Micro SD (Micro Secure Digital ) Card是一種極小的快閃記憶體卡。它常應用在可攜式產品，例如：數位相機、手提電腦、個人數位助理、衛星導航系統等等…。Micro SD Card體積小、容量高、處理速度快且攜帶方便，因此極適合無線通訊。Micro SD Card具有特定的規格標準，並以轉接卡來兼容各類電子週邊設備。為了避免不合格的Micro SD Card造成電線短路或產品無法正常運作，本論文探討如何使用影像處理技術來量測其尺寸以找出瑕疵的產品。

本論文發展一能達到工業精確度和計算時間需求的Micro SD Card檢測方法。首先，我們以教讀一標準產品的影像來定出檢測區域，利用圖樣比對法找到待量測影像的偏移量以找出該影像的相對檢測區域。然後，使用DOB (Difference of Boxes) 找出邊緣並以邊緣追隨法剔除缺裂的邊緣點，再以ZOMs (Zernike Orthogonal Moments；澤尼克正交矩) 修正邊緣位置到次像素精度。將所得到的弧角邊緣，利用直線和弧相切的關係，找到切點以排除部份直線邊以保留真正的圓弧邊緣。最後，將所得的邊緣點經由線性回歸得到最小平方差的直線和圓，經由幾何運算得到所需的量測數據。

本論文首先以人工合成影像來評估所發展方法的效能。實驗結果顯示，在沒有雜訊干擾的情況下，中心點位置誤差小於0.02 pixel，而偏向角誤差小於0.02度；在高斯雜訊(σ=25)干擾下，平均誤差約為0.014 pixel。對解析度為12.7 um/pixel的實際影像，中心點位置誤差小於4 um，直邊間距標準差小於5 um，弧角半徑標準差小於12 um。執行速度方面，在一台AMD Athlon 64 3000+ 處理器的電腦上，完成整個運算所需的時間約750毫秒，所處理的影像大小為1040x1392像素。

The Micro SD (Micro Secure Digital) card is a tiny flash-based memory card. It is used in portable devices, including digital cameras, handheld computers, PDAs and GPS units etc. There are many advantages of the Micro SD Card like high capacity, high speed and small volume, so the Micro SD Card was mainly designed for wireless communication. In order to achieve better electric transmitting effect and be compatible with various electric products, a Micro SD Card with standard specifications can be slotted into designated adapters. In order to avoid unqualified Micro SD Cards to cause short circuit or malopration, Micro SD Cards are inspected by image processing techniques to detect defective products.

In order to meet the requirement of accuracy and efficiency in industry, this thesis develops software for measuring the dimensions of a Micro SD Card. At first, owing to the region of product to be inspected are numerous and complex, we teach a model image to delimit region of interest. Second, pattern matching is applied to align a test image with the model image. Then we extract edge elements of boundaries of the inspected region by using DOB (Difference of Boxes) and eliminate false edges by edge following. After that, the locations of edge points are refined to subpixel level accuracy by using the ZOMs (Zernike Orthogonal Moments). Points of tangency of line and arc are calculated to exclude false edge points from the boundaries of arc. Finally, measurements of Micro SD Card are found by line fitting, circle fitting and geometric calculation.

Synthetic images are first used to evaluate the performance of the developed software in term of precision and time cost. The experiment results indicate that the errors of central position and orientation are under 0.02 pixels and 0.02 degrees respectively without noise interference; the average errors of rotation angle is less than 0.014 pixel with Gaussian noise of σ = 25. For practical image with resolution 12.7 um/pixel, the error of central position is under 4 um, the standard deviation of inspected distances is less than 5 um and the standard deviation of radius of arcs is less than 12 um. It takes approximately 750 milliseconds to complete the whole operation for a 1040x1392 image using a PC with a processor of AMD Athlon 64 3000+.

[1]T. J. Bin, A. Lei, C. Jiwen, K. Wenjing and L. Dandan, “Subpixel Edge Location Based on Orthogonal Fourier-Mellin Moments,” Image and Vision Computing, Vol. 26, pp. 563-569, 2008.
[2]J. F. Canny, “A Computation Approach to Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-8, No. 6, pp. 679-698, Nov. 1986.
[3]J. F. Canny, “Finding Edges and Lines in Images,” Technical Report 720, MIT Artificial Intelligence Lab., 1983.
[4]N. Chernov and C. Lesort, “Least Squares Fitting of Circles,” Journal of Mathematical Imaging and Vision, Vol. 23, No. 3, pp. 239-252, Nov. 2005.
[5]D. Demigny, “On Optimal Linear Filtering for Edge Detection,” IEEE Transactions on image Processing, Vol. 11, No. 7, pp. 728-737, July 2002.
[6]S. Ghosal and R. Mehrotra, “A Moment-Based Unified Approach to Image Feature Detection,” IEEE Transactions on image processing, Vol. 6, No. 6, June 1997.
[7]S. Ghosal and R. Methrotra, “Edge Detection Using Orthogonal Moment-Based Operators,” Proceedings of the 11th Image, Speech and Signal Analysis (IAPR) International Conference on Pattern Recognition, Vol. 3, pp. 413–416, 1992.
[8]R. C. Gonzalez and R. E. Woods, Digital Image Processing, Edition, Prentice Hall, USR, NJ, 2002.
[9]Y. H. Guo, “Subpixel Image Alignment Using Interpolation Functions,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2006.
[10]W. C. Hung, “Subpixel Image Alignment with Blurred Edge Model Using the Revised Newton Method,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2007.
[11]L. Jinquan, C. Shanben and W. Lin, “An Algorithm of Subpixel Edge Detection Based on ZOM and Application in Calibration for Robot Vision,” Intelligent Control and Automation, 2002. Proceedings of the 4th World Congress, Vol. 2, pp. 1210-1214, June 2002.
[12]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.
[13]A. Khotanzad, Y. H. Hong, “Invariant Image Recognition by Zernike Moments,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 12, No. 5, pp. 489-497, May 1990.
[14]M. Kisworo, S. Venkatesh and G. West, “Modeling Edges at Subpixel Accuracy Using the Local Energy Approach,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, No. 4, pp. 405-410, Apr. 1994.
[15]W. C. Lee, “Subpixel BGA Images Alignment Based on Moment Methods,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2005.
[16]J. P. Lewis, “Fast Normalized Cross-Correlation,” Vision Interface, pp. 120-123, 1995.
[17]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, No. 12, pp. 1293-1309, Dec. 1989.
[18]A. Mcamdrew, Introduction to Digital Image Processing with MATLAB, Thomson Course Technology, 2004.
[19]P. Mikulastik, R. Hover and O. Urfalioglu, “Error Analysis of Subpixel Edge Localisation,” Signal Processing for Image Enhancement and Multimedia Processing, Vol. 31, pp. 103-113, 2008.
[20]M. Petrou and J. Kittle, “Optimal Edge Detectors for Ramp Edges,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 5, May 1991
[21]Y. D. Qu, C. S. Cui, S. B. Chen and J. Q. Li, “A Fast Subpixel Edge Detection Method Using Sobel-Zernike Moments Operator,” Image and Vision Computing, Vol. 23, No. 1, pp.11-17, Jane 2005.
[22]Y. D. Qu, R. D. Li, X. G. Yuan, H, J. Huang and C. X. Li, “Analysis of Principle Deviation of Subpixel Zernike Moments Operator,” Optoelectronics Letters, Vol. 3, No. 5, Sep. 2007.
[23]M. Sonka, V. Hlavac and R. Boyle, Image Processing, Analysis, and Machine Vision, Edition, PWS Publisher, 1999.
[24]C. H. Toa, “A Study on Alignment of BGA Images for Automatic Visual Inspection,” Master Thesis, Dept. of Electrical Engineering, NCKU, June 2004.
[25]D. H. Xu, H. Z. Shu, X. D. Bao, H. Zhang, J. L. Dillenseger and L. M. Luo, “A Parabola Fitting Edge Operator by the Moments,” Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), Vol. 1, pp. 653-656, Sep. 2003.