在本篇論文中，我們提出一個新的方法去利用多張人臉影像的資訊，重建頭髮的3D模型，同時也整合了3D人臉重建，使之成為一個完整的人頭模型，並能用於擬真的人臉動畫。在我們的三維重建系統中，我們會先為每張影像的頭髮區域計算出頭髮的方向性，並且將這些二維的向量初始化為一個三維向量場。接著藉由最佳化一個同使考慮了多視角限制、三維向量限制、單根髮絲限制的成本函數，來修正三維向量場。我們在頭皮的區域事先規律地取樣了一些頭髮的起始點，接著我們的演算法會由這些起始點開始沿著三維向量場長出頭髮。最後，我們展示了一些重建的結果，並且做了些討論。

In this thesis, we propose a novel approach to 3D hair modeling from multi-view images of a specific person. The reconstructed 3D hair model can be integrated with the reconstructed 3D face model to obtain a complete human head model for vivid facial animation. In our 3D hair reconstruction system, we first estimate 2D orientation of the hair regions in each view, and estimate an initial 3D orientation field of hair according to the relative position to the reconstructed face model. Then the initial 3D orientations are refined by optimizing a cost function carefully designed to combine multi-view constraint, 3D orientation constraint, and strand constraint. Then, our algorithm grows the 3D hair strands from the root points, which are uniformly sampled on the pre-defined surface region of the reconstructed 3D head model, along the direction determined by the refined 3D orientation field. Finally, we show some experimental results of the reconstructed 3D hair strand models by using the proposed algorithm.

Table of Contents
致 謝 .i
摘 要 .ii
Abstract .iii

Chapter 1. Introduction 1
1.1 Motivation 1
1.2 Problem Description 2
1.3 Main Contributions 3
1.4 Thesis Organization 4

Chapter 2. Previous Works 5
2.1 User-interaction and Parametric Surface of Hair 5
2.2 Image-based Method for Hair Modeling 6
2.3 Application-driven Approach 7

Chapter 3. Proposed Multi-view Hair Modeling System 8
3.1 System Overview 8
3.2 Face Reconstruction 10
3.3 2D Orientation Estimation 11
3.4 Computing 3D Orientation Field 14
3.4.1 Multi-view Consrain 14
3.4.2 Orientation Constraint 16
3.4.3 Strand Constraint 17
3.4.4 Cost Function Minimizing 18
3.5 Hair Growing 19

Chapter 4. System Implemetation 21
4.1 Input Data 21
4.2 Face Reconstruction 23
4.3 Estimate Orientation for Images 25
4.4 Compute 3D Orientation Field 28

Chapter 5. Experimental Results 30
5.1 Discussion 31
5.2 Limitation 34

Chapter 6. Conclusion 35

References 36

References

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