vpHomographyMalis.cpp

/****************************************************************************
 *
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2019 by Inria. All rights reserved.
 *
 * This software is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * See the file LICENSE.txt at the root directory of this source
 * distribution for additional information about the GNU GPL.
 *
 * For using ViSP with software that can not be combined with the GNU
 * GPL, please contact Inria about acquiring a ViSP Professional
 * Edition License.
 *
 * See http://visp.inria.fr for more information.
 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 *
 * If you have questions regarding the use of this file, please contact
 * Inria at visp@inria.fr
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 * Description:
 * Homography estimation.
 *
 * Authors:
 * Eric Marchand
 *
 *****************************************************************************/

#include <visp3/core/vpDebug.h>
#include <visp3/core/vpMatrixException.h>
#include <visp3/vision/vpHomography.h>

#include <cmath>  // std::fabs
#include <limits> // numeric_limits

#ifndef DOXYGEN_SHOULD_SKIP_THIS
const double eps = 1e-6;

/**************************************************************************
 * NOM :
 * changeFrame
 *
 * DESCRIPTION :
 * Changement de repere Euclidien.
 *
 ****************************************************************************
 * ENTREES :
 * int pts_ref[4]   : Definit quels sont les points de reference, ils ne
 *            seront pas affectes par le changement de repere
 * int nb_pts       : nombre de points a changer de repere
 * double **pd  : La matrice des coordonnees des points desires
 * double **p   : La matrice des coordonnees des points courants
 *
 *
 * SORTIES :
 *
 * double **pt_des_nr   : La matrice des coordonnees des points desires
 *            dans le nouveau repere.
 * double **pt_cour_nr  : La matrice des coordonnees des points courants
 *            dans le nouveau repere
 * double **M   : ??
 * double **Mpd : pseudo inverse de M  ..
 *
 *
 ****************************************************************************
 */

void changeFrame(unsigned int *pts_ref, unsigned int nb_pts, vpMatrix &pd, vpMatrix &p, vpMatrix &pnd, vpMatrix &pn,
                 vpMatrix &M, vpMatrix &Mdp);
void HLM2D(unsigned int nb_pts, vpMatrix &points_des, vpMatrix &points_cour, vpMatrix &H);
void HLM3D(unsigned int nb_pts, vpMatrix &pd, vpMatrix &p, vpMatrix &H);
void HLM(unsigned int q_cible, unsigned int nbpt, double *xm, double *ym, double *xmi, double *ymi, vpMatrix &H);

void HLM(unsigned int q_cible, const std::vector<double> &xm, const std::vector<double> &ym,
         const std::vector<double> &xmi, const std::vector<double> &ymi, vpMatrix &H);

void changeFrame(unsigned int *pts_ref, unsigned int nb_pts, vpMatrix &pd, vpMatrix &p, vpMatrix &pnd, vpMatrix &pn,
                 vpMatrix &M, vpMatrix &Mdp)
{
  /* Construction des matrices de changement de repere */
  vpMatrix Md(3, 3);
  vpMatrix Mp(3, 3);

  for (unsigned int i = 0; i < 3; i++) {
    for (unsigned int j = 0; j < 3; j++) {
      M[j][i] = p[pts_ref[i]][j];
      Md[j][i] = pd[pts_ref[i]][j];
    }
  }

  /*calcul de la pseudo inverse  */
  Mp = M.pseudoInverse(1e-16);
  Mdp = Md.pseudoInverse(1e-16);

  if (pts_ref[3] > 0) {
    double lamb_des[3];
    double lamb_cour[3];

    for (unsigned int i = 0; i < 3; i++) {
      for (unsigned int j = 0; j < 3; j++) {
        lamb_cour[i] = Mp[i][j] * p[pts_ref[3]][j];
        lamb_des[i] = Mdp[i][j] * pd[pts_ref[3]][j];
      }
    }

    for (unsigned int i = 0; i < 3; i++) {
      for (unsigned int j = 0; j < 3; j++) {
        M[i][j] = M[i][j] * lamb_cour[j];
        Md[i][j] = Md[i][j] * lamb_des[j];
      }
    }

    Mdp = Md.pseudoInverse(1e-16);
  }

  /* changement de repere pour tous les points autres que
     les trois points de reference */

  unsigned int cont_pts = 0;
  for (unsigned int k = 0; k < nb_pts; k++) {
    if ((pts_ref[0] != k) && (pts_ref[1] != k) && (pts_ref[2] != k)) {
      for (unsigned int i = 0; i < 3; i++) {
        pn[cont_pts][i] = 0.0;
        pnd[cont_pts][i] = 0.0;
        for (unsigned int j = 0; j < 3; j++) {
          pn[cont_pts][i] = pn[cont_pts][i] + Mp[i][j] * p[k][j];
          pnd[cont_pts][i] = pnd[cont_pts][i] + Mdp[i][j] * pd[k][j];
        }
      }
      cont_pts = cont_pts + 1;
    }
  }
}

/**************************************************************************
 * NOM :
 * Homographie_CrvMafEstHomoPointsCible2D
 *
 * DESCRIPTION :
 * Calcul de l'homographie entre une image courante et une image desiree dans
 *le cas particulier d'une cible planaire de points (cible pi). Cette
 *procedure est appellee par "Homographie_CrvMafCalculHomographie".
 *
 ****************************************************************************
 * ENTREES :
 * int  Nb_pts : nombre de points
 * double   **pd : tableau des coordonnees des points desires
 * couble   **p : tableau des coordonnees des points courants
 *
 * SORTIES :
 *
 * double **H           matrice d homographie
 *
 ****************************************************************************
 * AUTEUR : BOSSARD Nicolas.  INSA Rennes 5eme annee.
 *
 * DATE DE CREATION : 02/12/98
 *
 * DATES DE MISE A JOUR :
 *
 ****************************************************************************/
void HLM2D(unsigned int nb_pts, vpMatrix &points_des, vpMatrix &points_cour, vpMatrix &H)
{
  double vals_inf;
  unsigned int contZeros, vect;

  vpMatrix M(3 * nb_pts, 9);
  vpMatrix V(9, 9);
  vpColVector sv(9);

  for (unsigned int j = 0; j < nb_pts; j++) {
    M[3 * j][0] = 0;
    M[3 * j][1] = 0;
    M[3 * j][2] = 0;
    M[3 * j][3] = -points_des[j][0] * points_cour[j][2];
    M[3 * j][4] = -points_des[j][1] * points_cour[j][2];
    M[3 * j][5] = -points_des[j][2] * points_cour[j][2];
    M[3 * j][6] = points_des[j][0] * points_cour[j][1];
    M[3 * j][7] = points_des[j][1] * points_cour[j][1];
    M[3 * j][8] = points_des[j][2] * points_cour[j][1];

    M[3 * j + 1][0] = points_des[j][0] * points_cour[j][2];
    M[3 * j + 1][1] = points_des[j][1] * points_cour[j][2];
    M[3 * j + 1][2] = points_des[j][2] * points_cour[j][2];
    M[3 * j + 1][3] = 0;
    M[3 * j + 1][4] = 0;
    M[3 * j + 1][5] = 0;
    M[3 * j + 1][6] = -points_des[j][0] * points_cour[j][0];
    M[3 * j + 1][7] = -points_des[j][1] * points_cour[j][0];
    M[3 * j + 1][8] = -points_des[j][2] * points_cour[j][0];

    M[3 * j + 2][0] = -points_des[j][0] * points_cour[j][1];
    M[3 * j + 2][1] = -points_des[j][1] * points_cour[j][1];
    M[3 * j + 2][2] = -points_des[j][2] * points_cour[j][1];
    M[3 * j + 2][3] = points_des[j][0] * points_cour[j][0];
    M[3 * j + 2][4] = points_des[j][1] * points_cour[j][0];
    M[3 * j + 2][5] = points_des[j][2] * points_cour[j][0];
    M[3 * j + 2][6] = 0;
    M[3 * j + 2][7] = 0;
    M[3 * j + 2][8] = 0;
  }

  M.svd(sv, V);

  /*****
        La meilleure solution est le vecteur de V associe
        a la valeur singuliere la plus petite en valeur absolu.
        Pour cela on parcourt la matrice des valeurs singulieres
        et on repere la plus petite valeur singuliere, on en profite
        pour effectuer un controle sur le rang de la matrice : pas plus
        de 2 valeurs singulieres quasi=0
  *****/
  vals_inf = fabs(sv[0]);
  vect = 0;
  contZeros = 0;
  if (fabs(sv[0]) < eps) {
    contZeros = contZeros + 1;
  }
  for (unsigned int j = 1; j < 9; j++) {
    if (fabs(sv[j]) < vals_inf) {
      vals_inf = fabs(sv[j]);
      vect = j;
    }
    if (fabs(sv[j]) < eps) {
      contZeros = contZeros + 1;
    }
  }

  if (contZeros > 2) {
    // vpERROR_TRACE("matrix is rank deficient");
    throw(vpMatrixException(vpMatrixException::matrixError, "matrix is rank deficient"));
  }

  H.resize(3, 3);
  for (unsigned int i = 0; i < 3; i++) {
    for (unsigned int j = 0; j < 3; j++) {
      H[i][j] = V[3 * i + j][vect];
    }
  }
}

/**************************************************************************
 * NOM :
 * Homographie_CrvMafEstHomoPointsC3DEzio
 *
 * DESCRIPTION :
 * Calcul de l'homographie entre une image courante et une image desiree dans
 *le cas particulier d'une cible non planaire de points (cible pi). Cette
 *procedure est appellee par "Homographie_CrvMafCalculHomographie".
 *
 *
 ****************************************************************************
 * ENTREES :
 * int  Nb_pts : nombre de points
 * double   **pd : tableau des coordonnees des points desires
 * couble   **p : tableau des coordonnees des points courants
 *
 * SORTIES :
 *
 * double **H           matrice d'homographie
 * double epipole[3]        epipole
 *
 ****************************************************************************
 **/
void HLM3D(unsigned int nb_pts, vpMatrix &pd, vpMatrix &p, vpMatrix &H)
{
  unsigned int pts_ref[4]; /*** definit lesquels des points de
                        l'image sont les points de reference***/

  vpMatrix M(3, 3);
  vpMatrix Mdp(3, 3);
  vpMatrix c(8, 2); // matrice des coeff C

  vpColVector d(8);
  vpMatrix cp(2, 8); // matrice pseudo-inverse de C

  vpMatrix H_int(3, 3);
  vpMatrix pn((nb_pts - 3), 3); // points courant nouveau repere

  vpMatrix pnd((nb_pts - 3), 3); // points derives nouveau repere

  /* preparation du changement de repere */
  /****
       comme plan de reference on choisit pour le moment
       arbitrairement le plan contenant les points 1,2,3 du cinq
  ****/
  pts_ref[0] = 0;
  pts_ref[1] = 1;
  pts_ref[2] = 2;
  pts_ref[3] = 0;

  /* changement de repere pour tous les points autres que les trois points de
   * reference */

  changeFrame(pts_ref, nb_pts, pd, p, pnd, pn, M, Mdp);

  unsigned int cont_pts = nb_pts - 3;

  if (cont_pts < 5) {
    // vpERROR_TRACE(" not enough point to compute the homography ... ");
    throw(vpMatrixException(vpMatrixException::matrixError, "Not enough point to compute the homography"));
  }

  // nl = cont_pts*(cont_pts-1)*(cont_pts-2)/6 ;
  unsigned int nc = 7;

  /* Allocation matrice CtC */
  vpMatrix CtC(nc, nc);

  /* Initialisation matrice CtC */
  for (unsigned int i = 0; i < nc; i++)
    for (unsigned int j = 0; j < nc; j++)
      CtC[i][j] = 0.0;

  /* Allocation matrice M */
  vpColVector C(nc); // Matrice des coefficients

  /* construction de la matrice M des coefficients dans le cas general */
  /****
       inconnues du nouveau algorithme
       x1 = a  ; x2 = b  ; x3 = c ;
       x4 = ex ; x5 = ey ; x6 = ez ;
       qui deviennent apres changement :
       v1 = x1*x6 ; v2 = x1*x5 ;
       v3 = x2*x4 ; v4 = x2*x6 ;
       v5 = x3*x5 ; v6 = x3*x4 ;
  ****/
  unsigned int cont = 0;
  for (unsigned int i = 0; i < nb_pts - 5; i++) {
    for (unsigned int j = i + 1; j < nb_pts - 4; j++) {
      for (unsigned int k = j + 1; k < nb_pts - 3; k++) {
        /* coeff a^2*b  */
        C[0] = pn[i][2] * pn[j][2] * pn[k][1] * pnd[k][0]               //
                   * (pnd[j][0] * pnd[i][1] - pnd[j][1] * pnd[i][0])    //
               + pn[i][2] * pn[k][2] * pn[j][1] * pnd[j][0]             //
                     * (pnd[i][0] * pnd[k][1] - pnd[i][1] * pnd[k][0])  //
               + pn[j][2] * pn[k][2] * pn[i][1] * pnd[i][0]             //
                     * (pnd[k][0] * pnd[j][1] - pnd[k][1] * pnd[j][0]); //
        /* coeff a*b^2 */
        C[1] = pn[i][2] * pn[j][2] * pn[k][0] * pnd[k][1]               //
                   * (pnd[i][0] * pnd[j][1] - pnd[i][1] * pnd[j][0])    //
               + pn[i][2] * pn[k][2] * pn[j][0] * pnd[j][1]             //
                     * (pnd[k][0] * pnd[i][1] - pnd[k][1] * pnd[i][0])  //
               + pn[j][2] * pn[k][2] * pn[i][0] * pnd[i][1]             //
                     * (pnd[j][0] * pnd[k][1] - pnd[j][1] * pnd[k][0]); //
        /* coeff a^2 */
        C[2] = +pn[i][1] * pn[k][1] * pn[j][2] * pnd[j][0]           //
                   * (pnd[k][2] * pnd[i][0] - pnd[k][0] * pnd[i][2]) //
               + pn[i][1] * pn[j][1] * pn[k][2] * pnd[k][0]          //
                     * (pnd[i][2] * pnd[j][0] - pnd[i][0] * pnd[j][2]) +
               pn[j][1] * pn[k][1] * pn[i][2] * pnd[i][0]             //
                   * (pnd[j][2] * pnd[k][0] - pnd[j][0] * pnd[k][2]); //

        /* coeff b^2 */
        C[3] = pn[i][0] * pn[j][0] * pn[k][2] * pnd[k][1]               //
                   * (pnd[i][2] * pnd[j][1] - pnd[i][1] * pnd[j][2])    //
               + pn[i][0] * pn[k][0] * pn[j][2] * pnd[j][1]             //
                     * (pnd[k][2] * pnd[i][1] - pnd[k][1] * pnd[i][2])  //
               + pn[j][0] * pn[k][0] * pn[i][2] * pnd[i][1]             //
                     * (pnd[j][2] * pnd[k][1] - pnd[j][1] * pnd[k][2]); //

        /* coeff a */
        C[5] = pn[i][1] * pn[j][1] * pn[k][0] * pnd[k][2]               //
                   * (pnd[i][0] * pnd[j][2] - pnd[i][2] * pnd[j][0])    //
               + pn[i][1] * pn[k][1] * pn[j][0] * pnd[j][2]             //
                     * (pnd[k][0] * pnd[i][2] - pnd[k][2] * pnd[i][0])  //
               + pn[j][1] * pn[k][1] * pn[i][0] * pnd[i][2]             //
                     * (pnd[j][0] * pnd[k][2] - pnd[j][2] * pnd[k][0]); //
        /* coeff b */
        C[6] = pn[i][0] * pn[j][0] * pn[k][1] * pnd[k][2]               //
                   * (pnd[i][1] * pnd[j][2] - pnd[i][2] * pnd[j][1])    //
               + pn[i][0] * pn[k][0] * pn[j][1] * pnd[j][2]             //
                     * (pnd[k][1] * pnd[i][2] - pnd[k][2] * pnd[i][1])  //
               + pn[j][0] * pn[k][0] * pn[i][1] * pnd[i][2]             //
                     * (pnd[j][1] * pnd[k][2] - pnd[j][2] * pnd[k][1]); //
        /* coeff a*b */
        C[4] = pn[i][0] * pn[k][1] * pn[j][2]                                                   //
                   * (pnd[k][0] * pnd[j][1] * pnd[i][2] - pnd[j][0] * pnd[i][1] * pnd[k][2])    //
               + pn[k][0] * pn[i][1] * pn[j][2]                                                 //
                     * (pnd[j][0] * pnd[k][1] * pnd[i][2] - pnd[i][0] * pnd[j][1] * pnd[k][2])  //
               + pn[i][0] * pn[j][1] * pn[k][2]                                                 //
                     * (pnd[k][0] * pnd[i][1] * pnd[j][2] - pnd[j][0] * pnd[k][1] * pnd[i][2])  //
               + pn[j][0] * pn[i][1] * pn[k][2]                                                 //
                     * (pnd[i][0] * pnd[k][1] * pnd[j][2] - pnd[k][0] * pnd[j][1] * pnd[i][2])  //
               + pn[k][0] * pn[j][1] * pn[i][2]                                                 //
                     * (pnd[j][0] * pnd[i][1] * pnd[k][2] - pnd[i][0] * pnd[k][1] * pnd[j][2])  //
               + pn[j][0] * pn[k][1] * pn[i][2]                                                 //
                     * (pnd[i][0] * pnd[j][1] * pnd[k][2] - pnd[k][0] * pnd[i][1] * pnd[j][2]); //

        cont = cont + 1;
        /* construction de la matrice CtC */
        for (unsigned int ii = 0; ii < nc; ii++) {
          for (unsigned int jj = ii; jj < nc; jj++) {
            CtC[ii][jj] = CtC[ii][jj] + C[ii] * C[jj];
          }
        }
      }
    }
  }

  /* calcul de CtC */
  for (unsigned int i = 0; i < nc; i++) {
    for (unsigned int j = i + 1; j < nc; j++)
      CtC[j][i] = CtC[i][j];
  }

  // nl = cont ;   /* nombre de lignes   */
  nc = 7; /* nombre de colonnes */

  /* Creation de matrice CtC termine */
  /* Allocation matrice V */
  vpMatrix V(nc, nc);
  /*****
        Preparation au calcul de la svd (pseudo-inverse)
        pour obtenir une solution il faut au moins 5 equations independantes
        donc il faut au moins la mise en correspondence de 3+5 points
  *****/
  vpColVector sv(nc); // Vecteur contenant les valeurs singulieres

  CtC.svd(sv, V);

  /*****
        Il faut un controle sur le rang de la matrice !!
        La meilleure solution est le vecteur de V associe
        a la valeur singuliere la plus petite en valeur
        absolu
  *****/

  vpColVector svSorted = vpColVector::invSort(sv); // sorted singular value

  /*****
        Parcours de la matrice ordonnee des valeurs singulieres
        On note "cont_zeros" le nbre de valeurs quasi= a 0.
        On note "vect" le rang de la plus petite valeur singliere
        en valeur absolu
  *****/

  unsigned int vect = 0;
  int cont_zeros = 0;
  cont = 0;
  for (unsigned int j = 0; j < nc; j++) {
    // if (fabs(sv[j]) == svSorted[cont]) vect = j ;
    if (std::fabs(sv[j] - svSorted[cont]) <= std::fabs(vpMath::maximum(sv[j], svSorted[cont])))
      vect = j;
    if (std::fabs(sv[j] / svSorted[nc - 1]) < eps)
      cont_zeros = cont_zeros + 1;
  }

  if (cont_zeros > 5) {
    //    printf("erreur dans le rang de la matrice: %d \r\n ",7-cont_zeros);
    HLM2D(nb_pts, pd, p, H);
  } else {

    //     estimation de a = 1,b,c ; je cherche le min de somme(i=1:n)
    //     (0.5*(ei)^2)
    //    e1 = V[1][.] * b - V[3][.] = 0 ;
    //    e2 = V[2][.] * c - V[3][.] = 0 ;
    //    e3 = V[2][.] * b - V[3][.] * c = 0 ;
    //    e4 = V[4][.] * b - V[5][.] = 0 ;
    //    e5 = V[4][.] * c - V[6][.] = 0 ;
    //    e6 = V[6][.] * b - V[5][.] * c = 0 ;
    //    e7 = V[7][.] * b - V[8][.] = 0 ;
    //    e8 = V[7][.] * c - V[9][.] = 0 ;
    d[0] = V[2][vect];
    d[1] = V[4][vect];
    d[2] = V[1][vect];
    d[3] = V[0][vect];
    d[4] = V[3][vect];
    d[5] = V[4][vect];
    d[6] = V[0][vect];
    d[7] = V[1][vect];

    c[0][0] = V[5][vect];
    c[0][1] = 0.0;
    c[1][0] = V[6][vect];
    c[1][1] = 0.0;
    c[2][0] = V[3][vect];
    c[2][1] = 0.0;
    c[3][0] = V[4][vect];
    c[3][1] = 0.0;
    c[4][0] = 0.0;
    c[4][1] = V[6][vect];
    c[5][0] = 0.0;
    c[5][1] = V[5][vect];
    c[6][0] = 0.0;
    c[6][1] = V[2][vect];
    c[7][0] = 0.0;
    c[7][1] = V[4][vect];

    cp = c.pseudoInverse(1e-6);

    vpColVector H_nr(3), temp; // Homographie diagonale
    // Multiplication de la matrice H_nr par le vecteur cp
    temp = cp * d;

    H_nr[0] = temp[0];
    H_nr[1] = temp[1];
    H_nr[2] = 1.0;

    vpMatrix T(9, 3);
    T = 0;
    T[0][0] = -V[1][vect];
    T[0][1] = V[0][vect];
    T[1][0] = V[4][vect];
    T[1][2] = -V[2][vect];
    T[2][0] = -V[6][vect];
    T[2][1] = V[2][vect];
    T[3][0] = V[6][vect];
    T[3][2] = -V[0][vect];
    T[4][0] = -V[3][vect];
    T[4][1] = V[6][vect];
    T[5][0] = V[3][vect];
    T[5][2] = -V[1][vect];
    T[6][0] = -V[5][vect];
    T[6][1] = V[4][vect];
    T[7][0] = V[5][vect];
    T[7][2] = -V[6][vect];
    T[8][1] = -V[5][vect];
    T[8][2] = V[2][vect];

    vpMatrix Hd(3, 3); //  diag(gu,gv,gw)
    for (unsigned int i = 0; i < 3; i++)
      Hd[i][i] = H_nr[i];

    // H = M diag(gu,gv,gw) M*-1
    H = M * Hd * Mdp;
  }
}

void HLM(unsigned int q_cible, const std::vector<double> &xm, const std::vector<double> &ym,
         const std::vector<double> &xmi, const std::vector<double> &ymi, vpMatrix &H)
{
  unsigned int nbpt = (unsigned int)xm.size();

  /****
       on regarde si il y a au moins un point mais pour l'homographie
       il faut au moins quatre points
  ****/
  vpMatrix pd(nbpt, 3);
  vpMatrix p(nbpt, 3);

  for (unsigned int i = 0; i < nbpt; i++) {
    /****
   on assigne les points fournies par la structure robot
   pour la commande globale
    ****/
    pd[i][0] = xmi[i];
    pd[i][1] = ymi[i];
    pd[i][2] = 1.0;
    p[i][0] = xm[i];
    p[i][1] = ym[i];
    p[i][2] = 1.0;
  }

  switch (q_cible) {
  case (1):
  case (2):
    /* La cible est planaire  de type points   */

    HLM2D(nbpt, pd, p, H);

    break;
  case (3): /* cible non planaire : chateau */
    /* cible non planaire  de type points   */
    HLM3D(nbpt, pd, p, H);
    break;
  } /* fin switch */

} /* fin procedure calcul_homogaphie */

#endif // #ifndef DOXYGEN_SHOULD_SKIP_THIS

void vpHomography::HLM(const std::vector<double> &xb, const std::vector<double> &yb, const std::vector<double> &xa,
                       const std::vector<double> &ya, bool isplanar, vpHomography &aHb)
{
  unsigned int n = (unsigned int)xb.size();
  if (yb.size() != n || xa.size() != n || ya.size() != n)
    throw(vpException(vpException::dimensionError, "Bad dimension for HLM shomography estimation"));

  // 4 point are required
  if (n < 4)
    throw(vpException(vpException::fatalError, "There must be at least 4 matched points"));

  // The reference plane is the plane build from the 3 first points.
  unsigned int q_cible;
  vpMatrix H; // matrice d'homographie en metre

  if (isplanar)
    q_cible = 1;
  else
    q_cible = 3;

  ::HLM(q_cible, xa, ya, xb, yb, H);

  aHb = H;
}