本論文探討BGA和CMOS防護鏡次像素晶片定位的問題。BGA是一成熟的封裝技術，因其具有良好的電氣、散熱性質而廣泛被用在電子產品中，而藉由精準的定位可以將該晶片的型號雷射刻印在晶片上。防護鏡乃用來隔離紅外線防止其進入CMOS感光元件，數位相機上的CMOS感光元件可感應範圍約在350nm~1200nm，包括紅外線，但是紅外線會讓影像失真，所以數位相機必須在CMOS與鏡頭之間加裝紅外線濾光片以降低紅外線的干擾，而精確的定位可以加速、穩定化其封裝程序。

本論文使用的方法的步驟如下：先將原影像對水平和垂直方向做投影界定出感興趣區域，使用DOB得到像素精準度的邊緣點而後使用邊緣追隨法剔除掉物體缺裂的邊緣點，再運用ㄧ模糊邊界模型配合修正型牛頓法得到最佳的模型參數將所得到的邊緣點修正到次像素的精準度，最後以最小平方差直線匹配的回歸運算和幾何運算定出晶片的中心點和偏向角。

對無雜訊的合成影像，實驗結果顯示平移定位的誤差皆小於0.1像素，而偏向角定位的誤差皆小於0.01度。對不同程度高斯雜訊下的合成影像，偏向角誤差的標準差皆在0.01度之下。對兩種實際影像，當掺雜微量的雜訊時，晶片中心位置和偏向角的標準差皆小於0.07像素和0.02度。

The thesis studies the subpixel alignment of BGA and the IR cut filter of the CMOS sensor. BGA is a mature technique of packaging and widely applied in electronic manufactures because of its better electric and heat dissipation property. Under more accurate alignment, we can mark the package accurately. The IR cut filter is used to cut off infrared rays and avoid its disturbance to the CMOS sensor. The CMOS sensor of digital camera responds to the range of optical spectrum from 350nm to 1200nm, it can detect infrared ray but infrared ray will make image to be distorted so digital camera must install the filter in order to reduce the interference of the infrared ray. We can accelerate and stabilize the procedure of packaging if we have accurate alignment.

The algorithm employed by the thesis consists of the following steps: project the package on x and y axis to delimit the ROI (region of interest) and find the edge elements by using DOB (difference of boxes) operator, then apply edge following to eliminate defected edge points and improve the edge points to subpixel accuracy using the blurred edge model modified by the revised Newton method, finally, find the center position and the sloped angle of the package by linefitting and geometric calculation.

For synthetic images without noise, the detected errors of displacement in horizontal are smaller than 0.1 pixel and the errors of sloped angle are smaller than 0.01 degree. For synthetic images corrupted by Gaussian noise, the standard deviation of the sloped angle error is smaller than 0.01 degree. Finally, we evaluate two types of practical packages. Under the conditions of slight noise, the standard deviation of the center position and the sloped angle are less than 0.07 pixel and 0.02 degree respectively.

[1]. J. F. Canny, “A computational approach to edge detection,” IEEE Trans. on Pattern Anal. Machine Intelligence, Vol. 8, No. 6, pp. 679-698, Nov. 1986.
[2]. J. H. Elder and S. W. Zucker, “Local scale control for edge detection and blur estimation,” IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol.20, No. 7, pp. 699–716, July 1998.
[3]. S. Ghosal and R. Mehrotra, “Edge detection using orthogonal moment-based operators,” ICPR(C), pp. 413-416, Sep. 1992.
[4]. Bill Green, “Canny edge detection tutorial,” 2002
[5]. R. C. Gonzalez and R. E. Woods, “Digital image processing,” 2nd Edition, Prentice-Hall, NJ, 2002.
[6]. Y. H. Guo, “ Subpixel image alignment using interpolation functions,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2006.
[7]. Z. R. Huang, “A study on orientation, measurement and recognition of an automatic inspection system,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2003.
[8]. M. Kisworo, S. Venkatesh and G. West, “Modeling edges at subpixel accuracy using the local energy approach,” IEEE Trans. Pattern Anal. Machine Intelligence, Vol. 16, No. 4, pp. 405-410, Apr. 1994.
[9]. A. A. Kassim, H. Zhou and S. Ranganath, “Automatic IC orientation checks,” Machine Vision and Applications, Vol. 12, No. 3, pp. 107-112, Oct. 2000.
[10]. E. P. Lyvers, O. R. Mitchell, M. L. Akey and A. P. Reeves, “Subpixel measurements using a moment-based edge operator,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, pp. 1293–1309, Dec. 1989.
[11]. W. C. Lee, “Subpixel BGA images alignment based on moment methods,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2005.
[12]. John H. Mathews, “Numerical analysis project-modules for numerical methods & numerical analysis,” Department of Mathematics California State University Fullerton.
[13]. D. Marr and E. Hildreth, “Theory of edge detection,” Proceedings of the Royal Society of London, Vol. B 207, pp. 187-217, 1980.
[14]. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. on System, Man and Cybernetics, Vol. 9, No. 1, pp. 62-66, Jan. 1979.
[15]. M. Petrou and J. Kittler, “Optimal edge detectors for ramp edges,” IEEE Trans. on Pattern Anal. Machine Intell., Vol. 13, No. 5, pp. 483-491, May 1991.
[16]. S. Sarkar and K. Boyer, “On optimal infinite impulse response edge detection Filters,” IEEE Trans. on Pattern Anal. Machine Intell,, Vol. 13, No. 11, pp. 1154-1171, Nov.1991.
[17]. A. J. Tabatabai and O. R. Mitchell, “Edge location to subpixel values in digital imagery,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, pp. 188–201, Mar. 1984.
[18]. W. H. Tsai, “Moment-preserving thresholding: a new approach,” Computer Vision, Graphics and Image Processing, Vol. 29, pp. 377-393, 1985.
[19]. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, “Numerical recipes in C — The art of scientific computing,” Cambridge University Press, 1992.
[20]. C. H. Tao, “A study on alignment of BGA images for automatic visual inspection,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2004.
[21]. Huang Feng Tzeng, “The development of computer vision teaching materials,” Master Thesis, Department of Mechanical Engineering, NPUST, June 2005.
[22]. M. Kisworo, S. Venkatesh and G. West, “2-D Edge feature extraction to subpixel accuracy using the generalized energy approach” TENCON '91.1991 IEEE Region 10 International Conference on EC3-Energy, Computer, Communication and Control Systems, Vol. 3, pp. 344-348, Aug. 1991.
[23]. D. Vollath "Automatic focusing by correlative methods" J. Microsc. Vol. 147, No. 3, pp. 279-288. Sept. 1987.
[24]. Jian Ye, Gongkang Fu and Upendra P. Poudel, “High-accuracy edge detection with blurred edge model,” Image and Vision Computing, Vol. 23, pp. 453–467, 2005.
[25]. Y. Zhong, Q. Lv, L. Yang and Y. Xue, “A subpixel edge detection algorithm for the high-precision automatic alignment system,” Third International Symposium on Precision Mechanical Measurements, Proceedings of SPIE, Vol. 6280, pp. 62802T-1~62802T-7, Oct. 2006.
[26]. D. Ziou and S. Tabbone, “A multi-scale edge detector,” Pattern Recognition, Vol. 26, No. 9, pp. 1305-1314, 1993.