@article{Chum-CVIU05,
  IS = { zkontrolovano 11 Nov 2005 },
  UPDATE  = { 2004-11-27 },
        AUTHOR = {Chum, Ond{\v r}ej and Pajdla, Tom{\' a}{\v s} and 
                  Sturm, Peter},
        TITLE = {The geometric error for homographies},
        JOURNAL = {Computer Vision and Image Understanding},
        YEAR = {2005},
        month =  {January},
        VOLUME = {97},
        NUMBER = {1},
        PAGES = {86-102},
        publisher =  {Elsevier Science},
        KEYWORDS = {Homography; Geometric error; Sampson's error;
                    Triangulation},
        address = {Amsterdam, The Netherlands},
        issn = {1077-3142},
        annote = {We address the problem of finding optimal point
          correspondences between images related by a homography:
          given a homography and a pair of matching points, determine
          a pair of points that are exactly consistent with the
          homography and that minimize the geometric distance to the
          given points. This problem is tightly linked to the
          triangulation problem, i.e., the optimal 3D reconstruction
          of points from image pairs. Our problem is non-linear and
          iterative optimization methods may fall into local
          minima. In this paper, we show how the problem can be
          reduced to the solution of a polynomial of degree eight in a
          single variable, which can be computed numerically. Local
          minima are thus explicitly modeled and can be avoided. An
          application where this method significantly improves
          reconstruction accuracy is discussed. Besides the general
          case of homographies, we also examine the case of affine
          transformations, and closely study the relationships between
          the geometric error and the commonly used Sampson?s error,
          its first order approximation. Experimental results
          comparing the geometric error with its approximation by
          Sampson's error are presented.},
        keywords = {Homography, Geometric error, Sampson's error, Triangulation},
        project = { GACR 102/01/0971, IST-2001-39184 BeNoGo, Aktion 34p24,
                    MSM 6840770013, CTU 0306013, STINT Dur IG2003-2 062},
        psurl = {DOI},
        authorship = {50-40-10},
}