本研究發展一套多視角相機群組空間座標系統整合的流程。基於輪廓法(Shape-from-Silhouette, SFS)方向進行三維模型重建時，通常會利用旋轉平台輔助拍攝，也因為旋轉平台的緣故，於拍攝欲建模之物件時，其頂部與底部往往會因為資訊獲得不足甚至無法取得，導致於重建三維模型時產生假面，造成三維模型與實際物件外形產生落差。 本研究透過改變物件放置於旋轉盤上的方式，拍攝物件不同角度之影像，以補足物件頂部、底部甚至其他角度特徵之資訊，並利用所有資訊重建三維模型，使其能夠更接近物件之外表形貌。拍攝環境之空間座標系統為透過校正物進行建立，因此改變放置方式進行拍攝之輔助視角資訊必須依附初次拍攝之主要視角所建立的座標系統，故本研究開發一套影像匹配對位法(Alignment by Image Matching, AIM)進行座標系統的整合。藉由計算原始三維模型之投影影像以及輔助視角物件影像之間的空間關係，進而換算各視角相機群組於三維空間中之轉換關係，便可利用更充足之資訊重建三維模型。 本論文最後舉出三個不同的範例，利用本研究提出之多視角相機群組空間座標系統整合流程以及AIM方法，將多組輔助視角的相機群組資訊進行整合，並輸入至應用端進行三維模型的重建，以此驗證本研究之正確性及可行性。

This study develops a process of the integration of coordinate systems from multi-view
camera groups for shape-from-silhouette (SFS) technique. The popular 3D modeling technique
which based on the SFS method usually through the rotatory table to obtain geometry and color
information of object. However, the rotatory table only rotate in one axis, and it causes that the
object has the limitation of the shooting angle especially at the top/bottom view. In SFS method,
this limitation leads the artifacts of 3D model generated at the top/bottom.
If the object can tip over, reposition on the rotatory table, and retake the images, the
missing information of 3D model from top/bottom view could be replenished. In order to
integrate the entire silhouette data taken from different views into a single coordinate system,
this study develops an alignment by image matching (AIM) algorithm to establish the spatial
distribution of all camera positions. In this algorithm, the silhouette data obtained in tipped
positions is setting as targets. The 3D model transforms into a predicted positon to simulate one
of tipped positions and projects the shape onto the imaging plane of the camera to obtain the
predicted silhouette data as a subject. Then, this subject silhouette data will make the
comparison with corresponding target. The AIM algorithm used to minimize the difference
between these two data and calculate the corresponding translation and rotation of the subject
needed to adjust in 3D space. When the sum of differences in all tipped positions is minimum,
all camera position (in auxiliary views) can integrate into a coordinate system of primary view.
A complete 3D model can be rebuilt by the SFS method with all silhouette data in all views.
At last, this study will demonstrate three examples which were rebuilt by the development
of process of the integration of coordinate systems from multi-view camera groups for shapefrom-
silhouette technique to verify our proposed process.

目錄
1
摘要 ............................................................................................................................................ I
ABSTRACT ............................................................................................................................. II
致謝 ......................................................................................................................................... III
目錄 ......................................................................................................................................... IV
圖目錄 ..................................................................................................................................... VI
表目錄 ..................................................................................................................................... XI
第一章 緒論 .............................................................................................................................. 1
1-1 研究背景 ..................................................................................................................................................... 1
1-2 文獻回顧 ..................................................................................................................................................... 3
1-3 先前成果 ..................................................................................................................................................... 8
1-4 研究動機 ................................................................................................................................................... 11
1-5 研究目的 ................................................................................................................................................... 12
1-6 論文大綱 ................................................................................................................................................... 13
第二章 理論說明 .................................................................................................................... 14
2-1 相機模型 ................................................................................................................................................... 14
2-2 影像處理 ................................................................................................................................................... 19
2-3 邊緣偵測與簡化 ....................................................................................................................................... 23
2-4 奇異值分解 ............................................................................................................................................... 28
2-5 最佳化設計 ............................................................................................................................................... 29
第三章 多視角相機群組空間座標系統整合流程 ................................................................ 36
3-1 流程介紹 ................................................................................................................................................... 37
3-2 影像匹配對位法 ....................................................................................................................................... 40
3-3 相機群組座標系統之建立 ....................................................................................................................... 54
3-4 粗定位流程 ............................................................................................................................................... 57
3-5 精定位流程 ............................................................................................................................................... 68
第四章 結果與驗證 ................................................................................................................ 76
4-1 人機介面與開源資料庫介紹 ................................................................................................................... 76
4-2 範例物件三維模型投影影像驗證 ............................................................................................................ 79
4-3 多視角相機群組資訊重建物件三維模型驗證 ........................................................................................ 92
第五章 結論與未來展望 ...................................................................................................... 106
5-1 結論 ......................................................................................................................................................... 106
5-2 未來展望 ................................................................................................................................................. 107
參考文獻 ................................................................................................................................ 108

[1] 羅至中，「單視域之遞迴式深度估測補償」，碩士論文，國立交通大學，新竹，民
國101 年。
[2] W. Niem, “Robust and Fast Modelling of 3D Natural Object from Multiple Views,” Image
and Video Processing II, pp. 388-397, 1994.
[3] Q. Wang, L. Fu and Z. Liu, “Review on Camera Calibration,” Proceedings of the IEEE
Control and Decision Conference (CCDC), pp. 3354-3358, 2010.
[4] A. Laurentini, “The Visual Hull Concept for Silhouette-Based Image Understanding,”
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, No. 2, 1994.
[5] Daniel Lau, “Leading Edge Views: 3-D Imaging Advances Capabilities of Machine
Vision,” http://www.vision-systems.com/articles/print/volume-17/issue-4/departments/
leading-edge-views/3-d-imaging-advances-capabilities-of-machine-vision-part-i.html,
2012.
[6] Y. Yemez and F. Schmitt, “3D Reconstruction of Real Objects with High Resolution
Shape and Texture,” Image and Vision Computing 22, pp. 1137–1153, 2004.
[7] W. Niem and J. Wingbermühle, “Automatic Reconstruction of 3D Objects Using a Mobile
Monoscopic Camera,” Proceedings of International Conference on Recent Advances in 3-
D Digital Imaging and Modeling, pp.173-180, 1997.
[8] Z. Zhang, “A Flexible New Technique for Camera Calibration,” IEEE Transactions on
Pattern Analysis and Machine Intelligence, Vol. 22, pp. 1330-1334, 2000.
[9] N.D.F. Campbell, G. Vogiatzis, C. Hernández, and R. Cipolla “Automatic 3D Object
Segmentation in Multiple Views Using Volumetric Graph-Cuts,” Image and Vision
Computing 28, pp. 14–25, 2010.
[10] Y. Yemez and Y. Sahillioğlu, “Shape from Silhouette Using Topology-Adaptive Mesh
Deformation,” Pattern Recognition Letters, 2009.
[11] Y. Guo, W. J. Veneman, H. P. Spaink, and F. J. Verbeek, “Three-Dimensional
Reconstruction and Measurements of Zebrafish Larvae from High-Throughput Axial-
View in Vivo Imaging,” Biomedical Optics Express, pp.2611-2634, 2017.
[12] B. Moghaddam, J. Lee, H. Pfister, and R. Machiraju, “Model-Based 3D Face Capture with
Shape-from-Silhouettes,” IEEE International Workshop on Analysis and Modeling of
Faces and Gestures, 2003.
109
[13] C. Hernández, F. Schmitt, and R. Cipolla, “Silhouette Coherence for Camera Calibration
under Circular Motion,” IEEE Transactions on Pattern Analysis and Machine Intelligence,
Vol. 29, No. 2, pp.343-349, 2007.
[14] K-Y Kenneth Wong and R. Cipolla, “Reconstruction of Sculpture from its Profiles with
Unknown Camera Positions,” IEEE Transactions on Image Processing, Vol. 13, No. 3,
2004.
[15] 陳長城與張桂芳，拓樸學概論，滄海書局，台中，民國98 年。
[16] 李柏翰，「基於多視角影像擷取之三維模型重建系統開發」，碩士論文，國立中正
大學，桃園，民國100 年。
[17] P. S. Heckbert, “Survey of Texture Mapping,” IEEE Computer Graphics Association, Vol.
6, pp. 56-67, 1986.
[18] 廖紘億，「自動相機校正與二維影像輪廓萃取研究」，碩士論文，國立中央大學，
桃園，民國104 年。
[19] 熊郁昇，「應用於大型物體三維模型重建之多重二維校正板相機校正流程開發」，
碩士論文，國立中央大學，桃園，民國105 年。
[20] W. Phothong, T-C Wu, J-Y Lai, D. W. Wang, C-Y Liao, and J-Y Lee, “Fast and Accurate
Triangular Model Generation for The Shape-from-Silhouette Technique,” Computer-
Aided Design & Applications, 14(a), 2017.
[21] W. Phothong, T-C Wu, J-Y Lai, D. W. Wang, C-Y Liao, and J-Y Lee, “Editable Texture
Map Generation and Optimization Technique for 3D Visualization Presentation,”
Computer-Aided Design & Applications, 15(1), 2018.
[22] W. Phothong, T-C Wu, J-Y Lai, D. W. Wang, C-Y Liao, and J-Y Lee, “Quality
Improvement of 3D Models Reconstructed from Silhouettes of Multiple Images,”
Computer-Aided Design & Applications, 15(1), 2018.
[23] 耿繼業與何建娃，幾何光學，第三版，全華科技圖書，台北，民國99 年。
[24] 中央大學影像處理暨虛擬實境研究室，「影像處理簡介」，http://ip.csie.ncu.edu.tw/。
[25] 鍾國亮，資料壓縮的原理與應用，第二版，全華科技圖書，台北，民國95 年。
[26] Ming-Chin Chuang, “Digital Image Processing-Image Segmentation”.
[27] 鍾國亮，數位處理與電腦視覺，臺灣東華書局，台北，第22-30 頁，民國95 年。
[28] “Morphology (Introduction to Video and Image Processing) Part 1,” http://what-whenhow.
com/introduction-to-video-and-image-processing/morphology-introduction-tovideo-
and-image-processing-part-1/ .
110
[29] “Morphology (Introduction to Video and Image Processing) Part 2,” http://what-whenhow.
com/introduction-to-video-and-image-processing/morphology-introduction-tovideo-
and-image-processing-part-2/ .
[30] 同參考文獻27，第96-100 頁。
[31] R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd Edition, Prentice Hall,
New York, 2007.
[32] J. F. Canny, “A Computational Approach to Edge Detection,” IEEE Trans, Pattern Anal,
Machine intel, Vol. PAMI-88, pp. 679-698, 1986.
[33] 張維庭， “EmguCV Image Process: Filtering the Images,” http://yyprogramer.
blogspot.tw/2012/12/emgucv-image-process-filtering-images.html, 2012。
[34] A. Neubeck and L. V. Gool, “Efficient Non-Maximum Suppression,” The 18th
International Conference on Pattern Recognition (ICPR'06), 2006.
[35] 陳慶瀚，「單元六、邊緣偵測」，http://140.115.11.235/~chen/course/vision/ch6/ch6.htm,
2004。
[36] 張顯全、王繼軍與蔣聯源，「基於Freeman 鏈碼的圓識別方法」，計算機工程，第
33 卷，第15 期，民國96 年。
[37] J. Wang, W. Song, L, Zhao, W. Wang, “Application of Improved Freeman Chain Code in
Edge Tracking and Straight Line Extraction,” Journal of Signal Processing, Vol.30 Issue
4, pp. 422-430, 2014.
[38] G. Bradski and A. Kaehler, Leaning OpenCV, Oreilly, 2008.
[39] K-L Low, “Linear Least-Squares Optimization for Point-to-Plane ICP Surface
Registration,” Technical Report TR04-004, Department of Computer Science, University
of North Carolina at Chapel Hill, 2004.
[40] Otto Bretscher, Linear Algebra with Applications, 2nd Edition, Prentice Hall, New York,
2001.
[41] Paul J. Besl and Neil D. McKay, “A Method for Registration of 3-D Shapes,” IEEE
Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, 1992.
[42] 李國偉，線性代數的世界，天下遠見，台北，第469-477 頁，民國94 年。
[43] 劉惟信，機械最佳化設計，全華科技圖書，台北，第3-9 - 3-24 頁，民國85 年。