臺灣博碩士論文加值系統

本文發展多尺度的數值模擬方法，並提出四種不同尺度下的應用。這些應用分別是人臉辨識，改善3D醫學影像品質，奈米尺度下的真球度評估法，以及利用耗散性分子動力學預測靜態水滴的接觸角。本論文分為四個章節。在第一章中，我們提出一個嶄新的自動人臉驗證方法。此方法考慮了人臉的老化因素，進而在比對的過程將老化因素視為一個補償因子。我們的方法主要在於找尋雙對稱平面，並且利用對稱特性給予各特徵不同的加權值。雙對稱面是利用兩個內眼角與鼻尖所找到。此方法結合三維特徵過濾與二維特徵篩選進而找到臉部可用的特徵。由雙對稱面所衍生的對稱輪廓為兩模型比對的重要參考。文中所使用的比對方法為修正型ICP方法。任何一個配對的特徵皆給予一組相關性的權重值，再將這些對應點映射到齊次座標，以SVD方法計算出收斂的轉換矩陣。最後比較掃瞄模型與資料庫模型的差異度。驗證成功的模型則再度與資料庫模型進行線性混和，以更新原本資料庫的模型。從交叉比對的結果顯示，我們的方法有極高的識別率。第二章針對3D醫學影像提出一個平滑化方法。在傳統上的一序列醫學影像(DICOM)常以Marching Cubes方法建立的3D模型，然而這些3D模型往往存在尖銳不平滑的表面。我們提供一個後端處理的方式，針對這些由Marching Cubes所建立的3D STL影像進行局部與整體平滑化。我們採用八元樹法快速排除掉重複的點，並且建立3D資料點的多層次相鄰關係。藉著這些不同層次相鄰點的混合可達到平滑化的目的。由於平滑化所產生網格緊縮的現象，可由體積比做為補償係數。本方法可在線性時間內完成，並且有不錯的平滑化效果。在第三章中，我們提供了一個在微小尺度下，測量真圓度的方法。該方法以牛頓法為基礎，進而用疊代解出多維度的最小平方問題。我們以影像方法測量數張SEM照片上的球的真圓度，再進一步還原這些SEM照片的空間相對關係，最後再以這些還原後的空間座標點做為評估真球度的依據。我們以像素內差方法，可將原本的平面解析度提高一到二個數量級。實驗數據證實，經過約三十次的疊代，數值上的相對誤差為10–12的數量級，此數值遠低於SEM照片的解析數值(10–7)，也說明了該方法的數值誤差可以被忽略。在第四章中，我們以耗散性分子動力學模擬水滴在平版上的靜態行為。由於不同材料具有不同的表面能量，使得靜態水滴在平版上可能呈現出親水現象或斥水現象。我們以數值模擬，改變平板分子的表面能量特性，進而呈現不同程度的親水或斥水特性。藉著調整水分子與固體分子間的保守力(包括吸引力與斥力等參數)，我們可以模擬出靜態水滴的接觸角範圍從55度到165度。這些數值模擬數據，有助於幫助我們分析水滴在不同材料特性下的物理行為。

This dissertation presents multi-scale numerical simulations in four categories. They are face recognition/authentication, smoothing medical models, assessment of sphericity and dissipative particle dynamics simulations. In chapter 2, we present a novel method for automatic face authentication in which the variance of faces due to aging has been considered. A bilateral symmetrical plane is used for weighting the correspondences of the scanned model and database model upon model verification. This bilateral symmetrical plane is determined by the nose tip and two canthus features. The coupled 2D and 3D feature-extraction method is introduced to determine the positions of these canthus features. The central profile on this bilateral symmetrical plane is the foundation of the face recognition. A weighting function is used to determine the rational points for the correspondences of the optimized iterative closest point method. The discrepancy value is evaluated for the authentication and compensation between different models. We have implemented this method on the practical authentication of human faces. The result illustrates that this method works well in both self authentication and mutual authentication. The third chapter aims to present a method of smoothing medical STL models by linear blending. Marching cubes is a popular tool for constructing 3-D STL models from DICOM medical images. However, extra high curvatures and topological problems are the possible defects in STL models formed by marching cubes. Hence, some of the STL models are inapplicable. An octree data structure is used for avoiding redundant vertices of connected triangular facets for a STL model. The blending concept is induced for blending one point on STL models with its neighboring points to smooth the surface. It is also used to improve the surface quality of medical STL models. The compensation of the volume is also introduced to avoid shrinkage caused by smoothing iterations. In each iteration, this smoothing method processes in linear time. A constant blending factor and a variable blending factor associated with curvatures are applied for different smoothing goals. In chapter 4, we present a numerical method for the sphericity assessment of the pellet in micro/nano scale. The numerical method based on Newton’s method is used for solving the least square problem. In one SEM image, the minimum root mean square (RMS) circle is determined from the observed pellet. The sphericity assessment of the pellet needs at least two SEM images which are captured from different views. The measured points on each captured image are acquired by twice linear interpolations of sub-pixels which are located on the boundary of the observed pellet. Once these minimum RMS circles have been determined, the corresponding homogenous transformations are applied to all measured points in order to restore the 3D points. The normalized 3D points represent the observed pellet properly, and they are the foundation for sphericity assessment. In chapter 5, we present a three-dimensional dissipative particle dynamics simulation, which is independent of the initial conditions, for analyzing the wettability on liquid-solid interfaces. The model parameters are constructed based on simulation optimization. The contact angle of a droplet on the solid platforms which possess different surface energy is simulated. The normalized factors indicate the parameters of the surface energy. By tuning the attractive and repulsive effects between the platform and the droplet, the contact angles with wide range are found at steady states. In simulation result, the linear relation between contact angle and the normalized factor exists. The proper repulsive factor in the paper is recommended to from 15 to 20. The ranges of the contact angles are from about 55 to 165 degrees. Moreover, the local density and the equation of state are applied for determining the droplet''s self energy and compressibility. The simulation results will help us to predict the profile and internal physical behavior of a micro-droplet.

LISTS OF FIGURES VII
LIST OF TABLES XI
CHAPTER 1. Introduction 1
CHAPTER 2. Automatic face authentication with self compensation 5
2.1. Problem description 5
2.2. Automatic face authentication 8
2.2.1 Specified 3D curvatures 10
2.2.2 Coupled 2D and 3D features 13
2.2.3 Bilateral symmetrical plane 15
2.3. Self compensation 17
2.3.1 Rational point-point ICP 17
2.3.2 Self compensation with linear blending function 21
2.3.3 Selection of individual threshold 22
2.4. Result and discussion 24
2.5. Conclusion 30
CHAPTER 3. Improving the surface quality of STL models: Smoothing by linear blending of vertices 31
3.1. Problem description 31
3.2. Methods and Materials 33
3.2.1. Data structure for a STL model 34
3.2.2. Smoothing a point by a linear blending function 39
3.2.3. Specifying a blending factor 43
3.2.4. Smoothing for specified condition 43
3.3. Result and discussion 44
3.3.1 A constant blending factor for the whole model 44
3.3.2 A variant blending factor according to Gaussian curvature 48
3.3.3 The volume compensation 56
3.3.4 Efficiency analysis 58
3.4. Conclusion 58
CHAPTER 4. An enhanced numerical method for the sphericity assessment of the pellet in micro/nano scale 59
4.1. Problem description 59
4.2. The sphericity of the pellet 64
4.3. The enhanced accuracy in experimental measurement 69
4.4. Result and discussion 78
4.5. Conclusion 85
CHAPTER 5. Simulation and Analysis of Interfacial Wettability by Dissipative Particle Dynamics 86
5.1. Problem description 86
5.2. Simulation model 89
5.3. Simulation of surface wettability 93
5.4. Result and discussion 96
5.5. Conclusion 108
CHAPTER 6. Future works 109
REFERENCE 110
APPENDEX A. Schematic description for multi-scale numerical simulation in this dissertation. 116
APPENDEX B. Curvature approximation. 117
APPENDEX C. Mutual coupled 2D and 3D features Retrieving 3D features. 118
APPENDEX D. Bilateral symmetrical plane. 119
APPENDEX E. Iterative closest points (standard ICP). 120
APPENDEX F. Isosurface from DICOM. 121
APPENDEX G. Determination for local densities. 122
APPENDEX H. Examples for DPD particles initialization. 123
APPENDEX I. Simulation with independent of innitial states. 124
APPENDEX J. Evaluation of discrete particles’ density for constructing isosurfaces. 125
PUBLICATION LIST (1999~) 126

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