臺灣博碩士論文加值系統

3D立體顯像可以幫助臨床醫生做更準確的診斷或是擬定手術計畫，也可以做為住院醫生與學生的教學訓練。在本篇研究中，我們提出了一個容積顯像演算法，此演算法可以精確地計算顏色與透明度的累積量，最後得到最精準的顯像結果。

在現行的各種容積顯像演算法之中，3D-DDA(digital differential)演算法是目前最有效率的。而且也最容易與光線追蹤表面去除演算法做結合，應用在容積顯像上。藉由3D-DDA演算法，我們可以將光線所經過的Voxel，一一累積它們的不透明度與顏色資訊。但是目前的3D-DDA演算法並不計算光線在Voxel中所穿過的距離長度，如此一來在計算不透明度與顏色時，會造成顯像上的誤差。

本研究提出一個精確的DDA容積顯像演算法，此演算法可以精確地計算光線在穿過Voxel時的長度。如此一來，我們可以精準的得到光線所經過的顏色與不透明度資訊。我們也實際的使用醫學上的例子來證明此演算法是有效的。

3D rendition assists clinicians to make more accurate diagnosis, verify and modify surgical plans and train residents and students. In this research, we propose a volume rendering method that can accurately calculate accumulated color and opacity for precise rendering.
Among various volume rendering algorithms, the 3D-DDA (digital differential) algorithm is considered as more efficient than others. Moreover, it is easily combined with the ray tracing hidden surface removal algorithm that usually employed in the volume rendering. The 3D-DDA algorithm can accumulate the opacity and color when it hip a voxel for observation. However, current 3D-DDA algorithms do not calculate the distance it actually traverses in a voxel. This brings errors in the accumulation of color and opacity.
This research proposes an accurate DDA volume rendering algorithm that calculates the real distance that a ray traverses in a voxel. Thus, we can precisely obtain the total color and opacity for the ray. Some medical examples demonstrate the effectiveness of our algorithm

第一章 緒論
1.1 簡介....................................................1
1.2 顯像的問題及研究目的....................................2
1.3 論文架構................................................3
第二章 容積的形成與容積的顯像
2.1 容積空間................................................4
2.2 數位微分分析法（Digital Differential Analyzer）.........9
2.3 Bresenham 2D-DDA演算法.................................11
2.4 三維數位微分分析法 ( 3D-DDA )..........................15
2.5 容積顏色與透明度的計算.................................18
2.6 容積顯像表面加強計算...................................21
2.6.1 Phong Model..........................21
2.6.2 容積表面法向量的計算.................23
第三章 精確數位微分分析法處理容積資料
3.1 精確2D-DDA演算法.......................................25
3.2 精確3D-DDA演算法.......................................35
3.3 線段通過Voxel的長度計算................................39
3.4 精確數位微分分析演算法的容積成像.......................43
第四章 比較結果
4.1 顯像系統...............................................45
4.2 Volume Rendering顯像結果...............................45
4.3 Volume Rendering and Surface Rendering.................48
4.4 系統操作介面說明.......................................50
第五章 結論與未來展望.........................................54
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