臺灣博碩士論文加值系統

特徵擷取技術被使用在物件追蹤、物件切割、臉部偵測以及醫學影像分析等應用上。而大多數特徵擷取的演算法都是針對二維影像做處理，對於三維模型並不適用，主動輪廓模型(Active Contour Model)[1]是其中一個例子，Bischoff et al.於2005年提出適用於三角網格(Triangle Mesh)的三維主動輪廓模型[2]。然而三維主動輪廓模型有幾項缺點，在實作上有些問題需要改善。本研究基於三維主動輪廓模型，依據延拓法(Continuation Method)發展新的演算法，改善主動輪廓模型的缺點，能夠較為簡單及確實的對三角網格做特徵擷取。使用者讀取模型，搭配不同的輪廓線函數(Contour Function)能夠產生不同的輪廓線。本研究的方法可以動態的產生輪廓線以做出動畫效果，使用者也可以利用產生出的輪廓線對模型做進一步的處理。

Feature extraction methods are used in many applications, including object tracking, object segmentation, face detection and medical image analysis. Most feature extraction algorithms are designed for 2D images, not applicable for 3D models. Active contour model[1] is one such example. Bischoff et al. (2005)[2] proposed 3D active contour model on triangle meshes. However, 3D active contour model has several drawbacks.
In this study, we develop a new contouring algorithm based on continuation method. Our algorithm improves the shortcomings of original 3D active contour models, and facilitate real-time feature extraction on triangle meshes. Users load a 3D model, and produce different contours with different contour functions. Our algorithm can produce contours in real-time for animation effects, and allows users to edit 3D model with contours.

謝誌 i
摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vi
表目錄 viii
第一章 緒論 1
1.1 研究背景 1
1.2 研究目標 1
1.3 開發環境 2
1.4 論文架構 3
第二章 相關研究 4
2.1 主動輪廓模型 4
2.2 三維主動輪廓模型 5
2.3 三維主動輪廓模型的拓撲控制 6
2.4 三維主動輪廓模型的缺點 9
第三章 研究方法 10
3.1 以延拓法實作輪廓線 10
3.1.1 資料結構 10
3.1.2 建立輪廓線 12
3.1.3 Boundary Edge 處理 14
3.2 輪廓線函數 17
3.2.1 剪影 17
3.2.2 平面 19
3.2.3 高斯曲率 20
3.3 輪廓線應用 23
3.3.1 將輪廓線資料寫入三維模型 23
3.3.2 使用輪廓線做模型切割 24
第四章 結果與討論 26
4.1 延拓法與三維主動輪廓模型的比較 26
4.2 輪廓線的產生效率 27
第五章 結論與未來方向 29
參考文獻 30

[1] M. Kass, A. Witkin and D. Terzopoulos, “Snakes: Active contour models,” Internation Journal of Computer Vision, vol.1, pp. 321-331, 1988.
[2] S. Bischoff, T. Weyand and L. Kobbelt, “Snakes on triangle meshes,” Bildverarbeitung fur die Medizin, pp. 208-212, 2005.
[3] S. Bischoff and L. P. Kobbelt, “Parameterization-free active contour models,” The Visual Computer, vol.20, pp. 217-228, 2004.
[4] K. Karsch and J. C. Hart, “Snaxels on a plane,” Non-Photorealistic Animation and Rendering, pp. 35-42, 2011.
[5] E. L. Allgower and K. Georg, “Introduction to Numerical Continuation Methods,” Society for Industrial and Applied Mathematics, 1990.
[6] M. Botsch, L. Kobbelt, M. Pauly, P. Alliez, and B. Levy, “Polygon Mesh Processing,” A K Peters, Ltd., 2010.
[7] M. Meyer, M. Desbrun, P. Schroder, and A. H. Barr, “Discrete differential-geometry operators for triangulated 2-manifolds,” In Visualization and Mathematics III, pp. 35-58, 2003.
[8] M. Botsch, S. Steinberg, S. Bischoff, and L. Kobbelt, “OpenMesh - a generic and efficient polygon mesh data structure,” OpenSG Symposium, 2002.
[9] Y. Lee and S. Lee, “Geometric snakes for triangular meshes,” Computer Graphics Forum, vol.21, pp. 229-238, 2002.
[10] Y. Lee, S. Lee, A. Shamir, D. Cohen-Or and H. P. Seidel, “Intelligent mesh scissoring using 3D snakes,” Pacific Conference on Computer Graphics and Applications, pp. 279-287, 2004.
[11] Z. Ji, L. Liu, Z. Chen and G. Wang, “Easy mesh cutting,” Computer Graphics Forum, vol.25, pp. 283-291, 2006.
[12] K. Lawonn, R. Gasteiger, C. Rossl and B. Preim, “Adaptive and robust curve smoothing on surface meshes,” Computers & Graphics, vol.40, pp. 22-35, 2014.