本文主要的研究目標是利用逆向工程的技術來辨識模具表面點群之曲面特徵，重建模具表面的曲面資料結構。研究的內容包括了點雷射深度量測之路徑規劃，曲面的區域分割，曲面的辨識以及曲面的重建。利用影像編碼技術，空間點群座標料可以轉換成影像資料格式，利用影像的邊界搜尋、區域分割、迴路追跡與迴路分割，各個區域曲面與邊界上的點群資料就可以被擷取出來。根據曲面上兩筆特徵截痕點群的曲線擬合結果，各個區域曲面可以被辨識為平面、旋轉面或者是自由曲面這三種曲面類型。曲面的重建分為平面、旋轉面、自由曲面與垂直壁面四種，因為垂直壁面在編碼影像上僅為一段邊界，並不構成一個區域，所以垂直壁面的辨識必須根據與邊界相鄰的兩個曲面其空間中的關係來作判斷，並且垂直壁面的重建也是要利用相鄰曲面邊界重建的結果來進行。

　　This paper uses the image process and computational geometry techniques to recognize the geometrical features of a mold surface and reconstruct its 3D model. The geometric reverse engineering processes include path planning for depth measurement system, point cloud segmentation, surface recognition and reconstruction. By employing the image encoding skill, the point cloud is transformed into a range image format. The point cloud in each individual surface and the corresponding edges are obtained by using boundary search, image segmentation, loop tracing and loop segmentation. The surface is recognized by curve fitting of two sectional depth data through the major axes of the surface loop. And then the surface can be recognized according to the recognized curves. The surface reconstruction is sorted as plane, surface of revolution, freeform surface, and wall surface. The wall surface is only a segment of a boundary loop in the range image. Its existence must be examined by the gap of the two neighbor surfaces. Consequently, the wall surface reconstruction is base on the geometric reasoning from the intersection conditions of the two neighbor surfaces.

[1] Besl, Paul J., Mckay, Neil D., A method for registration of 3-D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, pp. 239-256, 1992.

[2] Johnson, A. E., Hebert, M., Surface registration by matching oriented points, International Conference on Recent Advances in 3-D Digital Imaging and Modeling, pp. 121-128, 1997.

[3] Dorai, C., Wang, G., Jain, A. K., Mercer, C., Registration and integration of multiple object views for 3D model construction, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 20, No.1, pp. 83-89, 1998.

[4] Yamany, S. M., Farag, A. A., Free-form surface registration using surface signatures, Proceedings of the Seventh International Conference on Computer Vision, Vol. 2, pp. 1098-1104, 1999.

[5] Yau, H. T., Chen, C. Y., Wilhelm, R. G., Registration and integration of multiple laser scanned data for reverse engineering of complex 3D models, International Journal of Production Research, Vol. 38, No. 2, pp. 269-285, 2000.

[6] Huber, D. F., Hebert, M., Fully automatic registration of multiple 3D data sets, Image and Vision Computing, Vol. 21, No. 7, pp. 637-650, 2003.

[7] Wan, W., Ventura, J. A., Segmentation of planar curves into straight-line segments and elliptical arcs, Graphical Models and Image Processing, Vol. 59, No. 6, pp. 484-494, 1997.

[8] Ray, B. K., Pandyan, R., ACORD − An adaptive corner detector for planar curves, Pattern Recognition, Vol. 36, No. 3, pp. 703-708, 2003.

[9] Wu, W. Y., Dominant point detection using adaptive bending value, Image and Vision Computing, Vol. 21, No. 6, pp. 517-525, 2003.

[10] Ahn, S. J., Rauh, W., Warnecke, H. J., Least-square orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola, Pattern Recognition, Vol. 34, No. 12, pp. 2283-2303, 2001.

[11] Park, H., Choosing nodes and knots in closed B-spline curve interpolation to point data, Computer-Aided Design, Vol. 33, No. 13, pp. 967-974, 2001.

[12] Horng, J. H., An adaptive smoothing approach for fitting digital planar curves with line segments and circular arcs, Pattern Recognition Letters, Vol. 24, No. 1-3, pp. 565-577, 2003.

[13] Park, H., Kim, K., Smooth surface approximation to serial cross-sections, Computer-Aided Design, Vol. 28, No. 12, pp. 995-1005, 1996.

[14] Bae, S. H., Choi, B. K., NURBS surface fitting using orthogonal coordinate transform for rapid product development, Computer-Aided Design, Vol. 34, No. 10, pp. 683-690, 2002.

[15] Horn, B. K. P., Hilden, H. M., Negahdaripour, S., Closed-form solution of absolute orientation using orthonormal matrices, Journal of the Optical Society A, Vol. 5, No. 7, pp. 1127-1135, 1988.

[16] Naccache, N. J., Shinghal, R., SPTA: A proposed algorithm for thinning binary patterns, IEEE Transactions on System, Man and Cybernetics, Vol. SMC-14, No. 3, pp. 409-418, 1984.

[17] Sugimoto, K., Tomita, F., Boundary segmentation by detection of corner, inflection and transition points, IEEE Workshop on Visualization and Machine Vision, Proceedings, pp. 13-17, 1994

[18] Rao, S. S., Engineering Optimization: Theory and Practice, 3rd Edition, Wiley-Interscience, 1996.

[19] Fitzgibbon, A., Pilu, M., Fisher, R. B., Direct least square fitting of ellipses, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 21, No. 5, pp. 476-480, 1991.

[20] Korn, Granino A., Korn, Theresa M., Mathematical Handbook for Scientists and Engineers, 2nd Edition, McGRAW-HILL, 1968.

[21] Piegl, L., Tiller, W., The NURBS Book, 2nd Edition, Springer-Verlag, 1997.

[22] Park, H. J., Kim, K. S., Smooth surface approximation to serial cross-sections, Computer-Aided Design, Vol. 28, No. 12, pp. 995-1005, 1996.

[23] IGES/PDES Organization, Initial graphics exchange specification (IGES), Version 5.1.

[24] Spiegel, Murray R., Liu, J., Mathematical Handbook of Formulas and Tables, 2nd Edition, McGRAW-HILL, 1999.

[25] Jones, Richard M., Introduction to MFC programming with Visual C++, Prentice Hall PRT, 2000.

[26] 蔡明俊，影像編碼壓縮方法及具人體特徵的資料結構，中華民國專利，發明第195369號，2004。

[27] 蔡明俊，韋志昇，魏緒強，應用影像處理技術於模具邊界之幾何特徵辨識，中華民國自動化科技學會第十屆全國自動化科技研討會，論文集第二冊，第801-808頁，中華民國86年。

[28] 蔡明俊，許又仁，安乃駿，模具表面幾何特徵辨識之研究，中國機械工程學會第十九屆學術研討會論文集，固力與設計（中），第841-848頁，中華民國91年。

[29] 黃佳豪，以特徵為基礎的交談式電腦視覺模具幾何辨識系統，國立成功大學機械工程研究所碩士論文，中華民國89年。

[30] 林希達，焊接機器人離線程式系統之發展，國立成功大學機械工程研究所碩士論文，中華民國79年。

[31] 許又仁，應用電腦視覺技術於模具表面幾何特徵辨識之研究，國立成功大學機械工程研究所碩士論文，中華民國91年。

[32] 蔡明俊，魏緒強，黃佳豪，二次曲面之影像辨識方法研究，中華民國自動化科技學會第十一屆全國自動化科技研討會，論文集上冊，第623-628頁，中華民國88年。

[33] 洪維恩，數學運算大師MATHEMATICA 4，碁峰資訊股份有限公司，中華民國90年。

[34] 蔡明志譯，C++教學範本，碁峰資訊股份有限公司，中華民國89年。

[35] 胡哲源，掌握Visual C++ — MFC程式設計與剖析，文魁資訊股份有限公司，中華民國89年。