電子產品近年來一直朝著體積縮小與功能多樣化的方向發展，使得電子元件密度不斷提高，自動光學檢測所需檢測的瑕疵面積與反差也逐漸降低，在影像放大倍率與解析度無法繼續提高的情況下，必須提高小倍率影像定位精度，才可有效提高瑕疵檢測效率。
本研究的主要目的是以特徵法則為基礎，使用次像素直線邊跡作為定位特徵， 同時考慮測試影像中瑕疵的影響，提供一個有效率的直線特徵比對演算法，針對高反差直線圖形提出一個完整的次像素定位流程，在影像放大倍率不足時，仍有精確可靠的定位結果。
本研究所提出的次像素定位流程可約略分為特徵萃取、特徵匹配和定位參數估測 3 大步驟。在定位特徵萃取的過程中，使用差量碼分辨不同角度的直線邊跡與瑕疵邊跡，並利用剛體運動時影像各物件相對位置不變的特性，以直線相對角度和相對距離作為不變量建立定位特徵匹配，定位參數即可藉由匹配特徵的相對位置以最小平方誤差估測求得。
最後以重新取樣完成定位校正，利用樣板比對方法比較次像素和像素級定位在各種應用條件下的差異，包括不同放大倍率的影像以及測試影像含有各種不同型態瑕疵等，用以驗證次像素定位相對於像素級定位而言，確實能在小倍率影像的應用上具有較為精確且穩定的定位結果，提供自動光學檢測一個實用的技術以及極具價值的改善方向。

[1] B. Zitovà and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing, vol. 21, pp. 977-1000, 2003.
[2] P. Thévenaz, U. E. Ruttimann, and M. Unser, “A pyramidal approach to subpixel registration based on intensity,” IEEE Transactions on Image Processing, vol. 7, no. 1, pp. 27-41, Jan. 1998.
[3] Y. Keller and A. Averbuch, “Fast motion estimation using bidirectional gradient methods,” IEEE Transactions on Image Processing, vol. 13, no. 8, Aug. 2004.
[4] H. Foroosh, J. Zerubia, and M. Berthod, “Extension of phase correlation to subpixel registration,” IEEE Transactions on Image Processing, vol. 11, no. 3, pp. 188-200, Mar. 2002.
[5] H. S. Stone, M. Orchard, E.-C. Chang, and S. Martucci, “A fast direct Fourier-based algorithm for subpixel registration of images,” IEEE Transactions on Geoscience and Remote Sensing, vol. 39, no. 10, pp. 2235-2243, Oct. 2001.
[6] Q. Chen, M. Defrise, and F. Deconinck, “Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 12, pp. 1156-1168, Dec. 1994.
[7] B. S. Reddy and B. N. Chatterji, “An FFT-based technique for translation, rotation, and scale-invariant image registration,” IEEE Transactions on Image Processing, vol. 5, no. 8, pp. 1266-1270, Aug. 1996.
[8] Y. Keller, A. Averbuch, and M. Israeli, “Pseudopolar-based estimation of large translations, rotations, and scalings in images,” IEEE Transactions on Image Processing, vol. 14, no. 1, pp. 12-22, Jan. 2005.
[9] R. J. Althof, M. G. J. Wind, and J. T. Dobbins, “A rapid and automatic image registration algorithm with subpixel accuracy,” IEEE Transactions on Medical Imaging, vol. 16, no. 3, pp. 308-316, June 1997.
[10] H. L. Li and C. Chakrabarti, “Motion estimation of two-dimensional objects based on the straight line Hough transform: a new approach,” Pattern Recognition, vol. 29, no. 8, pp. 1245-1258, 1996.
[11] J. W. Hsieh, H. Y. M. Liao, K. C. Fan, M.T. Ko, Y.P. Hung, “Image registration using a new edge-based approach,” Computer Vision and Image Understanding, vol. 67, no. 2, pp. 112-130, Aug. 1997.
[12] D. P. Huttenlocher, G. Klanderman, and W. Rucklidge, “Comparing images using the Hausdorff distance,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 850-863, Sept. 1993.
[13] X. Yi and O. I. Camps, “Line-based recognition using a multidimensional Hausdorff distance,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 8, Sep. 1999.
[14] H. S. Alhichri and M. Kamel, “Multi-resolution image registration using multi-class Hausdorff fraction,” Pattern Recognition Letters, vol. 23, pp. 279-286, 2002.
[15] J. R. Beveridge and E. M. Riseman, “How easy is matching 2D line models using local search?” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 6, June 1997.
[16] B. Kamgar-Parsi and B. Kamgar-Parsi, “Algorithms for Matching 3D Line Sets,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 5, May 2004.
[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] S. Ghosal and R. Mehrotra, “Orthogonal moment operators for subpixel edge detection,” Pattern Recognition, vol. 26, no. 2, pp. 295-206, 1993.
[19] V. S. Nalwa and T. O. Binford, “On detecting edges,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 699-714, Nov. 1986.
[20] Y. Shan and G. W. Boon, “Subpixel location of edges with non-uniform blurring: a finite closed-form approach,” Image and Vision Computing, vol. 18, no. 13, pp. 1015-1023, Oct. 2000.
[21] F. Bouchara, “Efficient algorithm for computation of the second-order moment of the subpixel-edge position,” Applied Optics, vol. 43, no. 23, Aug. 2004.
[22] D. Ziou and S. Tabbone, “A multi-scale edge detector,” Pattern Recognition, vol. 26, no. 9, pp. 1305-1314, 1993.
[23] F. Truchetet, F. Nicolier, and O. Laligant, “Subpixel edge detection for dimensional control by artificial vision,” Journal of Electronic Imaging, vol. 10, no. 1, pp. 234-239, Jan. 2001.
[24] F. Pedersini, A. Sarti, and S. Tubaro, “Improving the performance of edge localization techniques through error compensation,” Signal Processing: Image Communication, vol. 12, pp. 33-47, 1998.
[25] A. V. Oppenheim and R. W. Schafer, “Discrete-time Signal Processing,” Prentice Hall, 1999.
[26] R. C. Gonzalez and R. E. Woods, “Digital Image Processing,” Prentice Hall, 2002.
[27] R. A. Wagner and M. J. Fischer, “The string-to-string correction problem,” Journal of the Association for Computing Machinery, vol. 21, no. 1, pp. 168-173, 1974.
[28] 龔威儒，”局部遮蔽圖形之自動比對”，清華大學碩士論文，2003.
[29] F. L. Chen and S. W. Lin, “Subpixel estimation of circle parameters using orthogonal circular detector,” Computer Vision and Image Understanding, vol. 78, no. 2, May 2000.