic approach based on CNN’s in getting this problem clarified. After applying CNN’s to image documentation, we focus on incorporating CNN’s with some fundamental analysis in image processing. Thus, texture analysis we showed in this thesis provides a versatile

solution for any other image processing techniques when it always plays an essential role in the fundamental researches related to properties of digital images. Unlike the traditional approaches based on CNN’s for texture analysis, the structure proposed in this thesis gives a more flexible mechanism for CNN argument optimization and the developed features make texture analysis based on CNN’s apply to more complicated problems in image processing. To make our main content of this thesis more clearly, we organized this thesis in the following order: fundamentals of Cellular Neural Network (CNN) and Genetic Algorithm (GA), image descreening based on GA-CNN texture classification, texture discrimination based on GA-CNN proliferation structure, and conclusions and perspectives.

2. Fundamentals of Cellular Neural

Network and Genetic Algorithm

Since this thesis describes the methodology and applications that can be implemented by CNN’s, we here illustrate the basic structure of CNN and the formation of CNN basic theory. Also, a more generalized model and formulas have to be given in this chapter for high-order image processing. We do not put our emphasis on the discussions of CNN stability and robustness, and we will not over focus on the derivation of dynamic plots in CNN structure because the related proofs of theories have been given in the literature. Instead, we will bring in the image processing field more practical uses by illustrating some basic and simple examples of applications based on CNN’s. These simple instances could give broad descriptions about how the elements in CNN templates can be associated with the properties of digital images, which also speed up optimizing CNN templates by GA. That is why we in this chapter introduce the selected CNN templates in the original CNN library for edge and corner detection, image thresholding, connected component detection, half-toning and inverse half-toning, histogram generation. Besides, we will introduce some essentials and important adjustments about GA in the back of this chapter.

2.1 The Fundamental Architecture of CNN

CNN is more appropriate to be the acronym for Cellular Nonlinear Networks than Cellular Neural Network in this thesis since we would use CNN as a nonlinear processing mechanism rather than a learning mapping in some complicated applications. CNN still has the characteristics of networks, a spatial arrangement of locally-coupled cells where each cell can be regarded as a dynamic system with an input, an output, and a defined state which can be prescribed by some dynamic rules. In this thesis, we will put our stress on some applications of image processing based

on CNN’s. We hence only illustrate the two-dimensional CNN architecture throughout this section. Before we introduce the whole CNN structure, we would describe the components and variables of an isolated cell. For any arbitrary isolated cell, there are four general variables for the definition of a standard CNN structure. They are the input uij, output yij, state xij, and threshold zij, respectively, where each

variable represents an essential segment in the standard formulas of CNN’s, and the subscript indicates the corresponding location in the neighborhood of this isolated cell. In general, the threshold is usually a constant scalar for simplicity and the other three variables can be considered as the functions of continuous time t or the discrete time in the special case. The initial state can be given for some specific application or adjusted at any time during the processes. That is to say, for any fixed threshold zij ,

the given initial state xij , and the processed input uij , the state xij at time t of the

isolated cell Cij will be evolved according to a time variant state function defined

below. N j and M i for t u t z t x f t xij = _{ij ij ij ij} ≤ ≤ ≤ ≤ ⋅ 1 1 )) ( ), ( ), ( ( ) ( (1) where the current state xij can be seen as the function of combination of the last state

xij , the threshold zij , and the input uij. It can be easily observed that all the cells are

identical in image applications. Also, (1) can be regarded as the formal ordinary differential equations. Without loss of generality, we have used the simplest output function which is defined as (2).

y_ij(t)=g_ij(x_ij(t)) (2) The output function here is simply the predefined transformation from the current state xij to the output yij. The detailed mathematical formulas of an isolated CNN cell

were proposed by Chua and Yang in 1988 and widely used in the past applications, which could be listed as follows.

State equation: ij x_ij a_ijf x_ij b_iju_ij z_ij dt dx + + + − = ( ) (3) where a and _ij b are the weighting coefficients. _ij

Output function: ) ( _ij ij g x y = where ⎪ ⎩ ⎪ ⎨ ⎧ − ≤ − < ≥ = − − + = 1 , 1 1 , 1 , 1 ) 1 1 ( 2 1 ) ( ij ij ij ij ij ij ij x x x x x x x g (4)

To illustrate the isolated cell and its related variables, we have Fig. 2.1_1 to simply describe the relationship among theses four variables.

Fig. 2.1_1 Expression of an isolated cell

We have described the simple architecture and the basic theory of CNN, and we will specially introduce the basic CNN formulas and the general CNN model for the digital image applications in the following two sections.

2.1.1 Basic CNN formula

For the image size MxN in the CNN applications, the image size is equivalent to the CNN array and the state equation (3) can be rewritten in a more formal way as (5).

∑

∑

referred to as each pixel of an image. Hence i and j would run from 1 to M and N, Output Threshold

u

z

x

y

C

respectively. Equation (5) would totally has MxN nonlinear ordinary differential equations. For the basic CNN formulas, the same equation can be defined as (4). In definition, (5) only extends its generality only inside the boundary of CNN array. In order to make (5) more complete, the additional boundary conditions have to be defined. The three boundary conditions which have been used widely in the literature could be listed as follows.

A. Fixed boundary condition

This boundary condition assigns the state xkl of each cell xkl in (5) inside the

boundary to be a fixed constant. B. Zero flux boundary condition

This boundary condition confines the states xkl of the corresponding cells in

the neighbor perpendicular to the boundaries to be the same. C. Periodic boundary condition

In this boundary condition, the first and last rows/columns of the CNN array are similar to be periodic.

After giving the boundary conditions, the preparation of CNN could be done if the initial state for all cells were specified. For image processing in particular, the initial state could be assigned via the gray-level in an image which has to be normalized first between -1 and 1. From all the above essentials in the standard CNN structure, we would have the specific CNN template for the specific application.

2.1.2 General CNN model

The equations that we have introduced for a standard CNN array could not be applied to all applications, so a more generalized CNN model would be preferred by giving different dynamics and coupling laws of each cell. Hence, a general MxN CNN model could be given as long as the following conditions would be specified, i.e. the state equations and the coupling laws of each isolated cell, the boundary and

initial conditions. With the specified definitions in more details, equations (1) and (2) would well describe the general CNN model. As for image processing applications, the ordinary differential equations can be recast in the following matrix form. The matrix representations for CNN arrays provide more choices for image processing, and more image applications could be carried out by incorporating CNN into the simulated processes. X =F( X) ⋅ (6) where ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 22 21 1 12 11 2 1 2 22 21 1 12 11 MN M M n n MN M M n n x f x f x f x f x f x f x f x f x f X F x x x x x x x x x X L L M L L M M M L L M M L L L L L L M L L M M M L L M M L L L L

2.2 CNN Templates for Digital Image Processing

As we know, CNN’s can be applied to many applications by specifying the weighting coefficients defined in (3). More systematically, there are several requirements that have to be assigned for a specific image application. Since the specific image processing can be looked upon as a transformation from an input image U (uij representing the mapped value of each pixel of the input image) to an

output image Y (yij representing the mapped value of each pixel of the output image)

with a series of operations, we have to specify the types of input image for using CNN simulation in the first step. Take the gray-scale image and true color image for

instance, we have the first-order and third-order of cells defined for the state xij,

respectively. After that, the initial state and the boundary condition for the specific image application have to be selected or designed according to the specified requirements. Besides, the most important matter in the design of CNN structure associating with some image application lies in the decision of a combination of parameters in CNN’s, called CNN template. Once the CNN template could be determined, the problem of image could also be overcome. In the following sections, we would survey several predefined CNN templates for image processing in binary and gray-scale format. We selected these examples of templates in the literature simply because we regard these CNN templates in some basic image applications as the shortcut to the higher-order image applications based on CNN’s.

2.2.1 Edge Detection CNN Template

Descriptions: Extract edges of the objects of the input image.

Rules: Each black pixel which has at least one white pixel in the defined

neighborhood is defined to be an edge cell.

Boundary Condition: Fixed boundary condition Initial State: 0x_ij(0)= (0 means white in an image)

Cloning Template: 0.5 1 1 1 1 8 1 1 1 1 0 0 0 0 2 0 0 0 0 − = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − − − − = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = B z A Example:

(a)

(b)

Fig. 2.2.1_1 Edge detection example by some specified template for (a) the binary image (b) the gray-level image (Left: the original image, Right: the processed

image)

2.2.2 Color Inverse CNN Template

Descriptions: Inverse colors of the objects in a digital image.

Rules: The color of the input image would be equivalently inversed via the

middle of the color range in CNN format.

Boundary Condition: Fixed boundary condition Initial State: 0x_ij(0)= (0 means white in an image)

Cloning Template: 0 0 0 0 0 5 . 2 0 0 0 0 0 0 0 0 25 . 0 0 0 0 0 = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − = B z A Example:

(a)

(b)

Fig. 2.2.2_1 Inverse operation example by some specified template for (a) the binary image (b) the gray-level image (Left: the original image, Right: the processed

image)

2.2.3 Image Thresholding CNN Template

Descriptions: Transform a gray-level image into a binary image by some

predefined threshold.

Rules: Each pixel of a gray-level image can be labeled as ‘pure white’ if and only

if its transformed intensity in CNN format (between -1 and 1) is higher than some predefined threshold z*.

Boundary Condition: Fixed boundary condition Initial State: )x_ij(0)=u_ij(0

* 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 z z B A = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = Example:

Fig. 2.2.3_1 Thresholding example by some specified template (Left: the original image, Right: the processed image)

2.2.4 Low-pass Filtering CNN Template

Descriptions: Do the low-pass filtering for the gray-level image..

Rules: The pixels with some specific color range (usually in the low band) can be

labeled as ‘black’ pixels while the others are labeled as ‘white’ pixels.

Boundary Condition: Fixed boundary condition Initial State: 0x_ij(0)= (0 means white in an image)

Cloning Template:

A notspecified B z notspecified 1 2 1 2 4 2 1 2 1 16 1 = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ × = = Example:

Fig. 2.2.4_1 Low-pass filtering example by some specified template (Left: the original image, Right: the processed image)

2.2.5 Laplacian CNN Template

Descriptions: Laplacian operation for the digital image.

Rules: Each pixel of the input image would be filtered via the defined Laplace

filter.

Boundary Condition: Fixed boundary condition Initial State: 0x_ij(0)= (0 means white in an image)

Cloning Template: specified not z B specified not A 0 25 . 0 0 25 . 0 1 25 . 0 0 25 . 0 0 = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − = = Example: (a)

(b)

Fig. 2.2.5_1 Laplacian operation example by some specified template for (a) the binary image (b) the gray-level image (Left: the original image, Right: the processed

image)

2.2.6 Half-toning CNN Template

Descriptions: Transform a gray-level image into a half-toned binary image which

preserves the major characteristics of the original image.

Rules: The gray-level intensity of an input image would be re-sampled to obtain

a binary image via half-toning which could resume the original image intensity by inverse half-toning.

Boundary Condition: Fixed boundary condition defined by the constant values of

the initial state and the input image.

Initial State: )x_ij(0)=u_ij(0 Cloning Template: 0 07 . 0 1 . 0 07 . 0 1 . 0 32 . 0 1 . 0 07 . 0 1 . 0 07 . 0 07 . 0 1 . 0 07 . 0 1 . 0 15 . 1 1 . 0 07 . 0 1 . 0 07 . 0 = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − − − − = B z A Example:

(a)

(b)

Fig. 2.2.6_1 Image half-toning by some specified template for (a) the natural gray-level image (b) the human gray-level image (Left: the original image, Right:

the processed image)

2.3 CNN Justifications

In this section, we shall discuss the related justifications about CNN. Also, we would like to elucidate some querying points for those who might be concerned about using CNN in the related applications of image processing in three aspects.

A. Discussions of CNN equations

As what we have mentioned in the earlier part of this chapter, the most crucial part of applying CNN to image processing is to determine the corresponding arguments of CNN templates. In addition, the structure of CNN depends on the state and output equations as (3) and (4). Those who are good at image processing but not familiar with CNN might doubt the relationship between these two equations and might be curious about the resultant images after using CNN. In fact, many original studies

about CNN have proved that the processed images after CNN should be in the binary form on account of the following theorem [68].

Theorem 2.3.1.

The output y of every cell at any stable equilibrium point of a completely _ij stable standard CNN defined by (3) and (4) is equal to either plus 1, or minus 1, if the center element a of the A template satisfies _ij a_ij >1.

Also, without loss of generality, the processed images could be binarized if a_ij ≠1 as to meet the bistable criterion of CNN.

B. Justifications of CNN circuit

Some might be concerned about the pros of cons by using CNN. Therefore, in this section we shall briefly introduce some significant reasons for applying CNN’s to applications of images. As we know, CNN is very attractive in its successful implementation of an analog input/output CNN universal machine which can also be referred to as a CNN universal chip. The analog circuit is very different from the digital one in the sense that the analog could truly transmit and process most signals in the undistorted way. Furthermore, a single silicon chip is regarded as a completely dynamic array stored-program computer where the CNN chromosome can be executed and programmed on the chip at a tremendously high speed (given 1012 analog instructions per second based on a 100x100 CNN chip). Also, the chip design by the CNN universal machine would differ from that by a digital circuit because it could be carried out in the completely nonlinear dynamics. Hence, we would like to take advantage of some dominant and distinguishing characteristics of CNN’s in more complicated applications of images.

C. Sensitivity of CNN’s

concerned about its sensitivity when applying CNN to various applications. In this thesis, we used CNN’s in image documentation and texture analysis. For CNN applications that we discussed in this thesis, we have to find the appropriate templates of CNN with respect to some specific purpose. We in here make use of GA to optimize the related arguments of CNN templates. Naturally, the desired patterns in some sense should be specified beforehand. Unlike the concept of classic cellular automata, CNN cannot be defined by local rules directly but can be simply defined by iterating the CNN genes. That is why GA could be broadly applied to every sort of image applications. Speaking to the proposed applications in the chapter 3, we do not need to accurately pre-specify the desired patterns of CNN templates because only the ratio of black and white pixels in the CNN output would be quite sufficient to provide a proper decision in the later processes. The related explanations about sensitivity in optimizing CNN arguments when using GA have been given in some important works of the literature [13], [43]. As they concluded, the form of desired patterns in black/white or white/black arrangement has no influence on the final results even for some applications in need of high accuracy. Therefore, in the point of view in using CNN for pattern selection, the arrangement of black/white or white/black in setting the desired patterns shows no difference in the final performance if GA is applied to optimize the CNN templates.

2.4 Concluding Remarks of CNN

It is observed that the CNN templates in all introduced examples are defined by the sphere of influence in radius r = 1. That is to say, only 19 parameters in the triplet template {A, B, z} have to be determined. The main reason is that this kind of CNN template would be much more efficient for various image applications by experienced rules and practical uses. Besides, the examples demonstrated above try to associate