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研究生:林晏
研究生(外文):Yen Lin
論文名稱:廣義高斯混合模型快速參數估計方法及其應用
論文名稱(外文):A Fast Estimation Method for the Generalized Gaussian Mixture Distributions and Its Applications
指導教授:范書愷范書愷引用關係
指導教授(外文):Shu-Kai S. Fan
學位類別:博士
校院名稱:元智大學
系所名稱:工業工程與管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:92
中文關鍵詞:廣義高斯函數形狀參數最大概似估計動差匹配估計期望最優化估計粒子質群最佳化
外文關鍵詞:Generalized Gaussian distribution (GGD)Shape parameterExpectation maximization (EM)Particle swarm optimization (PSO)Moment matching estimatorMaximize likelihood estimator
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本論文針對廣義高斯混合模型 (Generalized Gaussian Mixture Distribution, GGMD) 提供一個快速參數估計方法。在一般性訊號處理研究,不論是人造或是自然產生的訊號,為了辨識訊號的樣態與行為,了解其分佈 (distribution) 是首要步驟。而本論文以極具配適彈性的GGMD模型來逼近真實的訊號分佈,藉以獲得隱藏在大量資料底下的訊號樣態及其行為模式,便於後續訊號解析與樣態分類等研究工作。如此,如何快速地獲得GGMD的適當參數組合,便成為本研究主要目的。本研究藉助傳統的估計方法,諸如最大概似估計法 (Maximum Likelihood Estimator, MLE),動差匹配法 (Moment Matching Estimator, MME),以及期望最優化演算法 (Expectation Maximization, EM) 等,結合啟發式的粒子質群最佳化演算法 (Particle Swarm Optimization, PSO),發展出一個廣義高斯混合模型的快速參數估計方法,稱為EP2估計方法。該EP2估計方法是針對GGMD模型進行設計,適用於混合模型之中參雜著形狀具異的機率分佈,諸如超高斯分佈 (super-Gaussian) 與次高斯分佈 (sub-Gaussian) 等使得其他估計方法無法快速有效解決的複合式機率分佈。根據初步的模擬資料實驗結果,證明EP2估計方法可以有效地解決GGMD的參數估計問題,而影像灰階訊號的機率密度函數估計實驗成果呈現,則顯示EP2方法對於具有非高斯分佈結構的訊號,可以快速地估計出適切的機率密度函數,進而有效解析出影像分佈隱藏的特徵。
In this dissertation, a fast estimation method which is developed for estimating the parameters of the generalized Gaussian distribution (GGD) mixture model is presented. In practice, the signal frequency observed from both man-made and natural data is modeled as a random variable, which could be approximated by the GGD mixture model. To seek the “best-practice” parameter estimates of the model, the new hybrid method intends to combine the merits of the estimation efficiency via statistical estimators and the computation efficiency via evolutionary algorithms. It relies on three statistical estimation methods, such as maximum likelihood estimator (MLE), moment matching estimator (MME), expectation maximization (EM) algorithm and a state-of-the-art evolutionary algorithm: particle swarm optimization (PSO), collectively termed the EP2 method that aims to find the best parameter estimates for the GGD mixture model. The EP2 method is designed particularly for estimating widely ranged shape parameters that characterizes the Gaussian family densities, including sub- and super-Gaussian densities. The preliminary experimental results obtained by modeling both simulated data and complex image histogram data arising from non-Gaussian sources are employed to illustrate the estimation effectiveness and efficiency of the proposed method. The applications to medical image separation and color image segmentation are assessed and reported to show that the EP2 method could provide the optimal estimates of the GGD mixture model for the parametric thresholding method, such as Kittler-Illingworth’s method, to obtain quality segmented outputs from the complex images with non-Gaussian histogram.
摘要 iii
ABSTRACT iv
誌謝 vi
LIST OF FIGURES x
LIST OF TABLES xii

CHAPTER 1. INTRODUCTION 1
1.1 Background 1
1.2 Motivation 2
1.3 Description of Histogram Curve Fitting with the GGD Mixture Model 3
1.4 Research Objectives 5
1.5 Organization of the Dissertation 6
CHAPTER 2. LITERATURE REVIEW ON OPTIMIZATION AND ESTIMATION ALGORITHMS 7
2.1 Optimization Algorithms for the Minimization Problem 7
2.1.1 Particle Swarm Optimization 8
2.1.2 Nelder-Mead PSO 10
2.2 EM Algorithm for Estimating the Gaussian Mixture Model 15
2.3 EM-PSO Method for Estimating the Gaussian Mixture Model 18
2.4 EM-GA Method for Estimating the GGD Mixture Model 22
2.5 Methods for Estimating Shape Parameter of the Single GGD Model 25
2.5.1 Maximum Likelihood Estimator (MLE) 26
2.5.2 Moment Matching Estimator (MME) 27
2.5.3 Entropy Matching Estimator (EME) 28
2.6 Summary of the Literature Review 29
CHAPTER 3. HYBRIDIZED EM-BASED ESTIMATION MEHTOD 32
3.1 Objective Function of the GGD Mixture Model Fitting 32
3.2 EM Algorithm for Estimating the GGD Mixture Model 33
3.3 A Hybridized EM-based Estimation Method, EP2 35
3.3.1 PHASE I of the EP2 Method 36
3.3.2 PHASE II of the EP2 Method 38
3.4 Procedure of the EP2 Method .40
CHAPTER 4. PRELIMINARY EXPERIMENTAL RESULTS 43
4.1 Experiments on Simulated Data 43
4.2 Experiments on Standard Image Histogram Data 47
4.3 Experiments on Complex Image Histogram Data 50
4.4 Estimation Methods Comparison in Real Image
Experiments 57
4.5 Experiments for Multiple Level GGD Mixture Model Estimating 59
4.6 Summary of the Preliminary Experiments 61
CHAPTER 5. APPLICATIONS OF IMAGE SEGMENTATION 62
5.1 Image Thresholding by Parametric Approach 62
5.2 Minimum Error Thresholding 63
5.3 Medical Image Separation 65
5.4 Color Image Segmentation 72
CHAPTER 6. CONCLUSIONS 78
6.1 Concluding Remarks 78
6.2 Future Research 80
APPENDIX I
Multivariate Gaussian Mixture Model Fitting 81
REFERENCES 89
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