Advertisement

Positioning by Resection Methods

  • Joseph L. Awange
  • Béla Paláncz
Chapter

Abstract

In Chap.  15, ranging method for positioning was presented where distances were measured to known targets. In this chapter, an alternative positioning technique which uses direction measurements as opposed to distances is presented. This positioning approach is known as the resection. Unlike in ranging where measured distances are affected by atmospheric refraction, resection methods have the advantage that the measurements are angles or directions which are not affected by refraction.

Keywords

Orientation Parameter Pareto Optimality Total Little Square Regular Tetrahedron Space Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 12.
    Ansermet A (1910) Eine Auflösung des Rückwärtseinschneidens. Zeitschrift des Vereins Schweiz. Konkordatsgeometer, Jahrgang 8, pp 88–91Google Scholar
  2. 17.
    Awange JL (2002) Groebner bases, multipolynomial resultants and the Gauss-Jacobi combinatorial algorithms-adjustment of nonlinear GPS/LPS observations. Ph.D. thesis, Department of Geodesy and GeoInformatics, Stuttgart University, Germany. Technical reports, Report Nr. 2002 (1)Google Scholar
  3. 18.
    Awange JL (2002) Groebner basis solution of planar resection. Surv Rev 36:528–543CrossRefGoogle Scholar
  4. 30.
    Awange JL, Grafarend EW (2003) Groebner basis solution of the three-dimensional resection problem (P4P). J Geod 77:327–337CrossRefGoogle Scholar
  5. 31.
    Awange JL, Grafarend EW (2003) Multipolynomial resultant solution of the threedimensional resection problem (P4P). Bollettino di Geodesia e Science Affini 62:79–102Google Scholar
  6. 32.
    Awange JL, Grafarend EW (2003) Explicit solution of the overdetermined three-dimensional resection problem. J Geod 76:605–616CrossRefGoogle Scholar
  7. 33.
    Awange JL, Grafarend EW (2005) From space angles to point position using sylvester resultant. Allgemeine Vermessungs-Nachrichten 112:265–269Google Scholar
  8. 38.
    Awange JL, Fukuda Y, Takemoto S (2004) B. Strumfel’s resultant solution of planar resection problem. Allgemeine Vermessungs-Nachrichten 111(6):214–219Google Scholar
  9. 44.
    Awange JL, Grafarend EW (2005) Solving algebraic computational problems in geodesy and geoinformatics. Springer, BerlinGoogle Scholar
  10. 69.
    Bähr HG (1991) Einfach überbestimmtes ebenes Einschneiden, differentialgeometrisch analysiert. Zeitschrift für Vermessungswesen 116:545–552Google Scholar
  11. 85.
    Bil WL (1992) Sectie en Projectie. NGT (Dutch Geodetic Magazine) Geodesia 92-10:405–411Google Scholar
  12. 92.
    Bock W (1959) Mathematische und geschichtliche Betrachtungen zum Einschneiden. Schriftenreihe Niedersaechsisches Landesvermessungsamt. Report 9, HannoverGoogle Scholar
  13. 100.
    Brandstätter G (1974) Notiz zur analytischen Lösung des ebenen Rückwärtsschnittes. Österreichische Zeitschrift für Vermessungswesen 61:34–136Google Scholar
  14. 109.
    Censor Y (1977) Pareto optimality in multiobjective problems. Appl Math Optim 4:41–59CrossRefGoogle Scholar
  15. 130.
    Chrystal G (1964) Textbook of algebra, vol 1. Chelsea, New YorkGoogle Scholar
  16. 159.
    Felus YA, Schaffrin B (2005) Performing similarity transformations using the errors-in-variable model. In: ASPRS Annual Conference, BaltimoreGoogle Scholar
  17. 169.
    Finsterwalder S, Scheufele W (1937) Das Rückwartseinschneiden im Raum. Sebastian Finsterwalder zum 75 Geburtstage. Verlag Hebert Wichmann, Berlin, pp 86–100Google Scholar
  18. 171.
    Fischler MA, Bolles RC (1981) Random sample consensus: a paradigm for modell fitting with application to image analysis and automated cartography. Commun ACM 24:381–395CrossRefGoogle Scholar
  19. 183.
    Geisler J, Trächtler A (2009) Control of the Pareto optimality of systems with unknown disturbances. In: IEEE International Conference on Control and Automation Christchurch, New Zealand, 9–11 Dec 2009, pp 695–700Google Scholar
  20. 191.
    Golub GH, Van Loan CF (1980) An analysis of the total least-squares problem. SIAM J Numer Anal 17(6):883–893CrossRefGoogle Scholar
  21. 196.
    Gordon SJ, Lichti DD (2004) Terrestrial laser scanners with a narrow field of view: the effect on 3D resection solutions. Surv Rev 37:448–468CrossRefGoogle Scholar
  22. 197.
    Gotthardt E (1940) Zur Unbestimmtheit des räumlichen Rückwärtseinschnittes, Mitteilungen der Ges. f. Photogrammetry e.V., Jänner 1940, Heft 5Google Scholar
  23. 198.
    Gotthardt E (1974) Ein neuer gefährlicher Ort zum räumlichen Rückwärtseinschneiden, Bildm. u. Luftbildw.Google Scholar
  24. 204.
    Grafarend EW (1989) Photogrammetrische Positionierung. Festschrift für Prof. Dr.-Ing. Dr. h.c Friedrich Ackermann zum 60. Geburtstag, Institut für Photogrammetrie, Univerität Stuttgart, Heft 14, pp 44–55, StuttgartGoogle Scholar
  25. 213.
    Grafarend EW, Kunz J (1965) Der Rückwärtseinschnitt mit dem Vermessungskreisel. Bergbauwissenschaften 12:285–297Google Scholar
  26. 225.
    Grafarend EW, Shan J (1997) Closed form solution of the twin P4P or the combined three dimensional resection-intersection problem in terms of Möbius barycentric coordinates. J Geod 71:232–239CrossRefGoogle Scholar
  27. 229.
    Grafarend EW, Lohse P, Schaffrin B (1989) Dreidimensionaler Rückwärtsschnitt. Zeitschrift für Vermessungswesen 114:61–67, 127–137, 172–175, 225–234, 278–287Google Scholar
  28. 236.
    Grunert JA (1841) Das Pothenotsche Problem in erweiterter Gestalt; nebst Bemerkungen über seine Anwendungen in der Geodäsie. Grunerts Archiv für Mathematik und Phsyik 1:238–241Google Scholar
  29. 247.
    Hochman HM, Rodgers JD (1969) Pareto optimal redistribution. Am Econ Rev 59(4):542–557. Part 1Google Scholar
  30. 255.
    Hammer E (1896) Zur graphischen Ausgleichung beim trigonometrischen Einschneiden von Punkten. Optimization methods and softwares 5:247–269Google Scholar
  31. 259.
    Haralick RM, Lee C, Ottenberg K, Nölle M (1991) Analysis and solution of the three point perspective pose estimation problem. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Lahaina, pp 592–598Google Scholar
  32. 260.
    Haralick RM, Lee C, Ottenberg K, Nölle M (1994) Review and analysis of solution of the three point perspective pose estimation problem. Int J Comput Vis 13(3):331–356CrossRefGoogle Scholar
  33. 277.
    Horaud R, Conio B, Leboulleux O (1989) An analytical solution for the perspective 4-point problem. Comput Vis Graph Image Process 47:33–44CrossRefGoogle Scholar
  34. 296.
    Kahmen H, Faig W (1988) Surveying. Walter de Gruyter, BerlinCrossRefGoogle Scholar
  35. 298.
    Kapur D, Saxena T, Yang L (1994) Algebraic and geometric reasoning using Dixon resultants. In: ACM ISSAC 94, International Symposium on Symbolic and Algebraic Computation, Oxford, July 1994, pp 99–107CrossRefGoogle Scholar
  36. 299.
    Killian K (1990) Der gefährliche Ort des überbestimmten räumlichen Rückwärtseinschneidens. Öst. Zeitschrift für Vermessungswesen und Photogrammetry 78:1–12Google Scholar
  37. 317.
    Lin JG (1976) Multiple-objective problems – Pareto-optimal solutions by method of proper equality constraints. IEEE Trans Autom Control AC-21:641–650Google Scholar
  38. 328.
    Lewis RH (2002) Using the Dixon resultant on big problems. In: CBMS Conference, Texas A&M University. http://www.math.tamu.edu/conferences/cbms/abs.html. Accessed 27 Aug 2008
  39. 330.
    Lewis RH (2008) Heuristics to accelerate the Dixon resultant. Math Comput Simul 77(4):400–407CrossRefGoogle Scholar
  40. 341.
    Linnainmaa S, Harwood D, Davis LS (1988) Pose determination of a three-dimensional object using triangle pairs. IEEE Trans Pattern Anal Mach Intell 105:634–647CrossRefGoogle Scholar
  41. 342.
    Lohse P (1990) Dreidimensionaler Rückwärtsschnit. Ein Algorithmus zur Streckenberechnung ohne Hauptachsentransformation. Zeitschrift für Vermessungswesen 115:162–167Google Scholar
  42. 354.
    Manocha D (1994) Algorithms for computing selected solutions of polynomial equations. Extended abstract appearing in the proceedings of the ACM ISSAC 94Google Scholar
  43. 356.
    Manocha D (1994) Solving systems of polynomial equations. IEEE Comput Graph Appl 14:46–55CrossRefGoogle Scholar
  44. 358.
    Manocha D, Canny J (1991) Efficient techniques for multipolynomial resultant algorithms. In: Proceedings of the International Symposium on Symbolic Computations, Bonn, 15–17 July 1991, pp 86–95Google Scholar
  45. 369.
    Merritt EL (1949) Explicit three-point resection in space. Phot Eng 15:649–665Google Scholar
  46. 370.
    Mikhail EM, Bethel JS, McGlone CJ (2001) Introduction to modern photogrammetry. Wiley, New YorkGoogle Scholar
  47. 377.
    Müller FJ (1925) Direkte (Exakte) Lösungen des einfachen Rückwarscnittseinschneidens im Raum. 1 Teil. Zeitschrift für Vermessungswesen 37:249–255, 265–272, 349–353, 365–370, 569–580Google Scholar
  48. 378.
    Nakos G, Williams R (2002) A fast algorithm implemented in Mathematica provides one-step elimination of a block of unknowns from a system of polynomial equations, Wolfram Library Archive, MathSource. http://library.wolfram.com/infocenter/MathSource/2597/. Accessed 27 Aug 2008
  49. 389.
    Neitzel F (2010) Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation. J Geod. doi:10.1007/s00190-010-0408-0Google Scholar
  50. 390.
    Pressl B, Mader C, Wieser M (2010) User-specific web-based route planning. In: Miesenberger K et al (eds) ICCHP 2010, Part I. LNCS, vol 6179. Springer, Berlin/Heidelberg, pp 280–287Google Scholar
  51. 433.
    Runge C (1900) Graphische Ausgleichung beim Rückwätseinchneiden. Zeitschrift für Vermessungswesen 29:581–588Google Scholar
  52. 453.
    Sonnier DL (2010) A Pareto-optimality based routing and wavelength assignment algorithm for WDM networks. J Comput Sci Coll Arch 25(5):118–123Google Scholar
  53. 495.
    Van Mierlo J (1988) Rückwärtschnitt mit Streckenverhältnissen. Algemain Vermessungs Nachrichten 95:310–314Google Scholar
  54. 506.
    Warr PG (1982) Pareto optimal redistribution and private charity. J Public Econ 19(1):131–138. doi:10.1016/0047-2727(82)90056-1CrossRefGoogle Scholar
  55. 508.
    Wilson PB, Macleod MD (1993) Low implementation cost IIR digital filter design using genetic algorithms. In: IEE/IEEE Workshop on Natural Algorithms in Signal Processing, Chelmsford, pp 4/1–4/8Google Scholar
  56. 517.
    Werkmeister P (1916) Trigonometrische Punktbestimmung durch einfaches Einschneidenmit Hilfe von Vertikalwinkeln. Zeitschrift für Vermessungswesen 45:248–251Google Scholar
  57. 519.
    Werkmeister P (1920) Über die Genauigkeit trigonometrischer Punktbestimmungen. Zeitschrift für Vermessungswesen 49:401–412, 433–456Google Scholar
  58. 520.
    Werner D (1913) Punktbestimmung durch Vertikalwinkelmessung. Zeitschrift für Vermessungswesen 42:241–253Google Scholar
  59. 523.
    Wild F (2001) Test an der Geschlossenen Lösung des “Twin P4P-Problems”: Dreidimensionaler Vorwärts- und Rückwärtsschnitt. Studienarbeit, Geodetic Institute, Stuttgart UniversityGoogle Scholar
  60. 552.
    Zitler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRefGoogle Scholar
  61. 554.
    Zwanzig S (2006) On an application of deconvolution techniques to local linear regression with errors in variables. Department of Mathematics Uppsala University, U.U.D.M. report 2006:12Google Scholar
  62. 555.
    Ameller MA, Triggs B, Quan L (2000) Camera pose revisited – new linear algorithms. In: European Conference on Computer Vision (ECCV), DublinGoogle Scholar
  63. 556.
    Atkinson KB (1996) Close range photogrammetry and machine vision. Whittles, CaithnessGoogle Scholar
  64. 557.
    Awange JL, Kiema JBK (2013) Environmental geoinformatics – monitoring and management. Springer, BerlinCrossRefGoogle Scholar
  65. 558.
    Awange JL, Grafarend EW, Paláncz B, Zaletnyik P (2010) Algebraic geodesy and geoinformatics. Springer, BerlinCrossRefGoogle Scholar
  66. 559.
    Bartoli A (2002) A unified framework for quasi-linear bundle adjustment. In: Proceedings of the Sixteenth IAPR International Conference on Pattern Recognition (ICPR02), Quebec City, Aug 2002, vol Ii, pp 560-563Google Scholar
  67. 560.
    Börlin N (2002) Comparison of resection: intersection algorithms and projection geometries in radiostereometry. ISPRS J Photogramm Remote Sens 56:390–400. doi:10.1016/S0924-2716(02)00068-0CrossRefGoogle Scholar
  68. 561.
    Chen Q, Medioni G (1999) Efficient iterative solution to M-view projective reconstruction. In: Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference. doi:10.1109/CVPR.1999.784608Google Scholar
  69. 562.
    Coello CA (1999) A comprehensive survey of evolutionary-based multi-objective optimization techniques. Knowl Inf Syst 1(3):269–308CrossRefGoogle Scholar
  70. 563.
    Dunn E, Olague G, Lutton E, Schoenauer M (2004) Pareto optimal sensing strategies for an active vision system. In: IEEE Congress on Evolutionary Computation, Portland, 19–23 June 2004, vol 1, pp 457–463Google Scholar
  71. 564.
    Fekete K, Schrott P (2008) Qualification of optical capturing devices for data gathering phase of the face reconstruction process. In: Proceedings of the Third Hungarian Conference on Biomechanics, Budapest, pp 83–88Google Scholar
  72. 565.
    Forsyth DA, Ponce J (2003) Computer vision – a modern approach. Pearson Education, Pearson ClothGoogle Scholar
  73. 567.
    Grafarend E, Shan J (1997a) Closed form solution to the P4P or the three dimensional resection problem in terms of Möbius barycentric coordinates. J Geod 71:217–231. doi:10.1007/s001900050089CrossRefGoogle Scholar
  74. 568.
    Grafarend E, Shan J (1997b) Closed form solution to the twin P4P or the combined three dimensional resection-intersection problem in terms of Möbius barycentric coordinates. J Geod 71(4):232–239. doi:10.1007/s001900050090CrossRefGoogle Scholar
  75. 569.
    Grafarend E, Shan J (1997c) Estimable quantities in projective geometry I and II. Z fuer Vermess 122(Heft 5 and 7):218–225, 323–333Google Scholar
  76. 570.
    Grussenmeyer P, Al Khalil O (2002) Solution of exterior orientation in photogrammetry, a review. Photogramm Rec Int J Photogramm 17(100):615–634. doi:10.1111/j.1477-9730.2002.tb01907.xCrossRefGoogle Scholar
  77. 571.
    Han JY, Guo J, Chou JY (2011) A direct determination of the orientation parameters in the collinearity equations. IEEE Geosci Remote Sens Lett 8:313–316. doi:10.1109/LGRS.2010.2066955CrossRefGoogle Scholar
  78. 572.
    Hartley R, Zisserman A (2003) Multiple view geometry in computer vision. Cambridge University Press, Cambridge, UKGoogle Scholar
  79. 574.
    McGlone JC (1989) Analytic data-reduction schemes in non-topographic photogrammetry. In: American Society of Photogrammetry and Remote Sensing, chapter 4, Falls Church, vol 554, pp 37–55Google Scholar
  80. 575.
    Mirza P, Almir K (2010) Pareto-based genetic algorithm in multi-objective geospatial analysis. In: Proceedings of the 33rd International Convention (MIPRO 2010), Opatija, 24–28 May 2010, pp 680–685Google Scholar
  81. 576.
    Mahamud S, Herbert M, Omori Y, Ponce J (2001) Provably-convergent iterative methods for projective structure and motion. In: Proceedings of the Computer Vision and Pattern Recognition (CVPR 2001). IEEE Computer Society Conference, vol 1, page(s): I-1018–I-1025. doi:10.1109/CVPR.2001.990642Google Scholar
  82. 578.
    Olague G, Trujillo L (2012) Interest point detection through multiobjective genetic programming. Appl Soft Comput 12(8):2566–2582. doi:10.1016/j.asoc.2012.03.058CrossRefGoogle Scholar
  83. 579.
    Olague G, Trujillo L (2011) Evolutionary-computer-assisted design of image operators that detect interest points using genetic programming. Image Vis Comput 29:484–498. doi:10.1016/j.imavis.2011.03.004CrossRefGoogle Scholar
  84. 580.
    Olsson C, Byröd M, Kahl F (2009) Globally optimal least squares solutions for quasiconvex 1D vision problems. In: Salberg A-B, Hardeberg JY, Jenssen R (eds) SCIA 2009. LNCS, Springer, Heidelberg/New York, vol 5575, pp 686–695Google Scholar
  85. 581.
    Paláncz B, Awange JL (2012) Application of Pareto optimality to linear models with errors-in-all-variables. J Geod 86(7):531–545. doi:10.1007/s00190-011-0536-1CrossRefGoogle Scholar
  86. 582.
    Remondino F (2002) 3-D reconstruction of articulated objects from uncalibrated images. In: Three-dimensional image capture and application V, SPIE electronic imaging, proceedings of SPIE 4661, San Jose, Jan 2002Google Scholar
  87. 583.
    Saadatseresht M, Mansourian A, Taleai M (2009) Evacuation planning using multi-objective evolutionary optimization approach. Eur J Oper Res 198:305–314. doi:10.1016/ j.ejor.2008.07.032CrossRefGoogle Scholar
  88. 584.
    Schaffrin B, Snow K (2010) Total Least-Squares regularization of Tykhonov type and an ancient racetrack in Corinth. Linear Algebra Appl 432:2061–2076. doi:10.1016/ j.laa.2009.09.014Google Scholar
  89. 585.
    Triggs B, McLauchlan P, Hartley R, Fitzgibbon A (2000) Bundle adjustment – a modern synthesis. In: Vision algorithms: theory and practice, 2000. Springer, LondonGoogle Scholar
  90. 586.
    Werner T, Schaffalitzky F, Zisserman A (1999) Automated architecture reconstruction from close-range photogrammetry. In: The proceedings of the international CIPA symposium, 2001. http://www.robots.ox.ac.uk/ vgg/publications/papers/werner01a.pdf. Accessed on 19/10/2012 Potsdam, GermanyGoogle Scholar
  91. 587.
    Kwon Y-H (1998) DLT method. www.kwon3d.com/theory/dlt/dlt.html. Accessed on 17/11/2011Google Scholar
  92. 588.
    Zitler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength of pareto approach. IEEE Trans Evol Comput 3(4):257–271. doi:10.1109/4235.797969Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Joseph L. Awange
    • 1
  • Béla Paláncz
    • 2
  1. 1.Curtin UniversityPerthAustralia
  2. 2.Budapest University of Technology and EconomicsBudapestHungary

Personalised recommendations