軟性電路板因為其具可撓曲特性而被廣泛地應用在各產業，也因為其獨特的可撓曲特性，所以在佈線方式與一般電路板有所的不同。一般電路板上的佈線有轉角，而軟性電路板上的佈線則是用弧線取代轉角，此種做法的目的有三：1.在於降低電流在流經轉角時所產生的雜訊；2.不要讓軟性電路板在撓曲時於佈線轉角處產生應力集中的現象，因為應力集中會使得軟性電路板上的佈線較容易發生斷裂的問題；3.為配合產品結構的形狀及避免佈線的路徑與電路板上電子元件的位置起衝突，軟性電路板在線路轉彎處均將用圓弧狀來佈線。軟性電路板的製造精密化也為軟性電路板帶來了許多技術上需要克服的障礙，因此本研究將針對軟性電路板上的佈線弧度之自動化檢測與製程管制的探討。
本研究首先應用影像處理技術找出軟性電路板上之佈線弧度的範圍，並藉由電腦視覺方法得到電路板上佈線的座標值，接著進行本研究所提出之改良式曲率法之計算，以累和演算法對具方向性之改良式曲率做微量偏移的管制。當偵測出曲率值異常時，利用累和演算法可回溯製程開始偏移處的特性，可找到正確轉角點的位置。為了能夠更精準地發揮此曲率累和法偵測轉角點之效果，本研究規劃曲率累和法之參數因子實驗設計，找出影響曲率累和法偵測轉角點的顯著性因子，再根據此顯著性因子建立曲率累和法之參數設定建議值。此外，為驗證此曲率累和法為一可行且具效率之轉角點偵測方法，本研究還進行曲率累和法的敏感度(物件旋轉角度、尺寸改變)分析及曲率累和法與其他轉角點偵測方法的比較分析。在偵測到軟性電路板佈線弧度之轉角後，利用轉角點的資訊可擷取佈線弧度之特徵值，再以此特徵值發展出以累和管制圖為基礎的佈線弧度製程管制模式來監督此製程。
本研究以電腦視覺技術為基礎，搭配所提出的曲率累和法可找出軟性電路板上佈線弧度的轉角點，實驗之結果說明此方法偵測轉角點之正確率為98.8%。而轉角點的資訊可用來判斷線段類型及擷取佈線之弧度，最後再利用以累和管制圖為基礎的佈線弧度製程管制技術來監督此製程。在軟性電路板佈線轉角點偵測方面，本研究所提出之曲率累和法可以偵測各種佈線之轉角點；在軟性電路板佈線的管制方面，偵測到軟性電路板佈線轉角點後，擷取佈線弧度之特徵值進而管制佈線弧度之製程，此程序提供一個可行的佈線弧度製程管制的方法。
關鍵詞：自動化檢測、製程管制、曲率法、累和演算法、佈線弧度、軟性電路板、可撓曲特性。

Flexible printed circuit board (FPC) has been used extensively because of its flexibility. Tracks on the FPC are different from those on the printed circuit board (PCB) because of the bendability. Track’s shapes on the PCB are lines and corners but track’s shapes on the FPC are lines and arcs. Three reasons for the difference of the track’s shapes between FPC and PCB. First, to decrease electromagnetic interference when an electron current pass by a track turn. Second, to avoid stress appears at the track turn on the FPC. Stress can destroy the track’s structure on the flexible printed circuit board. Third, to match up the shape of a product body and to avoid the track pass through the position which has an electric component. Tracks on the FPC are designed as arcs when making a turn. Since the requirement of FPC manufacturing skills is getting more precisely. This tendency needs more techniques to conquer these difficulties. This research is going to study the automated inspection and process control of the track arcs of the FPC industry.
In this research, computer vision techniques are used to obtain the coordinates of the tracks on the FPC. A revised curvature method is proposed to compute the curvatures of the tracks. Then, the CUSUM algorithm is applied to obtain the coordinates of the corner of the tracks. Based on the information of the corner, we can measure the features of every track arc segment. Finally, these features can be utilized to develop a process control model based on the CUSUM control chart for the track process control of the FPC.
This research proposes and implements a computer vision system to find out the corner of the track by using “Curvature and CUSUM algorithm”.This method can detect 98.8 corners in 100 corners. And a process control model of the track arcs based on CUSUM control chart is also developed. This research contributes a solution to the common inspection and process control problems of the FPC track process.
Keyword：Computer-aided automatic inspection; Process control; Curveture; CUSUM algorithm; Track arc detection; Flexible printed circuit board; Bendability.

摘要 i
Abstract III
第一章 緒論 1
1-1 研究背景 1
1-2 軟性電路板製程簡介 4
1-3 動機與目的 7
第二章 文獻探討 13
2-1 影像二值化 13
2-2 邊緣偵測與轉角點偵測 13
2-3 圓弧量測與曲線配適方面 14
2-4 製程管制技術方面 15
2-5 模糊理論與類神經網路方面 16
第三章 研究方法 18
3-1 擷取待測軟性電路板之影像與影像處理 18
3-1-1 去除影像雜訊(Smoothing)： 18
3-1-2 增強影像 (Image enhancement)： 18
3-1-3 二值化影像： 18
3-1-4 細線化物件邊界： 20
3-2 分析與判斷軟性電路板線路之組合型態 21
3-3 曲率(Curvature)計算法進行轉角點偵測 22
3-4 曲率累和演算法計算法進行轉角點偵測 23
3-4-1 改良式曲率法 24
3-4-2 累和管制法 30
3-4-3 曲率累和法 31
3-4-4 曲率累和演算法之方向性 36
第四章 實例驗證 39
4-1 曲率累和法參數之設定 39
4-1-1 曲率累和法之因子實驗設計 39
4-1-2 曲率累和法參數設定之建議值 54
4-2 偵測影像轉角點方法之比較 60
4-2-1 曲率法與曲率累和法轉角偵測之比較 60
4-2-2 曲率累和法與其它方法之比較 72
4-2-3 曲率累和演算法之方向性 80
4-3 曲率累和法偵測軟性電路板佈線弧度影像轉角點之實例 81
4-3-1 影像前處理 81
4-3-2 曲率累和法偵測佈線轉角點 83
4-4 累和管制法於軟性電路板上佈線弧度之管制實例 84
4-5 實例驗證之結果分析 86
第五章 結論與未來研究方向 88
5-1 研究成果 88
5-2 未來研究方向 89
參考文獻 90
附錄 96
附錄A 曲率累和法因子實驗設計資料 97
附錄B 累和管制法管制佈線弧度之詳細資料 102

[01]吳永輝，電路板資訊第四十四期，pp.59~68，1991。
[02]李政宜，王文俊，"圓形實際物體之影像辨識"，中央大學電機工程研究所碩士論文，1997年。
[03]林垂宙、劉仲明，電路板資訊第二十二期，pp.38~47，1989。
[04]林振華、林振富，高密度性電路板入門，全華出版社，1995年。
[05]金進興，工業材料第163期，pp.119~129。
[06]柳美玲、田方治，"使用K曲率法則於二維物體的分斷點偵測之研究"，朝陽科技大學工業工程與管理研究所碩士論文，2000年。
[07]侯東旭、陳建諭，"使用輪廓座標與類神經網路於外形辨識研究"， 中國工業工程學刊，Vol. 13, No. 3, pp.271-281, 1996.
[08]洪志宏，蔡篤銘，"應用類神經網路估計數位影像中圓弧之圓心及半徑"，元智大學工業管理研究所碩士論文，1996年。
[09]洪瑞斌，陳梁軒，"應用電腦視覺系統於工件圓弧之量測"，成奶j學工業管理研究所碩士論文，1994年。
[10]高茂林，陳梁軒，"應用電腦視覺系統於圓形物體真圓度之檢測"，成功大學工業工管理研究所碩士論文，1993年。
[11]張宏佐，林宏達，"積層陶瓷電容製程中自動化電極印刷檢驗之探討"，朝陽科技大學工業工程與管理研究所碩士論文，1998年。
[12]陳雲岫、江行全，"利用統計模型對物件表面缺陷之分類研究-油封為例"，中國工業工程學刊，Vol. 13, No. 3, pp.283-294, 1996.
[13]曾國芳、蔡篤銘，"以類神經網路偵測數位曲線之轉角"，元智工學院工業工程研究所碩士論文，1995年.
[14]廖晏生，金甘平，"電腦視覺電路板檢測上的應用"，交通大學機械工程研究所碩士論文，1997年。
[15]廖英翔，林宏達，"具可撓曲特性之軟性電路板佈線弧度之檢測探討"，中國工業工程學會九十年度年會論文集，高雄，義守大學，2001年12月。
[16]劉繼煥，林宏達，"基層陶瓷電容製程中電容晶片端面弧度之自動化檢測與製程管制探討"，朝陽科技大學工業工程與管理研究所碩士論文，2000年。
[17]Aimo, Hakulinen and Juha, Hakkarainen, "A Network Approach to Quality Control of Padlock Manufacturing", Pattern Recognition Letters, Vol.17, pp.357-362, 1996.
[18]Anothai, Rattarangsi and Chin, Roland T., "Scale-Based Detection of Corners of Planar Curves", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.14, No.4, pp.430-449, 1992.
[19]Asoudegi, E. and Pan, Z., "Computer Vision for Quality Control in Automated Manufacturing System", Computer and Industrial Engineering, Vol.21, pp.141-145, 1989.
[20]Beus, H. L. and Tiu, S. H., "An Improved Corner Detection Algorithm Base on Chain-Code Plane Curves", Pattern Recognition, Vol.20, No.3, pp.291-296, 1987.
[21]Bookstein, F. C., "Fitting Conic Section to Scattered Data", Computer Graphics and Image Processing, Vol.9, pp.56-71, 1979.
[22]Carpinetti, C. R. and Cetwynd, D. G., "A New Strategy for Inspecting Roundness Features", Precision Engineering, Vol.16, pp.283-289, 1994.
[23]Charles, P. Q., "An SPC Approach to Compensating a Tool-Wear Process", Journal of Quality Technology, Vol.20, No.4, pp.220-229, 1988.
[24]Chen, J. M., Ventura, J. A. and Melloy, B. J., "An Optimization Algorithm for Shape Analysis of Regular Polygons", Machine Vision and Applications, No.7, pp.82-92, 1994.
[25]Chen, M. C., Tsai, D. M. and Tzeng, H. Y., "A Vision-Based Inspection System for Circular Components", Proceedings of the 1998 CIIE National Conference, 1998.
[26]Coope, I. D. and Dixon, L. C., "Circle Fitting by Linear and Nonlinear Least Squares", Journal of Optimization Theory and Application, Vol.76, No.2 pp.112-120, 1993.
[27]Davd, C. and Raghurm, K., "Curved Object Location by Hough Transformation and Inversions", Pattern Recognition, Vol.20, pp.181-188, 1987.
[28]Davies, E. R., "A High Speed Algorithm for Circular Object Location", Pattern Recognition Letters, Vol.6, pp.323-333, 1987.
[29]Eberly, D. and Lancater, J., "On Gray Scale Image Measurement: 1. Arc Length and Area", Computer Vision Graphics and Image Processing, Vol.53, pp.538-549, 1991.
[30]Eric, Saund, "Identifying Salient Circular Arc on Curves", CVGIP: Image Understanding, Vol.58, No. 3, pp.327-337, 1993.
[31]Faires, J. Douglas and Burden, Richard L., Numerical Analysis, Sixth Edition, 1997.
[32]Fant, E. W. and Foo, K. Yeen., "Automated Print Inspection for Cylindrical Surfaces", International Journal Production Research, Vol.32, No.8, pp.1811-1817, 1994.
[33]Freeman, H. and Davis, L. S., "A Corner-Finding Algorithm for Chain Coded Curves, " IEEE Transactions on Computer, pp.297-303, 1977.
[34]Gorman, J. W., Mitchell, O. R. and Kuhl, F. P. "Partial Shape Recognition Using Dynamic Programming", IEEE Transactions on Pattern Analysis and Machine Intellingence, Vol.10, No.2, pp257-266, 1988.
[35]Griffiths, B. J. and Wilkie, B., "A Low-Cost Vision System Combining Conventional and Artificial Intelligence Techniques for Complex Image Inspection and Verificaton", International Journal of Production Research, Vol.33, No.8, pp.2133-2146, 1995.
[36]Grimson, W. and Eric, L., "On the Recognition of Curved Objects", IEEE Transcations on Pattern Analysis and Machine Intelligence, Vol.11, No.6, pp.632-643, 1989.
[37]Howard, N. Z. and Dawn, L., "The role of vision in repetitive circle drawing", Acta Psychologica, Vol.92, pp.105-118, 1996.
[38]Jang, J. -S. R., Sun, C. T. and Mizutani, E., "Neuro-Fuzzy and Soft Computing", Prentice-Hall International, Inc., 1997.
[39]Jang, J. S. R., "ANFIS: Adaptive-Network-based Fuzzy Inference Systems", IEEE Transactions on Systems Man and Cybernetics, Vol.23, pp.665-685, May 1993.
[40]Jang, J. S. R., "Input Selection for ANFIS Learning", Proceedings of the IEEE International Conference on Fuzzy System, New Orleans, 1996.
[41]Jiang, Bernard C. and Jiang, S. J., "Machine Vision based Inspection of Oil Seals", Journal of Manufacturing System, Vol.17, No.3, pp.159-166, 1998.
[42]Joseph, S. H., "Unbiased least squares fitting of circular arcs", GVGIP：Grahical Models and Image Processing 56, pp.424-465, 1994.
[43]Kanagawa, Tamaki A. F. and Ohta, H., "Control Charts for Process Average and Variability Based on Linguistic Data", International Journal of Production Research, Vol.31, No.4, pp.913-922, 1993.
[44]Landau, U. M., "Estimation of a Circular Arc Center and its Radius", Computer Vision Graphics and Image Processing, Vol.38, pp.317-326, 1987.
[45]Lapreste, J. T., Richetin, M., Dhome, M. and Rives, G., "Inverse Perspective Transform Using Zero-Curvature Contour Points: Application to the Localization of Some Generalized Cylinders from a Single View", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.13, No.2, pp.185-192, 1991.
[46]Lim, Kah Bin, Xin, Kai Hong and Geok, Soon, "Detection and Estimation of Circular Arc Segments", Pattern Recognition Letters, Vol.16, pp.627-636, 1995.
[47]Mandel, B. J., "The Regression Control Chart", Journal of Quality Technology, Vol.1, No.1, pp.1-9, 1969.
[48]Medioni, G. and Yasumoto, Y., "Corner Detection and Curve Representation Using Cubic B-Splines", Computer Vision, Graphics, and Image Processing, Vol.39, pp.267-278, 1987.
[49]Montgomery, D. C., Introduction to Statistical Quality Control, John Wiley & Sons, Inc. Fourth Edition, 2000.
[50]Ostu, N., "A Threshold Selection Method from Gray-Level Histogram", IEEE Transactions on Systems, Man, and Cybernetics, Vol.9, No.1, pp.62-66, 1979.
[51]Pei, Soo-Chang, and Horng, Ji-Hwei, "Circular arc detection based on Hough Transform", Pattern Recognition Letters, Vol.16, pp.615-625, 1995.
[52]Pei, Soo-Chang, and Horng, Ji-Hwei, "Fitting Digital Curve Using Circular Arcs", Pattern Recognition, Vol.28, No.1, pp.107-116, 1995.
[53]Rosenfield, A. and Johnston, E., "Angle Detection on Digital Curves", IEEE Transactions on Computer, Vol.22, pp.875-878, 1977.
[54]Sahoo, P. K., Soltani, S. and Wong, A. K. C., "A Survey of Thresholding Techniques", Computer Vision, Graphics, and Image processing, Vol. 41, pp.233-260, 1988.
[55]Tech, C. H. and Chin, R. T., "On the Detection of Dominant Point on Digital Curves", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.8, pp.311-330, 1989.
[56]Tsai Du-Ming, "Boundary-Based Corner Detection Using Neural Networks", Pattern Recognition, Vol.30, pp85-97, 1997.
[57]Tsai Du-Ming, Hou H.-T. and Su H.-J., "Boundary-Based Corner Detection Using Eigenvalues of Covariance Matrices", Pattern Recognition Letters, Vol.20, pp31-40, 1999.
[58]Ventura, J. A., Chang, C. A. and Klein, C. M., "Automatic Inspection of Circular Parts", Computers and Industrial Engineering, Vol.15, pp.349-354, 1988.
[59]Ventura, J. A. and Yeralan, S., "The Minimax Center Estimation Problem for Automated Roundness Inspection", European Journal of Operational Reasearch, Vol.41, pp.64-72, 1989.
[60]Wang, J. H. and Raz, T., "Applying Fuzzy Set Theory in the Development of Quality Control Chart", International Industrial Engineering Conference Proceedings, Orlando, FL, pp.30-35, 1988.
[61]Wu Wen-Yen, Wang Mao-Jiun and Liu Chih-Ming, "Automated inspection of printed circuit boards through machine vision", Computers In Industry, Vol.28, pp.103-111, 1996.
[62]Yao, Yingxue, Li, Xiaoli and Yuan, Z., "Tool Wear Detection with Fuzzy Classification and Wavelet Fuzzy Neural Network", International Journal of Machine Tools & Manufacture, Vol.39, pp.1525-1538, 1999.
[63]Yeralan, S. and Ventura, J. A., "Computerized Roundness Inspection", International Journal of Production Research, Vol.26, No.12, pp.1921-1935, 1988.