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Student Number 93327009
Author Yu-Ming Kang(康育銘)
Author's Email Address No Public.
Statistics This thesis had been viewed 1714 times. Download 11 times.
Department opto-Mechatronics
Year 2005
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title 橢圓辨識演算法之最佳化與誤差分析
Date of Defense 2006-07-03
Page Count 76
Keyword
  • ellipse fitting
  • least square
  • Abstract The application of ellipse fitting is very extensive. Not only the digit image recognition but also the numerical analysis. The methods of ellipse fitting algorithm can roughly class as geometric methods and numerical methods. Although the geometric method has better performance on computation but get larger error of estimation on calculation result with considering the noise affection. The numerical methods as the least square algorithms can minimize the numerical error. So the purpose of this text is to look for the key influence of the least square based ellipse fitting method from the algorithm deriving and verify it via FLOPS testings and error analysis. Find out the best solution of performing the algorithm and make it optimization. In order to prove the least square based ellipse fitting algorithm bas better efficiency and easy to implement, we compare with B2AC algorithm via FLOPS and noise testings. By way of these testing methods, we prove that the algorithm can realize on real-time mechanical vision and image recognition system.
    Table of Content 論文摘要I
    ABSTRACTII
    致謝III
    目錄IV
    圖目VI
    表目VIII
    第一章序論1
    1.1 前言1
    1.2 研究動機1
    1.3 突破技術2
    1.4 論文架構3
    第二章LEAST SQUARE橢圓辨識4
    2.1 演算法推導回顧4
    2.2 最小平方法之解9
    2.3 QR FACTORIZATION12
    2.3.1 HOUSEHOLDER TRANSFORM13
    2.3.2 MODIFIED GRAM-SCHMIDT14
    2.4 SINGULAR VALUE DECOMPOSITION15
    2.5 RECURSIVE LEAST SQUARE16
    2.6 LEAST SQUARE ALGORITHM測試及比較17
    2.6.1 浮點運算時間17
    2.6.2 誤差分析20
    2.6.3 雜訊免疫力28
    2.6.4 強健性46
    2.6.5 測試結果與討論50
    第三章LEAST SQUARE橢圓辨識演算法與B2AC演算法性能測試51
    3.1 B2AC51
    3.2 浮點運算時間53
    3.3 雜訊免疫力57
    3.4 結果與討論59
    第四章演算法實作60
    4.1 演算法實作60
    4.1.1 影像擷取61
    4.1.2 影像處理63
    4.1.3 運算時間66
    4.2橢圓辨識68
    第五章結論與未來展望74
    5.1 結論74
    5.2 未來展望75
    參考文獻76
    Reference [1] Gene H. Golub, Charles F. Van Loan, "Matrix Computations", Second Edition, The Johns Hopkins University Press.
    [2]Andrew Fitzgibbon, Maurizio Pilu, and Robert B. Fisher, "Direct Least Square Fitting of Ellipses", IEEE PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 21, NO 5, MAY 1999.
    [3]George Lindfield, John Penny, "Numerical Methods Using Matlab", Second Edition, Pearson Education Company.
    [4]Jer-Nan Juang, "Applied System Identification", NASA Langley Research Center
    [5]趙清風編譯, "控制系統之系統識別", 全華科技圖書
    [6]陳章沂, "橢圓幾何參數鑑別之理論模擬及實作",國立中央大學機械工程研究所碩士論文.
    [7]許世璧, "非線性聯立方程式 數值方法", 中央圖書.
    [8]張銘華, "多媒體視訊程式設計─使用Delphi", 金禾資訊.
    Advisor
  • Shyh-Biau Jiang(江士標)
  • Tse-Liang Yeh(葉則亮)
  • Files
  • 93327009.pdf
  • disapprove authorization
    Date of Submission 2006-07-11

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