臺灣博碩士論文加值系統

在計算機圖學的研究領域中，網格重製技術一直扮演著後製處理的角色。因為在將現實物體轉換為虛擬三維模型的數位化過程中，由三維雷射掃瞄儀器產生的外形取樣點，會因為複雜的物體表面變化而無法均勻分佈。導致使用網格重建技術建立的模型網格必須透過網格重製演算法重新產生規則分佈的模型網格結構。
從執行效率的角度來看，必須經過兩個高複雜度的處理才能產生一個網格分佈規則的三維模型的傳統概念已經不符時宜。爲此，本論文提出一個兼顧網格規則度的網格重建演算法。這個演算法可以由不具法向量方向資訊的外形取樣點群中，直接重建出具備規則網格的三維模型。

For a regular mesh model, typically constructing a model that usually using two steps model reconstruction and remesh. First unorganized point cloud can be created by 3D scanner. Through point-based reconstruction technique, we can make a model approximate the original object. But the mesh of model always be irregular. Therefore, the second step remesh, adjusting the mesh of model and resampling the point cloud to make the final mesh more regular.
For mesh, not only model reconstruction but also remesh, both of them would create a mesh model finally. The difference between model reconstruction and remesh is shape of triangles and degree of vertices in mesh. Therefore, our paper presents a technique about mesh model reconstruction from unorganized points set. This technique can construct a regular mesh model from points set directly, and comparing with original object by eyes the features can be preserved. The most important concept is that regular mesh model reconstructing from unorganized point cloud directly, and no need two steps method to finish model reconstruction.

目錄
摘要 I
Abstract II
誌謝 III
圖目錄 VI
第 1 章 序論 1
1.1 研究動機及目標 1
1.2 系統架構流程 2
第 2 章 文獻探討 6
2.1 網格重建 7
2.2 網格重製 10
第 3 章 原始取樣點的分群 12
3.1 選取相鄰點 12
3.1.1 Circle R-Nearest Neighbors(CRNN) 13
3.1.2 BSP Neighbors 14
3.2 推算頂點法向量 15
3.2.1頂點法向量計算 15
3.2.2 法向量方向一致性修正 15
3.2.3 相鄰關係修正 18
3.3 自動決定取樣點群的初始分割結果 19
3.4 強化取樣點群分割結果 20
3.4.1 最小誤差外形近似分割法 20
3.4.2 尋找初始點 21
3.4.2計算分群調整步驟所需之誤差值 21
3.5 利用頂點分割結果建立各分割點區域之間的共用邊界頂點 24
第 4 章 拓展式區域網格重建 28
4.1重建分割點區域內的三角網格 30
4.2 修整重建區塊邊界區域的網格 31
4.2.1 定義重建區塊的邊界輪廓 31
4.2.2 偵測落於區塊邊界輪廓線上的取様點 34
4.2.3 偵測落於重建區塊邊界區域網格內的取様點 35
4.3 提升重建區塊內的網格規則度 36
4.3.1 Area-based 頂點調整法 36
4.3.3 Centroid-based 頂點調整技術 37
4.3.3 投影重製網格回 3D 空間 38
第 5 章 實驗結果 40
第 6 章 結論和未來展望 47
參考文獻 49

圖目錄
圖1.1. 系統流程架構圖 3
圖2.1. 透過不同的 7
圖2.2 使用[Gopi et al.2000]重建後的模型 8
圖2.3. 點群參數化過程 9
圖2.4. [Zhang et al. 2010]區塊網格重建全域模型過程 9
圖2.5. [Surazhsky et al. 2003 ]網格重製結果比較圖 10
圖2.6. [ Jong et al. 2010 ]結果比較圖 11
圖3.1. 相鄰點選取流程 14
圖3.2. 法向量一致性修正示意圖 16
圖3.3. 法向量一致性修正結果圖 18
圖3.4. 使用法向量進行相鄰點篩選 18
圖3.5. 將原始取樣點群做初始分割 20
圖3.6. 最小誤差分割法修正前後比較圖 23
圖3.7. 共用邊界頂點篩選結果圖 27
圖4.1. 拓展式網格重建示意圖 29
圖4.2. 分割點區域的虛擬網格重建結果 30
圖4.3. 邊界輪廓頂點偵測方法示意圖 33
圖4.4. 構成區域邊界輪廓之邊界輪廓線段 34
圖4.5. 偵測重建區塊邊界輪廓線與邊界區域上的特殊頂點方法示意圖。 36
圖4.6. 網格重製結果圖 38
圖4.7. 從二維空間中將取樣點利用重心座標投影技術投影回三維空間 39
圖5.1. Rabbit 模型重建過程 41
圖5.2. Moai 模型重建過程 42
圖5.3. Pensatore 模型重建過程 43
圖5.4. Skull 模型重建過程 43
圖5.5. 在不同方法下Skull模型比較圖 46

[1]B.S. Jong, C.H. Chiang, P.F. Lee, and T.W. Lin, “High quality surface remeshing with equilateral triangle grid”, The Visual Computer, Vol. 26, 2010, page:121–136.

[2] B.S. Jong, W.Y. Chung, P.F. Lee, and J.L. Tseng, “Efficient Surface Reconstruction Using Local Vertex Characteristics”, in Processing of the 2005 International Conference on Information, Communications and Signal ( ICICS 2005 ), 2005, page:1025–1029.

[3] M.S. Floater, M. Reimers, “Meshless parameterization and surface reconstruction”, Computer Aided Geometric Design, Vol. 18, No. 2, 2001, page:77–92.

[4] G.. Guennebaud., and M. Gross, “Algebraic point set surfaces” , International Conference on Computer Graphics and Interactive Techniques (ACM SIGGRAPH 2007), 2007.

[5] G. Guennebaud , L. Barthe and M. Paulin. “Interpolatory refinement for real-time processing of point-based geometry”, Computer Graphics Forum (Proceedings of Eurographics 05), Vol. 24, 2005, Page:657–666.

[6] H. Hoppe, T. DeRose, T. Duchamp, J. McDonaldz, and W. Stuetzle, “Surface reconstruction from unorganized points”, In Proceedings of ACM SIGGRAPH 1992 Conference, 1992, page:71–78.

[7] H. Edelsbrunner and E. P. Mucke, “Three-dimensional alpha shapes ”, ACM Transaction on Graphics, Vol. 13, No. 1, 1994, page:43–72.

[8] L. Zhang, L. Liu, C. Gotsman and H. Huang. “Mesh reconstruction by meshless denoising and parameterization” In Proceedings of Shape Modelling International (SMI) Conference 2010 (Computers and Graphics), Vol. 34, No. 2, 2010, page : 198-208.

[9] M. Gopi, S. Krishnan and C.T. Silva, “Surface reconstruction based on lower dimensional localized delaunay triangulation”, in Proceedings of EUROGRAPHICS 00, 2000, page:467–478.

[10] M. Gross and H. Pfister, “Pointbased graphics”, The Morgan Kaufmann Series in Computer Graphics, 2007, page:167–178.

[11] M. Kazhdan, M. Bolitho and H. Hoppe, “Poisson Surface Reconstruction”, ACM International Conference Proceeding Series(Proceedings of the fourth Eurographics symposium on Geometry processing), 2006, Vol. 256, page:61–70.

[12] M.Pauly, M. Gross, and L. P. Kobbelt, “Efficient simplification of point-sampled surfaces”, In Proceedings of 13th IEEE Visualization Conference, 2003, page:167–174.

[13] M.Pauly, “Point primitives for interactive modeling and processing of 3D geometry”, PhD Thesis, 2003, page:9–15.
.
[14] P. Cignoni, C. Rocchini, and R. Scopigno, “Metro: measuring error on simplified surfaces”, Computer Graphics Forum, Vol. 17, No. 2, 1998, page:167–174.

[15] S. Valette , J.-M. Chassery, R. Prost, “Generic remeshing of 3D triangular meshes with metric-dependent discrete voronoi diagrams”, IEEE Transaction on Visualization and Computer Graphics, 2008, Vol. 14, No. 2, page:369–381.

[16] T. K. Dey and J. Sun, “An adaptive mls surface for reconstruction with guarantees”, In Proceedings of the Eurographics Symposium on Geometry Processing, 2005, page:43–52

[17] V. Surazhsky and C. Gotsman, “Explicit surface remeshing”, In proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 2003, Vol. 43, page:17–28.