臺灣博碩士論文加值系統

　　在我們進行電腦圖學的各種高階應用之前，如compatible參數化、morph或骨架建立。我們常常需要對三維模型進行一個基礎分析，藉由分析了解模型的幾何特徵，分塊特徵，動畫特徵等等。有了這些特徵我們對於模型內的資訊或是模型間的對應就能夠了解，而這些模型內的資訊及模型間的對應在處理一個三維模型扮演著關鍵的角色。

　　本論文利用模型的突出型態、模型的幾何特徵與使用者要求的特徵來達成近似人類視覺化的切割。本論文演算法主要先建立起模型突出端點的資訊，以建立三維模型主要且基本的拓樸架構。接著由各種不同的幾何特徵﹙如曲率，表面距離﹚描述出局部變化的各種數值以建立起較為精準的切割，我們利用這些局部的幾何資訊計算出符合使用者特徵點之間最佳的切割位置，讓每個切塊有著最大的區分性。由上述演算法，我們希望模型切割的最後結果能夠將模型切割為有意義的區塊，使我們能夠更精準的描述整個模型。

　In computer graphics, mesh decomposition is a fundamental problem and it can benefit many applications including texture mapping, surface parameterization, morphing, shape matching/retrieval and modeling by parts, animation compression. In this thesis, we propose a novel algorithm called controllable mesh decomposition and also present its application to skeleton extraction of models/animation. The proposed method is based on Reeb-graph data structure to represent topology information for a given 3D model. Before reconstructing this topological data structure, we automatically compute salient features called protrusion degree on models using geodesic distance. Then, we build a constrained Reeb-graph where each leaf node only contains one salient feature. Sometimes, user would like the mesh decomposition to be controllable, i.e., user can give some hints. For this reason, the proposed scheme allows several user-specified points on models and we present a coloring scheme to paint each possible segmented part of models. With the combination of both a constrained Reeb-graph and a coloring scheme, the proposed scheme automatically partitions models into several meaningful parts. However, due to discrete property of mesh models, the cutting boundary may be not ideally smooth. We can further smooth boundary using a minimum-cut-maximum-flow and a snake algorithm. Finally, we experimentally evaluate the proposed method against a variety of 3D models. Furthermore, we also demonstrate its usefulness to skeleton extraction. With a good extracted skeleton, we can animate 3D models by mean of modifying the skeletons.

提要•••••••••••••••••••••••iii
英文提要•••••••••••••••••••••iv
誌謝•••••••••••••••••••••••v
目錄•••••••••••••••••••••••vi
表目錄••••••••••••••••••••••viii
圖目錄••••••••••••••••••••••ix
第一章　導論•••••••••••••••••••1
1.1研究動機••••••••••••••••••••••••1
1.2研究內容架構與流程•••••••••••••••••••2
1.3研究之主要貢獻•••••••••••••••••••••5
第二章　相關研究•••••••••••••••••7
2.1模型切割••••••••••••••••••••••••7
2.2活動輪廓演算法•••••••••••••••••••••13
2.3三角化•••••••••••••••••••••••••14
2.4計算幾何特徵••••••••••••••••••••••14
2.5模型檢索••••••••••••••••••••••••15
第三章　主要架構及演算法•••••••••••••16
3.1計算幾何測地線距離與幾何曲率••••••••••••••16
3.2分水嶺演算法及後處理••••••••••••••••••20
3.3建立Constrained Reeb-Graph•••••••••••••••29
3.4點選使用者特徵點••••••••••••••••••••38
3.5在Constrained Reeb-Graph資訊下將模型劃分為切割候選區域序列•••••••••••••••••••••••••••••44
3.5.1建立切割候選區域序列•••••••••••••••44
3.5.2建立切割候選區域序列條件增加全模型中心區域對模型點的幾何測地線•••••••••••••••••••••••50
3.6分析切割候選區域及找出最可能切割候選區域••••••••52
3.6.1重新定義切割候選序列的內容•••••••••••••58
3.7依照最可能切割候選區域找尋封閉模型點曲線••••••••62
3.8利用活動輪廓演算法來平滑化封閉模型點曲線••••••••66
3.8.1活動輪廓初始曲線分段•••••••••••••••68
3.8.2參數化分段曲線周圍的模型區域至2D平面•••••••69
3.8.3對每個分段的活動輪廓曲線分別進行活動輪廓演算法程序•••••••••••••••••••••••••••72
3.8.4將平面活動輪廓演算法的結果反投影回三維模型上，作為三維曲線的結果••••••••••••••••••••••73
3.8.5對分段的端點另外作活動輪廓演算法的程序••••••73
3.9三角化Snake Contour區域••••••••••••••••74
第四章　實驗結果•••••••••••••••••76
第五章　結論與未來展望••••••••••••••101
參考文獻•••••••••••••••••••••104
自述•••••••••••••••••••••••107

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