臺灣博碩士論文加值系統

本論文的目的為開發一套整合四面體網格變形技術之虛擬矯正模擬系統，藉由整合影像人臉貼圖與矯正規劃流程，達到矯正過程中預測人臉外表變化的效果。傳統牙齒矯正中，若欲讓患者了解手術前後之外觀變化，僅能透過簡單的繪圖法表示，效果欠缺真實；近年來雖有以電腦演算進行臉部變形模擬的研究，但均以2D平面方式作顯示，而無法得知整體外貌之變化。
本研究提出一套針對牙齒矯正前後人臉差異之3D即時臉部變形模擬技術，不僅使患者可清晰了解牙齒矯正後之外觀變化，也能作為牙醫師術前規劃之參考。
首先透過完整頭部之CT掃描資料建立出實體模型，並於編修過程中，分別建立出皮膚、軟組織、骨頭等部分，接著在模型表面進行貼圖，讓臉部模型能呈現栩栩如生之外觀；其後加入數位牙齒模型及矯正矩陣，藉由矩陣之轉換即可得知矯正過程中牙齒位置之變化。
接著將軟組織設定為四面體網格，並建立質量彈簧系統，藉此模擬出真實軟組織之變化情形，如此便能透過牙齒移動來帶動臉部外觀變化，達到牙齒矯正後外觀之變化模擬。

The purpose of this thesis is to develop a surgical simulation system applied to orthodontic treatment with tetrahedron mesh. In the traditional process of orthodontic treatment, drafting is the most usual way to make patients understand the differences of appearances before and after operations. However, for the patients, the simulation is not real enough. Recently, there are some of the simulations with computer calculation to do the researches about face deformation simulation, but they can only be presented in 2D and the changes of the whole appearance are still unable to know.
In this research, a 3D deformation simulation technology of the difference before and after orthodontic treatment in human face is developed. The patients can know the changes of appearances in the process of orthodontics via the technology developed in this research. Furthermore, this technology can also provide guidance for dentists before operation.
In this research, a solid model is established from CT files of the brain model. In the process of model creation, the skin, soft tissue, and bones are established. And then we post face photo in the appearance of model to make it become more real. After this process, the digital teeth model and orthodontics matrix are also added. Through the changes of matrix, the changes of teeth position in the process of orthodontic correction can be realized.
Next, we use tetrahedron mesh model to represent the soft tissue and establish a mass spring system to simulate the deformation of soft tissue. Through the deformation, the teeth movement can bring the transformation of human appearance to achieve the simulation of the appearance prediction after the orthodontic correction.

摘要 II
目錄 IV
圖目錄 VI
表目錄 XI
第一章 緒論 1
1.1 前言 1
1.2 研究動機 3
1.3 研究目的 5
1.4 文獻回顧 6
1.4.1 網格處理 6
1.4.2 變形 10
1.4.2.1 自由造型變形(Free-Form Deformation) 10
1.4.2.2 質量彈簧系統(Mass Spring System) 11
1.4.2.3 有限元素方法(Finite Element Method) 13
1.4.3 貼圖 15
1.4.4 手術模擬 17
1.4.5 材料參數設定 19
1.5 研究方法 22
第二章 網格建立 24
2.1 網格介紹 24
2.2 網格建立演算法 25
2.2.1 平面直線圖(Planar Straight Line Graph) 25
2.2.2 分段連續線性組合(Piecewise Linear Complex) 25
2.2.3 狄勞尼三角化(Delaunay Triangulation) 26
2.2.4 狄勞尼四面體化(Delaunay tetrahedrization) 28
2.2.4.1 Conforming Delaunay Triangulation 29
2.2.4.2 Constrained Conforming Delaunay Triangulation 30
2.3 網格細分 38
第三章 實體成像 43
3.1 資料格式 44
3.2 實體成像軟體 46
3.2.1 實體模型萃取 47
3.2.2 實體模型後處理 49
3.3 人臉貼圖 52
3.4 矯正排牙規劃 58
第四章 質量彈簧系統 61
4.1 質量彈簧系統介紹 61
4.2 Newmark Method 67
4.3 共軛梯度法(Conjugate gradient method) 70
4.4 碰撞偵測 72
第五章 虛擬矯正模擬成果 76
5.1 虛擬矯正模型建立 76
5.2 MSS變形成果 79
5.3 ANSYS變形成果 85
5.4 MSS和ANSYS變形成果比較 90
第六章 結論與未來展望 92
6.1 結論 92
6.2 未來展望 94

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