數位相機，本身是一個複雜的系統，含有許多的模組，如自動對焦、自動曝光、資料傳輸、影像處理、等等，其中自動對焦演算法在使用上的先決條件為即時性，而一般的搜尋法，在目前的百萬像素級的搜尋時間過於冗長，針對此問題提出本研究結合預測的方法，來改善此一問題。
本研究針對自動對焦上的問題，提出一個可以改善自動對焦速度及提高自動對焦可靠度的演算法，而演算法利用離線差分方程預測模型之優越的預測特性，可預測轉折點之效果與以少數的取樣點即可獲得預測曲線的趨勢，再利用模糊推論的方法，將離散差分方程預測模型的預測結果，作為推論的依據，進而可以決定步距的大小，大幅降低對焦所需的時間及減少取樣的點數。
在本研究中，我們提出模糊離散差分方程預測模型進行數位相機的離線測試與機上測試，其結果均能精準的預測對焦曲線的趨勢與最佳對焦點之區間。

Digital camera is a complex system. There are many modules included in a digital camera system, such as auto-focus, auto-exposure, data transmission, image process, and so on. Real time searching is the most important prerequisite of auto-focusing algorithm. To overcome this problem, we propose a novel method that combines with prediction.
This paper proposed an approach of auto-focusing algorithm, which can improve the velocity of the auto-focus, and it can make the auto-focus more reliable. We chosed Discrete differential equation prediction model (DDEPM) as prediction method for the turning point. By the experimental results, it can be found that the model has a better prediction result in the turning point, and it can improve the auto-focusing velocity. Utilizing the result of Discrete differential equation prediction model (DDEPM) as Fuzzy inference input variables, and we can use the fuzzy output to detemine the sapn.The method can reduce the time which camera focuses and captures a clear image and it can decrease the sampling.
We use this method to on-line and off-line test in camera. The results of testing show that the Fuzzy DDEPM can predict the Focus curve tendency and the appropriate focus region.

參考文獻
[1] Krotkov, E,”Focusing”,Int.J.Comput.Vis.,pp223-237,Jan,1987.
[2] Ligthart.G.,and Groen,F.”A comparison of different autofcous algorithms “.Proc.Int.conf.on Pattern Recognition,1982,pp.597-600
[3] Chih-Ming Chen, Chin-Ming Hong and Yu-Rong Hsieh, “A Modeling
Technique of Grey Prediction Model Using Discrete Difference
Equation,” The Journal of Grey System, vol.12, no.1, pp.65-72, 2000.
[4] Chih-Ming Chen and Hahn-Ming Lee, “An Efficient Gradient
Forecasting Search Method Utilizing the Discrete Difference Equation
Prediction Model,” Applied Intelligence, vol. 16, no. 1, pp. 43-58, 2002.
[5] L.A. Zadeh,“Fuzzy sets”, Inf. Control 8, pp.338-353, 1965.
[6] 耿繼業，”幾何光學”全華科技圖書，中華民國九十年九月
[7] Subbarao M., Tyan J.K., “The Optimal Focus Measure for Passive
Auto-focusing and Depth-from-Focus”, Proceedings of the SPIE
Conference on Videometrics IV, vol.2598, pp.89-99, Philadelphia,
Oct. 1995.
[8] 趙仁孝，建立全對焦影像與各景深場景還原技術，國立交通大學資訊工程系碩士論文，中華民國九十二年六月
[9] Nayar S.K. Nakagawa Y., “Shape from Focus,” Proceedings of the IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 4, no. 8,
pp.824-831, Aug 1994.
[10] Schlag,J.Sanderson,A.,Neuman,C.,and Wimberly,F.:’Implementation of
automatic focus algorithms for a computer vision system with camera control‘.CMU-RI-TR-83-14,RoboticsInstitute,Carnegie Mellon University.
[11] Widjaja J., Jutamulia S. “Wavelet Transform-Based Auto-focus
Camera Systems,” Proceedings of the IEEE Asia-Pacific Conference
On Circuits and Systems, pp.49-51, 1998.
[12] 黃嘉慶，高速被動式自動對焦技術，元智大學機械工程學系碩士論
文中華民國九十一年六月。
[13] Kesseler W., Fischer J. “Analytical Model of Autofocus Systems with CCD Camera” Proceedings of the International Society of Optical Engineering, International Conference on Sensors, Camera Systems for Scientific, Industrial and Digital Photography Applications, vol.3965, pp.396-380, May 2000.
[14] Ng Kuang Chern, N., Poo Aun Neow, and Ang, M.H., Jr., “Practical
Issues in Pixel-Based Autofocusing for Machine Vision,” Proceedings of
the IEEE International Conference on Robotics and Automation, vol.3,
pp.2791-2796, 2001.
[15] Baina J., Dublet J. “Automatic Focus and Iris Control for Video
Cameras” Fifth International Conference on Image Processing and its
Applications, pp.232-235, 1995.
[16] Scientific Computation WS 2001/2002 (http://linneus20.ethz.ch:8080/index.html)
[17] J. L. Deng, “Control Problems of Grey System,” Systems & Control
Letters, vol. 1, pp. 288-294, 1982.
[18] J. L. Deng, “Introduction to Grey System Theory,” The Journal of Grey
System, vol. 1, pp. 1-24, 1989.
[19] W. T. Miller, F. H. Glanz and L. G. Kraft, “Application of a General Learning Algorithm to the Control of Robotic Manipulators,” The International Journal of Robotics Research, Vol.6, No.2, pp.84-98,, 1987.
[20] 劉德順，“PID型模糊邏輯控制器之設計與解析”，國立清華大學動力
機械工程學系碩士班論文，1998。
[21] 王文俊，“認識Fuzzy-第二版”，全華科技圖書股份有限公司，2001。