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Three Dimensional Coordinate Reconstruction Using Multiple Images
|關鍵字:||coordinate extraction;座標重建;nonlinear least square method;非線性最小平方法||出版社:||電機工程學系所||引用:|| Hoon Yoo and Jechang Jeong , “Direction-oriented interpolation and its application to de-interlacing, ” IEEE Trans.Consumer Electronics, vol 48,Issue 4,pp.954-962,Nov.2003.  Coleman, T. F., Y. Li, “An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds,” SIAM Journal on Optimization, Vol. 6, pp. 418-445, 1996.  Coleman, T. F., Y. Li, “On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds,” Mathematical Programming, Vol. 67, Number 2, pp. 189-224, 1994.  Levenberg, K., “A Method for the Solution of Certain Problems in Least-Squares,” Quarterly Applied Math. 2, pp. 164-168, 1944.  Marquardt, D., “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” SIAM Journal Applied Math., Vol. 11, pp. 431-441, 1963.  Moré, J. J., “The Levenberg-Marquardt Algorithm: Implementation and Theory,” Numerical Analysis, ed. G. A. Watson, Lecture Notes in Mathematics 630, Springer Verlag, pp. 105-116, 1977.  HOMAS B. CRISS, MARILYN M. SOUTH (1998), “Multiple Image Coordinate Extraction (MICE) Technique for Rapid Targeting of Precision Guided Munitions, ” JOHNS HOPKINS APL TECHNICAL DIGEST, VOL. 19, No. 4  R. H. BYRD , R. B. SCHNABEL, “Approximate solution fo the turst region problem by minimization over two-dimensional subspaces,” Mathematical Programming, 40(1998), pp. 247-263. T. F. COLEMAN, C. HEMPEL, “Computing a trust region step for a penalty function,” SIAM Journal on Scientific and Statistical Computing, 11(1990), pp. 180-201. T. F. COLEMAN, L. A. HULBERT, “A direct active set algorithm for large sparse quadratic programs with simple bounds,” Mathematical Programming, 45(1989), pp.373-406. ----, “A globally and superlinearly convergent algorithm for convex quadratic program with simplebounds,”Tech.Rep.TR 90-1092, Com- puter Secience Department,Comell University, February, 1990(to appear in SIAM Journal on optimization). T. F. COLEMAN, Y. LI, “On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds,” Tech.Rep.TR 92-1314, Computer Science Department, Cormell Univer- sity,1992. ----, “A reflective Newton method for minimizing a quadratic function subject to bounds on the variables,” Tech.Rep.TR 92-1315,Computer Science Department, Comell University,1992. A. R. CONN, N. I. M. GOULD, P. L. TOINT, “Global convergence of a class of trust region algorithms for optimization with simple bounds,” SIAM Journal on Numerical Analysis,25(1998),pp.433-460. ----, “Testing a class of methods for solving minimization problems with simple bounds on the varivables,” Mathmatics of Computation, 50(1988),pp.399-430.  R. S. DEMBO, U. TULOWTTZKI, “On the minimization of quadratic functions subject to box constraints,” Tech.Rep.B 71,Yale University, 1983. R. FLETCHER, “An algorithm for solving linearly constrained optimization problems,” mprog,2(1972),pp.133-165. R. FLETCHER , M. P. JACKSON, “Minimization of a quadratic function of many variables subject only to lower and upper bounds,” Journal of the Institute for Mathematics and its Applications, 14(1974), pp.159-174. D. M. GAY, “Computing optimal locally constrained steps,” SIAM Journal on Scientific and Statistical Computing,2(1982),pp.186-197. P. GILL, W.MURRAY, “Minimization subject to bounds on the variables,” Tech. Rep. Report NAC 71, National Physical Laboratory, England, 1976. J. J. JUDICE, F. M. PIRES, “Direct methods for convex quadratic programs subject to box constraints, departamento de matematica, ” Universidade de Coimbra,3000 Coimbra,Portugal,1989. P. LOTSTEDT, “Solving the minimal least squares problem subject to bounds on the varables,” BIT,24(1984),pp.206-224. C. B. MOLER, J. LITTLE, S. BANGERT, S. KLEIMAN, “ProMatlab User'guide,” Math Works, Stherborn, MA, 1987. J. J. MORE, “Recent developments in algorithms and software for trust region methods, in Mathematical Programming: The State of the Art,” M.G. A. Bachem and e. B. Dorte. eds., Springer Verlag, Berlin, 1983. J. J. MORE, D. SORENSEN, “Computing a trust region step,” SIAM Journal on Scientific and Statistical Computing, 4(1983), pp. 553-572. J. J. MORE, G.TORALDO, “Algorithms for bound constrained quadratic programming problems,” Numerische Mathematik, 55(1989), pp. 377-400. D. P. O'LEARY, “A generalized conjugate gradient algorithm for solving a class of quadratic programming problems,” Linear Algebra and its Applications, 34 (1980), pp. 371-399. U. OREBORN, “A direct method for sparse nonnegative least suares problems,” phD thesis, Department of Mathematics, Linkoping University, Linkoping, Sweden, 1986. G. A. SCHULTZ, R. B. SCHNABEL, R.H.BYRD, “A family of trust-region- based algorithms for unconstrained minimization with strong global convergence properties,” SIAM Journal on Numerical Analysis, 22(1) (1985), pp. 47-67.||摘要:||
現今定位技術的應用有很多，例如:追蹤目標、面積的對映、面積大小的局部量測和軍事方面的應用等等，本論文發展一套多影像三維座標重建的系統，首先我們利用程式模擬一架飛機繞著目標物飛行並且拍攝一些照片，這些照片必須包括目標物和定位點，之後我們加上三維座標轉換和相似三角形的原理，便可算出定位點在照片中的二維座標，最後利用座標轉換與非線性最小平方法，我們便可以解出較為準確的定位點三維座標位置，而為了方便進行研究，我們撰寫了一套圖形使用者介面(Graphical User Interface,GUI)以方便觀察定位的誤差結果。
Today, there are many important applications using the coordinate extraction technique, for example, target tracking, area mapping, area measuring, and military applications. In this thesis, we develop a three-dimensional coordinate extraction system using multiple images. First, a program is utilized to simulate the situation that an airplane is flying around the target and some pictures are taken with a pre-specified camera system. These pictures must contain the common points on the target. Then we can compute the two-dimensional coordinates of the common points in the acquired images by using the three-dimensional coordinate transform. Finally, the coordinate transform and nonlinear least square techniques can be utilized to obtain more accurate three dimensional coordinates of the points. In order to facilitate the research, we write a graphical user interface (GUI) to select the points and to observe the errors of the coordinates.
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