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研究生：	顏韶威 Yen, Shao-Wei
論文名稱：	特徵對應之紋理貼圖技術 Texture Mapping on 3D Surface with Hard Constraints
指導教授：	李同益 Lee, Tong-Yee
學位類別：	博士 Doctor
系所名稱：	電機資訊學院 - 資訊工程學系 Department of Computer Science and Information Engineering
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	70
中文關鍵詞：	紋理貼圖、虛擬點、變形、翻轉、聚集、貼圖變形量、參數化、位置限制
外文關鍵詞：	texture stretch, clustering, virtual points, parameterization, warping, positional constraints, foldover, Steiner vertex, texture mapping
相關次數：	點閱：126 下載：3
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紋理貼圖是電腦繪圖上相當普遍的技術；藉由輸入的二維影像，紋理貼圖可以利用影像中豐富的資訊與細節來加以擬真三維網格模型。本論文包含了三個不同而有效的紋理貼圖演算法，這三個演算法的設計演進分別從無特徵對應的紋理貼圖技術至有特徵對應的紋理貼圖演算法。
第一個演算法可應用於任意的三維表面，主要的目標是著重於無失真的貼圖座標計算，但不考慮使用者給定的特徵位置對應。為了於三維模型上進行紋理貼圖，我們提出了一個架構來參數化任意三維表面至二維平面上。我們的方法不需要固定的參數化邊界，而且貼圖座標可以利用線性稀疏矩陣系統來有效率的求得解答；所以這個系統的執行表現可以達到互動式的操作反應。
第二個與第三個演算法為有特徵對應的紋理貼圖演算法。有特徵對應的紋理貼圖是一個在電腦圖學上重要而且相當具挑戰性的問題。第二個演算法的主要觀念是重複的切割參數化的平面，直到每個切割出來的子區域僅剩下一個特徵點為止。由於每個子區域只包含一個特徵點，所以特徵點的對齊問題已被大大的簡化，每個子區域只需單獨計算處理即可對齊所有的特徵點。
在第三個特徵對應的紋理貼圖方法中，我們一開始於二維平面空間裡推導一個理論上強健地、無翻轉三角形的變形演算法；之後我們應用此變形方法到有特徵對應的紋理貼圖。這個演算法可以在視覺上擁有更好的繪圖呈現，而主要的關鍵在於本方法只需增加了少數的Steiner vertices在參數化後的三角網格模型上，即可滿足使用者的特徵對應需求。

Texture mapping is a common and very useful technique in computer graphics. Texture mapping adds the detailed information of the user-specified image to the 3D models and represents the rendering result more vividly and realistically. This thesis contains three efficient algorithms from texture mapping on 3D surface without positional constraints to texture mapping with hard positional constraints.
The first one is to achieve distortion-free texture mapping on arbitrary 3D surfaces without constraints. To texture 3D models, we propose a scheme to flatten 3D surfaces into a 2D parametric domain. Our method does not require the two-dimensional boundary of flattened surfaces to be stationary. The first parameterization scheme can be efficiently realized by a linear sparse matrix system and yields interactive performance.
The second and third algorithms are texture mapping with hard positional constraints. Texture mapping with positional constraints is an important and challenging problem in computer graphics. The idea of second one is to partition the parametric map until each sub-region contains one feature points. Then we can easily handle each sub-region and complete the alignment of all feature points.
In the third algorithm, we first present a theoretically robust, foldover-free 2D mesh warping algorithm. Then we apply this warping algorithm to texture mapping on 3D triangle meshes with hard positional constraints. The third algorithm can generate more pleasing visual representation, add fewer Steiner vertices on the 3D mesh embedding domain, and satisfy all user-specified constraints without foldovers.

Chapter 1 Introduction                                 1
1 Background and Objectives                       1
2 Contribution                                    4
3 Organization                                    5
Chapter 2 Related Work                                 7
1 Parameterization without Constraints            7
2 Parameterization with Constraints              10
Chapter 3 General Texture Mapping on 3D Surfaces without Positional Constraints                                13
1 Overview                                       13
2 Methodology                                    14
2.1 The Initial Setup                         15
2.2 Reducing Distortion Using Clustering and Cutting                                               16
2.3 Virtual Points                            20
2.4 Smoothing                                 22
3 Experimental Results                           23
Chapter 4 Constrained Texture Mapping using Partition Scheme                                                28
1 Overview                                       28
2 Parameterization with feature points           28
2.1 Initial parameterization                  29
2.2 Feature matching using a partitioning approach                                              30
2.3 UV optimization                           32
3 Results                                        32
Chapter 5 Constrained Texture Mapping using Warping Scheme                                                34
1 Overview                                       34
2 Foldover-free 2D Triangle Mesh Warping         34
2.1 Definitions                               35
2.2 Theoretical Analysis and Algorithm        37
3 Texture Mapping with Hard Constraints          45
3.1 Overview and Definitions                  45
3.2 Constructing a Base Mesh                  47
3.3 Warping a Base Mesh                       49
3.4 Smoothing the Embedding                   50
4 Experimental Results and Discussion            51
4.1 Results                                   51
4.2 Discussion with Related Work              57
Chapter 6 Conclusion and Future Work                  60
1 Conclusion                                     60
2 Future Work                                    61
References                                            63
Vita                                                  69
                                    

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校內：2011-07-29公開
校外：2011-07-29公開

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