vpDot2.cpp

/****************************************************************************
 *
 * $Id: vpDot2.cpp 2135 2009-04-29 13:51:31Z fspindle $
 *
 * This file is part of the ViSP software.
 * Copyright (C) 2005 - 2013 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
 * ("GPL") version 2 as published by the Free Software Foundation.
 * 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://www.irisa.fr/lagadic/visp/visp.html for more information.
 * 
 * This software was developed at:
 * INRIA Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 * http://www.irisa.fr/lagadic
 *
 * 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:
 * Track a white dot.
 *
 * Authors:
 * Fabien Spindler
 * Anthony Saunier
 *
 *****************************************************************************/

//#define DEBUG


#include <visp/vpDisplay.h>

// exception handling
#include <visp/vpTrackingException.h>
#include <visp/vpMath.h>
#include <visp/vpIoTools.h>

#include <visp/vpDot2.h>
#include <math.h>
#include <iostream>    
#include <cmath>    // std::fabs
#include <limits>   // numeric_limits

/******************************************************************************
 *
 *      CONSTRUCTORS AND DESTRUCTORS
 *
 *****************************************************************************/
void vpDot2::init()
{
  cog.set_u(0);
  cog.set_v(0);

  width = 0;
  height = 0;
  surface = 0;
  mean_gray_level = 0;
  gray_level_min = 128;
  gray_level_max = 255;
  grayLevelPrecision = 0.80;
  gamma = 1.5 ;

  sizePrecision = 0.65;
  ellipsoidShapePrecision = 0.65;
  maxSizeSearchDistancePrecision = 0.65;
  setEllipsoidBadPointsPercentage();
  m00 = m11 = m02 = m20 = m10 = m01 = 0 ;

  bbox_u_min = bbox_u_max = bbox_v_min = bbox_v_max = 0;

  firstBorder_u = 0;
  firstBorder_v = 0;

  compute_moment = false ;
  graphics = false;
  thickness = 1;
}

vpDot2::vpDot2() : vpTracker()
{
  init();
}

vpDot2::vpDot2(const vpImagePoint &ip) : vpTracker()
{
  init() ;

  cog = ip;
}

vpDot2::vpDot2(const vpDot2& twinDot ) : vpTracker()
{
  *this = twinDot;
}

void vpDot2::operator=(const vpDot2& twinDot )
                      {
  cog = twinDot.cog;

  width    = twinDot.width;
  height   = twinDot.height;
  surface  = twinDot.surface;
  mean_gray_level = twinDot.mean_gray_level;
  gray_level_min = twinDot.gray_level_min;
  gray_level_max = twinDot.gray_level_max;
  grayLevelPrecision = twinDot.grayLevelPrecision;
  gamma = twinDot.gamma; ;
  sizePrecision = twinDot.sizePrecision;
  ellipsoidShapePrecision = twinDot.ellipsoidShapePrecision ;
  maxSizeSearchDistancePrecision = twinDot.maxSizeSearchDistancePrecision;
  allowedBadPointsPercentage_ = twinDot.allowedBadPointsPercentage_;
  area = twinDot.area;

  m00 = twinDot.m00;
  m01 = twinDot.m01;
  m11 = twinDot.m11;
  m10 = twinDot.m10;
  m02 = twinDot.m02;
  m20 = twinDot.m20;

  bbox_u_min = twinDot.bbox_u_min;
  bbox_u_max = twinDot.bbox_u_max;
  bbox_v_min = twinDot.bbox_v_min;
  bbox_v_max = twinDot.bbox_v_max;

  firstBorder_u = twinDot.firstBorder_u;
  firstBorder_v = twinDot.firstBorder_v;

  compute_moment = twinDot.compute_moment;
  graphics = twinDot.graphics;
  thickness = twinDot.thickness;

  direction_list = twinDot.direction_list;
  ip_edges_list =  twinDot.ip_edges_list;
}

vpDot2::~vpDot2(){}


/******************************************************************************
 *
 *      PUBLIC METHODS
 *****************************************************************************/

void vpDot2::display(const vpImage<unsigned char>& I, vpColor color,
                     unsigned int thickness)
{
  vpDisplay::displayCross(I, cog, 3*thickness+8, color, thickness);
  std::list<vpImagePoint>::const_iterator it;

  for (it = ip_edges_list.begin(); it != ip_edges_list.end(); ++it)
  {
    vpDisplay::displayPoint(I, *it, color);
  }
}


void vpDot2::initTracking(const vpImage<unsigned char>& I, unsigned int size)
{
  while ( vpDisplay::getClick(I, cog) != true) ;

  unsigned int i = (unsigned int)cog.get_i();
  unsigned int j = (unsigned int)cog.get_j();

  double Ip = pow((double)I[i][j]/255,1/gamma);

  if(Ip - (1 - grayLevelPrecision)<0){
    gray_level_min = 0 ;
  }
  else{
    gray_level_min = (unsigned int) (255*pow(Ip - (1 - grayLevelPrecision),gamma));
    if (gray_level_min > 255)
      gray_level_min = 255;
  }
  gray_level_max = (unsigned int) (255*pow(Ip + (1 - grayLevelPrecision),gamma));
  if (gray_level_max > 255)
    gray_level_max = 255;

  setWidth(size);
  setHeight(size);

  try {
    track( I );
  }
  catch(...)
  {
    vpERROR_TRACE("Error caught") ;
    throw ;
  }
}

void vpDot2::initTracking(const vpImage<unsigned char>& I,
                          const vpImagePoint &ip, unsigned int size)
{
  cog = ip ;

  unsigned int i = (unsigned int)cog.get_i();
  unsigned int j = (unsigned int)cog.get_j();

  double Ip = pow((double)I[i][j]/255,1/gamma);

  if(Ip - (1 - grayLevelPrecision)<0){
    gray_level_min = 0 ;
  }
  else{
    gray_level_min = (unsigned int) (255*pow(Ip - (1 - grayLevelPrecision),gamma));
    if (gray_level_min > 255)
      gray_level_min = 255;
  }
  gray_level_max = (unsigned int) (255*pow(Ip + (1 - grayLevelPrecision),gamma));
  if (gray_level_max > 255)
    gray_level_max = 255;

  setWidth(size);
  setHeight(size);

  try {
    track( I );
  }
  catch(...)
  {
    vpERROR_TRACE("Error caught") ;
    throw ;
  }
}

void vpDot2::initTracking(const vpImage<unsigned char>& I,
                          const vpImagePoint &ip,
                          unsigned int gray_level_min,
                          unsigned int gray_level_max,
                          unsigned int size)
{
  cog = ip ;

  this->gray_level_min = gray_level_min;
  this->gray_level_max = gray_level_max;

  setWidth(size);
  setHeight(size);

  try {
    track( I );
  }
  catch(...)
  {
    vpERROR_TRACE("Error caught") ;
    throw ;
  }
}



void vpDot2::track(const vpImage<unsigned char> &I)
{
  m00 = m11 = m02 = m20 = m10 = m01 = 0 ;

  // First, we will estimate the position of the tracked point

  // Set the search area to the entire image
  setArea(I);

  // create a copy of the dot to search
  // This copy can be saw as the previous dot used to check if the current one 
  // found with computeParameters() is similar to the previous one (see isValid() 
  // function).
  // If the found dot is not similar (or valid), we use this copy to set the current 
  // found dot to the previous one (see below).
  vpDot2 wantedDot(*this);

  //   vpDEBUG_TRACE(0, "Previous dot: ");
  //   vpDEBUG_TRACE(0, "u: %f v: %f", get_u(), get_v());
  //   vpDEBUG_TRACE(0, "w: %f h: %f", getWidth(), getHeight());
  bool found = false;
  found = computeParameters(I, cog.get_u(), cog.get_v());

  if (found) {
    // test if the found dot is valid (ie similar to the previous one)
    found = isValid( I, wantedDot);
    if (! found) {
      *this = wantedDot;
      //std::cout << "The found dot is not valid" << std::endl;
    }
  }

  if (! found) {
    //     vpDEBUG_TRACE(0, "Search the dot in a bigest window around the last position");
    //     vpDEBUG_TRACE(0, "Bad computed dot: ");
    //     vpDEBUG_TRACE(0, "u: %f v: %f", get_u(), get_v());
    //     vpDEBUG_TRACE(0, "w: %f h: %f", getWidth(), getHeight());

    // if estimation was wrong (get an error tracking), look for the dot
    // closest from the estimation,
    // i.e. search for dots in an area arround the this dot and get the first
    // element in the area.

    // first get the size of the search window from the dot size
    double searchWindowWidth, searchWindowHeight;
    //if( getWidth() == 0 || getHeight() == 0 )
    if( std::fabs(getWidth()) <= std::numeric_limits<double>::epsilon() || std::fabs(getHeight()) <= std::numeric_limits<double>::epsilon() )
    {
      searchWindowWidth = 80.;
      searchWindowHeight = 80.;
    }
    else
    {
      searchWindowWidth  = getWidth() * 5;
      searchWindowHeight = getHeight() * 5;
    }
    std::list<vpDot2> candidates;
    searchDotsInArea( I,
                      (int)(this->cog.get_u()-searchWindowWidth /2.0),
                      (int)(this->cog.get_v()-searchWindowHeight/2.0),
                      (unsigned int)searchWindowWidth,
                      (unsigned int)searchWindowHeight,
                      candidates);

    // if the vector is empty, that mean we didn't find any candidate
    // in the area, return an error tracking.
    if( candidates.empty() )
    {
      vpERROR_TRACE("No dot was found") ;
      throw(vpTrackingException(vpTrackingException::featureLostError,
                                "No dot was found")) ;
    }

    // otherwise we've got our dot, update this dot's parameters
    vpDot2 movingDot = candidates.front();

    setCog( movingDot.getCog() );
    setSurface( movingDot.getSurface() );
    setWidth( movingDot.getWidth() );
    setHeight( movingDot.getHeight() );

    // Update the moments
    m00 = movingDot.m00;
    m01 = movingDot.m01;
    m10 = movingDot.m10;
    m11 = movingDot.m11;
    m20 = movingDot.m20;
    m02 = movingDot.m02;

    // Update the bounding box
    bbox_u_min = movingDot.bbox_u_min;
    bbox_u_max = movingDot.bbox_u_max;
    bbox_v_min = movingDot.bbox_v_min;
    bbox_v_max = movingDot.bbox_v_max;
  }
  //   else {
  //     // test if the found dot is valid,
  //     if( ! isValid( I, wantedDot ) ) {
  //       *this = wantedDot;
  //       vpERROR_TRACE("The found dot is invalid:",
  //            "- could be a problem of size (width or height) or "
  //            "  surface (number of pixels) which differ too much "
  //            "  to the previous one "
  //            "- or a problem of the shape which is not ellipsoid if "
  //            "  use setEllipsoidShapePrecision(double ellipsoidShapePrecision) "
  //         "  which is the default case. "
  //            "  To track a non ellipsoid shape use setEllipsoidShapePrecision(0)") ;
  //       throw(vpTrackingException(vpTrackingException::featureLostError,
  //                "The found dot is invalid")) ;
  //     }
  //   }

  // if this dot is partially out of the image, return an error tracking.
  if( !isInImage( I ) )
  {
    vpERROR_TRACE("The center of gravity of the dot is not in the image") ;
    throw(vpTrackingException(vpTrackingException::featureLostError,
                              "No dot was found")) ;
  }

  // Get dots center of gravity
  // unsigned int u = (unsigned int) this->cog.get_u();
  // unsigned int v = (unsigned int) this->cog.get_v();
  // Updates the min and max gray levels for the next iteration
  // double Ip = pow((double)I[v][u]/255,1/gamma);
  double Ip = pow(getMeanGrayLevel()/255,1/gamma);
  //printf("current value of gray level center : %i\n", I[v][u]);

  //getMeanGrayLevel(I);
  if(Ip - (1 - grayLevelPrecision)<0){
    gray_level_min = 0 ;
  }
  else{
    gray_level_min = (unsigned int) (255*pow(Ip - (1 - grayLevelPrecision),gamma));
    if (gray_level_min > 255)
      gray_level_min = 255;
  }
  gray_level_max = (unsigned int) (255*pow(Ip + (1 - grayLevelPrecision),gamma));
  if (gray_level_max > 255)
    gray_level_max = 255;

  //printf("%i %i \n",gray_level_max,gray_level_min);
  if (graphics) {
    // display a red cross at the center of gravity's location in the image.

    vpDisplay::displayCross(I, this->cog, 3*thickness+8, vpColor::red, thickness);
    //vpDisplay::flush(I);
  }
}

void
vpDot2::track(const vpImage<unsigned char> &I, vpImagePoint &cog)
{
  track(I);

  cog = this->cog;
}


double vpDot2::getWidth() const
{
  return width;
}

double vpDot2::getHeight() const
{
  return height;
}

double vpDot2::getSurface() const
{
  return fabs(surface);
}

double vpDot2::getGrayLevelPrecision() const
{
  return grayLevelPrecision;
}

double vpDot2::getSizePrecision() const
{
  return sizePrecision;
}

double vpDot2::getEllipsoidShapePrecision() const
{
  return ellipsoidShapePrecision;
}

double vpDot2::getMaxSizeSearchDistancePrecision() const{
  return maxSizeSearchDistancePrecision;
}

double vpDot2::getDistance( const vpDot2& distantDot ) const
{
  vpImagePoint cogDistantDot = distantDot.getCog();
  double diff_u = this->cog.get_u() - cogDistantDot.get_u();
  double diff_v = this->cog.get_v() - cogDistantDot.get_v();
  return sqrt( diff_u*diff_u + diff_v*diff_v );
}




void vpDot2::setWidth( const double & width )
{
  this->width = width;
}

void vpDot2::setHeight( const double & height )
{
  this->height = height;
}

void vpDot2::setSurface( const double & surface )
{
  this->surface = surface;
}

void vpDot2::setGrayLevelPrecision( const double & grayLevelPrecision )
{
  double epsilon = 0.05;
  if( grayLevelPrecision<epsilon )
  {
    this->grayLevelPrecision = epsilon;
  }
  else if( grayLevelPrecision>1 )
  {
    this->grayLevelPrecision = 1.0;
  }
  else
  {
    this->grayLevelPrecision = grayLevelPrecision;
  }
}
void vpDot2::setSizePrecision( const double & sizePrecision )
{
  if( sizePrecision<0 )
  {
    this->sizePrecision = 0;
  }
  else if( sizePrecision>1 )
  {
    this->sizePrecision = 1.0;
  }
  else
  {
    this->sizePrecision = sizePrecision;
  }
}

void vpDot2::setEllipsoidShapePrecision(const double & ellipsoidShapePrecision) {

  if( ellipsoidShapePrecision<0 )
  {
    this->ellipsoidShapePrecision = 0;
  }
  else if( ellipsoidShapePrecision>1 )
  {
    this->ellipsoidShapePrecision = 1.0;
  }
  else
  {
    this->ellipsoidShapePrecision = ellipsoidShapePrecision;
  }
}

void vpDot2::setMaxSizeSearchDistancePrecision( const double & maxSizeSearchDistancePrecision )
{
  double epsilon = 0.05;
  if( maxSizeSearchDistancePrecision<epsilon )
  {
    this-> maxSizeSearchDistancePrecision = epsilon;
  }
  else if( maxSizeSearchDistancePrecision >1 )
  {
    this->maxSizeSearchDistancePrecision = 1.0;
  }
  else
  {
    this->maxSizeSearchDistancePrecision = maxSizeSearchDistancePrecision;
  }
}

void
vpDot2::setArea(const vpImage<unsigned char> &I)
{
  setArea(I, 0, 0, I.getWidth(), I.getHeight());
}

void
vpDot2::setArea(const vpImage<unsigned char> &I,
                    int u, int v,
                    unsigned int w, unsigned int h)
{
  unsigned int image_w = I.getWidth();
  unsigned int image_h = I.getHeight();

  // Bounds the area to the image
  if (u < 0) u = 0;
  else if (u >= (int)image_w) u = (int)image_w - 1;
  if (v < 0) v = 0;
  else if (v >= (int)image_h) v = (int)image_h - 1;

  if (((unsigned int)u + w) > image_w) w = image_w - (unsigned int)u - 1;
  if (((unsigned int)v + h) > image_h) h = image_h - (unsigned int)v - 1;

  area.setRect(u, v, w, h);
}

void
    vpDot2::setArea(const vpRect & a)
{
  area = a;
}


#ifdef VISP_BUILD_DEPRECATED_FUNCTIONS

vpList<vpDot2>* vpDot2::searchDotsInArea(const vpImage<unsigned char>& I)
{
  vpList<vpDot2>* niceDotsVector = new vpList<vpDot2>();

  // To avoid a warning due to the usage of the following deprecated function
  // we duplicate the code
  {
    // niceDotsVector = searchDotsInArea( I, 0, 0, I.getWidth(), I.getHeight());
  }
  {
    // Fit the input area in the image; we keep only the common part between this
    // area and the image.
    int area_u = 0;
    int area_v = 0;
    unsigned int area_w = I.getWidth();
    unsigned int area_h = I.getHeight();
    setArea(I, area_u, area_v, area_w, area_h);

    // compute the size of the search grid
    unsigned int gridWidth;
    unsigned int gridHeight;
    getGridSize( gridWidth, gridHeight );

    if (graphics) {
      // Display the area were the dot is search
      vpDisplay::displayRectangle(I, area, vpColor::blue, false, thickness);
      //vpDisplay::flush(I);
    }

    // start the search loop; for all points of the search grid,
    // test if the pixel belongs to a valid dot.
    // if it is so eventually add it to the vector of valid dots.
 //   vpList<vpDot2>* niceDotsVector = new vpList<vpDot2>();
    vpList<vpDot2>* badDotsVector  = new vpList<vpDot2>();

    vpDot2* dotToTest = NULL;
    vpDot2 tmpDot;

    unsigned int area_u_min = (unsigned int) area.getLeft();
    unsigned int area_u_max = (unsigned int) area.getRight();
    unsigned int area_v_min = (unsigned int) area.getTop();
    unsigned int area_v_max = (unsigned int) area.getBottom();

    unsigned int u, v;
    vpImagePoint cogTmpDot;

    for( v=area_v_min ; v<area_v_max ; v=v+gridHeight )
    {
      for( u=area_u_min ; u<area_u_max ; u=u+gridWidth )
      {
        // if the pixel we're in doesn't have the right color (outside the
        // graylevel interval), no need to check futher, just get to the
        // next grid intersection.
        if( !hasGoodLevel(I, u, v) ) continue;

        // Test if an other germ is inside the bounding box of a dot previoulsy
        // detected
        bool good_germ = true;
        niceDotsVector->front();
        while( !niceDotsVector->outside() && good_germ == true) {
          tmpDot = niceDotsVector->value();

          cogTmpDot = tmpDot.getCog();
          double u0 = cogTmpDot.get_u();
          double v0 = cogTmpDot.get_v();
          double half_w = tmpDot.getWidth()  / 2.;
          double half_h = tmpDot.getHeight() / 2.;

          if ( u >= (u0-half_w) && u <= (u0+half_w) &&
               v >= (v0-half_h) && v <= (v0+half_h) ) {
            // Germ is in a previously detected dot
            good_germ = false;
          }
          niceDotsVector->next();
        }

        if (! good_germ)
          continue;

        // Compute the right border position for this possible germ
        unsigned int border_u;
        unsigned int border_v;
        if(findFirstBorder(I, u, v, border_u, border_v) == false){
          // germ is not good.
          // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
          u = border_u;
          v = border_v;
          continue;
        }

        badDotsVector->front();
  #define vpBAD_DOT_VALUE (badDotsVector->value())
        vpImagePoint cogBadDot;

        std::list<vpImagePoint>::const_iterator it_edges;
        while( !badDotsVector->outside() && good_germ == true)
        {
          if( (double)u >= vpBAD_DOT_VALUE.bbox_u_min
              && (double)u <= vpBAD_DOT_VALUE.bbox_u_max &&
              (double)v >= vpBAD_DOT_VALUE.bbox_v_min
              && (double)v <= vpBAD_DOT_VALUE.bbox_v_max)
          {

            it_edges = ip_edges_list.begin();
            while (it_edges != ip_edges_list.end() && good_germ == true)
            {
              // Test if the germ belong to a previously detected dot:
              // - from the germ go right to the border and compare this
              //   position to the list of pixels of previously detected dots
              cogBadDot = *it_edges;
              //if( border_u == cogBadDot.get_u() && v == cogBadDot.get_v()) {
              if( (std::fabs(border_u - cogBadDot.get_u()) <= vpMath::maximum(std::fabs((double)border_u), std::fabs(cogBadDot.get_u()))*std::numeric_limits<double>::epsilon() )
                &&
                    (std::fabs(v - cogBadDot.get_v()) <= vpMath::maximum(std::fabs((double)v), std::fabs(cogBadDot.get_v()))*std::numeric_limits<double>::epsilon() ))
                {
                good_germ = false;
              }
              ++ it_edges;
            }
          }
          badDotsVector->next();
        }
  #undef vpBAD_DOT_VALUE

        if (! good_germ) {
          // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
          u = border_u;
          v = border_v;
          continue;
        }

        vpTRACE(4, "Try germ (%d, %d)", u, v);

        vpImagePoint germ;
        germ.set_u( u );
        germ.set_v( v );

        // otherwise estimate the width, height and surface of the dot we
        // created, and test it.
        if( dotToTest != NULL ) delete dotToTest;
        dotToTest = getInstance();
        dotToTest->setCog( germ );
        dotToTest->setGrayLevelMin ( getGrayLevelMin() );
        dotToTest->setGrayLevelMax ( getGrayLevelMax() );
        dotToTest->setGrayLevelPrecision( getGrayLevelPrecision() );
        dotToTest->setSizePrecision( getSizePrecision() );
        dotToTest->setGraphics( graphics );
        dotToTest->setGraphicsThickness( thickness );
        dotToTest->setComputeMoments( true );
        dotToTest->setArea( area );
        dotToTest->setEllipsoidShapePrecision( ellipsoidShapePrecision );

        // first compute the parameters of the dot.
        // if for some reasons this caused an error tracking
        // (dot partially out of the image...), check the next intersection
        if( dotToTest->computeParameters( I ) == false ) {
          // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
          u = border_u;
          v = border_v;
          continue;
        }
        // if the dot to test is valid,
        if( dotToTest->isValid( I, *this ) )
        {
          vpImagePoint cogDotToTest = dotToTest->getCog();
          // Compute the distance to the center. The center used here is not the
          // area center available by area.getCenter(area_center_u,
          // area_center_v) but the center of the input area which may be
          // partially outside the image.

          double area_center_u = area_u + area_w/2.0 - 0.5;
          double area_center_v = area_v + area_h/2.0 - 0.5;

          double thisDiff_u = cogDotToTest.get_u() - area_center_u;
          double thisDiff_v = cogDotToTest.get_v() - area_center_v;
          double thisDist = sqrt( thisDiff_u*thisDiff_u + thisDiff_v*thisDiff_v);

          bool stopLoop = false;
          niceDotsVector->front();

          while( !niceDotsVector->outside() &&  stopLoop == false )
          {
            vpDot2 tmpDot = niceDotsVector->value();

            //double epsilon = 0.001; // detecte +sieurs points
            double epsilon = 3.0;
            // if the center of the dot is the same than the current
            // don't add it, test the next point of the grid
            cogTmpDot = tmpDot.getCog();

            if( fabs( cogTmpDot.get_u() - cogDotToTest.get_u() ) < epsilon &&
                fabs( cogTmpDot.get_v() - cogDotToTest.get_v() ) < epsilon )
            {
              stopLoop = true;
              // Jump all the pixels between v,u and v, tmpDot->getFirstBorder_u()
              u = border_u;
              v = border_v;
              continue;
            }

            double otherDiff_u = cogTmpDot.get_u() - area_center_u;
            double otherDiff_v = cogTmpDot.get_v() - area_center_v;
            double otherDist = sqrt( otherDiff_u*otherDiff_u +
                                     otherDiff_v*otherDiff_v );


            // if the distance of the curent vector element to the center
            // is greater than the distance of this dot to the center,
            // then add this dot before the current vector element.
            if( otherDist > thisDist )
            {
              niceDotsVector->addLeft( *dotToTest );
              niceDotsVector->next();
              stopLoop = true;
              // Jump all the pixels between v,u and v, tmpDot->getFirstBorder_u()
              u = border_u;
              v = border_v;
              continue;
            }
            niceDotsVector->next();
          }
          vpTRACE(4, "End while (%d, %d)", u, v);

          // if we reached the end of the vector without finding the dot
          // or inserting it, insert it now.
          if( niceDotsVector->outside() && stopLoop == false )
          {
            niceDotsVector->end();
            niceDotsVector->addRight( *dotToTest );
          }
        }
        else {
          // Store bad dots
          badDotsVector->front();
          badDotsVector->addRight( *dotToTest );
        }
      }
    }
    if( dotToTest != NULL ) delete dotToTest;

    delete badDotsVector;

    //return niceDotsVector;
  }


  return niceDotsVector;

}

vpList<vpDot2>*
vpDot2::searchDotsInArea(const vpImage<unsigned char>& I,
                          int area_u,
                          int area_v,
                          unsigned int area_w,
                          unsigned int area_h)

{
  // Fit the input area in the image; we keep only the common part between this
  // area and the image.
  setArea(I, area_u, area_v, area_w, area_h);

  // compute the size of the search grid
  unsigned int gridWidth;
  unsigned int gridHeight;
  getGridSize( gridWidth, gridHeight );

  if (graphics) {
    // Display the area were the dot is search
    vpDisplay::displayRectangle(I, area, vpColor::blue, false, thickness);
    //vpDisplay::flush(I);
  }

  // start the search loop; for all points of the search grid,
  // test if the pixel belongs to a valid dot.
  // if it is so eventually add it to the vector of valid dots.
  vpList<vpDot2>* niceDotsVector = new vpList<vpDot2>();
  vpList<vpDot2>* badDotsVector  = new vpList<vpDot2>();

  vpDot2* dotToTest = NULL;
  vpDot2 tmpDot;

  unsigned int area_u_min = (unsigned int) area.getLeft();
  unsigned int area_u_max = (unsigned int) area.getRight();
  unsigned int area_v_min = (unsigned int) area.getTop();
  unsigned int area_v_max = (unsigned int) area.getBottom();

  unsigned int u, v;
  vpImagePoint cogTmpDot;

  for( v=area_v_min ; v<area_v_max ; v=v+gridHeight )
  {
    for( u=area_u_min ; u<area_u_max ; u=u+gridWidth )
    {
      // if the pixel we're in doesn't have the right color (outside the
      // graylevel interval), no need to check futher, just get to the
      // next grid intersection.
      if( !hasGoodLevel(I, u, v) ) continue;

      // Test if an other germ is inside the bounding box of a dot previoulsy
      // detected
      bool good_germ = true;
      niceDotsVector->front();
      while( !niceDotsVector->outside() && good_germ == true) {
        tmpDot = niceDotsVector->value();

        cogTmpDot = tmpDot.getCog();
        double u0 = cogTmpDot.get_u();
        double v0 = cogTmpDot.get_v();
        double half_w = tmpDot.getWidth()  / 2.;
        double half_h = tmpDot.getHeight() / 2.;

        if ( u >= (u0-half_w) && u <= (u0+half_w) &&
             v >= (v0-half_h) && v <= (v0+half_h) ) {
          // Germ is in a previously detected dot
          good_germ = false;
        }
        niceDotsVector->next();
      }

      if (! good_germ)
        continue;

      // Compute the right border position for this possible germ
      unsigned int border_u;
      unsigned int border_v;
      if(findFirstBorder(I, u, v, border_u, border_v) == false){
        // germ is not good.
        // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
        u = border_u;
        v = border_v;
        continue;
      }

      badDotsVector->front();
#define vpBAD_DOT_VALUE (badDotsVector->value())
      vpImagePoint cogBadDot;

      std::list<vpImagePoint>::const_iterator it_edges;
      while( !badDotsVector->outside() && good_germ == true)
      {
        if( (double)u >= vpBAD_DOT_VALUE.bbox_u_min
            && (double)u <= vpBAD_DOT_VALUE.bbox_u_max &&
            (double)v >= vpBAD_DOT_VALUE.bbox_v_min
            && (double)v <= vpBAD_DOT_VALUE.bbox_v_max)
        {

          it_edges = ip_edges_list.begin();
          while (it_edges != ip_edges_list.end() && good_germ == true)
          {
            // Test if the germ belong to a previously detected dot:
            // - from the germ go right to the border and compare this
            //   position to the list of pixels of previously detected dots
            cogBadDot = *it_edges;
            //if( border_u == cogBadDot.get_u() && v == cogBadDot.get_v()) {
            if( (std::fabs(border_u - cogBadDot.get_u()) <= vpMath::maximum(std::fabs((double)border_u), std::fabs(cogBadDot.get_u()))*std::numeric_limits<double>::epsilon() )
              &&
                  (std::fabs(v - cogBadDot.get_v()) <= vpMath::maximum(std::fabs((double)v), std::fabs(cogBadDot.get_v()))*std::numeric_limits<double>::epsilon() ))
              {
              good_germ = false;
            }
            ++ it_edges;
          }
        }
        badDotsVector->next();
      }
#undef vpBAD_DOT_VALUE

      if (! good_germ) {
        // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
        u = border_u;
        v = border_v;
        continue;
      }

      vpTRACE(4, "Try germ (%d, %d)", u, v);

      vpImagePoint germ;
      germ.set_u( u );
      germ.set_v( v );
      
      // otherwise estimate the width, height and surface of the dot we
      // created, and test it.
      if( dotToTest != NULL ) delete dotToTest;
      dotToTest = getInstance();
      dotToTest->setCog( germ );
      dotToTest->setGrayLevelMin ( getGrayLevelMin() );
      dotToTest->setGrayLevelMax ( getGrayLevelMax() );
      dotToTest->setGrayLevelPrecision( getGrayLevelPrecision() );
      dotToTest->setSizePrecision( getSizePrecision() );
      dotToTest->setGraphics( graphics );
      dotToTest->setGraphicsThickness( thickness );
      dotToTest->setComputeMoments( true );
      dotToTest->setArea( area );
      dotToTest->setEllipsoidShapePrecision( ellipsoidShapePrecision );

      // first compute the parameters of the dot.
      // if for some reasons this caused an error tracking
      // (dot partially out of the image...), check the next intersection
      if( dotToTest->computeParameters( I ) == false ) {
        // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
        u = border_u;
        v = border_v;
        continue;
      }
      // if the dot to test is valid,
      if( dotToTest->isValid( I, *this ) )
      {
        vpImagePoint cogDotToTest = dotToTest->getCog();
        // Compute the distance to the center. The center used here is not the
        // area center available by area.getCenter(area_center_u,
        // area_center_v) but the center of the input area which may be
        // partially outside the image.

        double area_center_u = area_u + area_w/2.0 - 0.5;
        double area_center_v = area_v + area_h/2.0 - 0.5;

        double thisDiff_u = cogDotToTest.get_u() - area_center_u;
        double thisDiff_v = cogDotToTest.get_v() - area_center_v;
        double thisDist = sqrt( thisDiff_u*thisDiff_u + thisDiff_v*thisDiff_v);

        bool stopLoop = false;
        niceDotsVector->front();

        while( !niceDotsVector->outside() &&  stopLoop == false )
        {
          vpDot2 tmpDot = niceDotsVector->value();

          //double epsilon = 0.001; // detecte +sieurs points
          double epsilon = 3.0;
          // if the center of the dot is the same than the current
          // don't add it, test the next point of the grid
          cogTmpDot = tmpDot.getCog();

          if( fabs( cogTmpDot.get_u() - cogDotToTest.get_u() ) < epsilon &&
              fabs( cogTmpDot.get_v() - cogDotToTest.get_v() ) < epsilon )
          {
            stopLoop = true;
            // Jump all the pixels between v,u and v, tmpDot->getFirstBorder_u()
            u = border_u;
            v = border_v;
            continue;
          }

          double otherDiff_u = cogTmpDot.get_u() - area_center_u;
          double otherDiff_v = cogTmpDot.get_v() - area_center_v;
          double otherDist = sqrt( otherDiff_u*otherDiff_u +
                                   otherDiff_v*otherDiff_v );


          // if the distance of the curent vector element to the center
          // is greater than the distance of this dot to the center,
          // then add this dot before the current vector element.
          if( otherDist > thisDist )
          {
            niceDotsVector->addLeft( *dotToTest );
            niceDotsVector->next();
            stopLoop = true;
            // Jump all the pixels between v,u and v, tmpDot->getFirstBorder_u()
            u = border_u;
            v = border_v;
            continue;
          }
          niceDotsVector->next();
        }
        vpTRACE(4, "End while (%d, %d)", u, v);

        // if we reached the end of the vector without finding the dot
        // or inserting it, insert it now.
        if( niceDotsVector->outside() && stopLoop == false )
        {
          niceDotsVector->end();
          niceDotsVector->addRight( *dotToTest );
        }
      }
      else {
        // Store bad dots
        badDotsVector->front();
        badDotsVector->addRight( *dotToTest );
      }
    }
  }
  if( dotToTest != NULL ) delete dotToTest;

  delete badDotsVector;

  return niceDotsVector;
}
#endif // VISP_BUILD_DEPRECATED_FUNCTIONS

void vpDot2::searchDotsInArea(const vpImage<unsigned char>& I, std::list<vpDot2> &niceDots)
{
  searchDotsInArea( I, 0, 0, I.getWidth(), I.getHeight(), niceDots);
}

void vpDot2::searchDotsInArea(const vpImage<unsigned char>& I,
                               int area_u,
                               int area_v,
                               unsigned int area_w,
                               unsigned int area_h,
                               std::list<vpDot2> &niceDots)

{
  // clear the list of nice dots
  niceDots.clear();

  // Fit the input area in the image; we keep only the common part between this
  // area and the image.
  setArea(I, area_u, area_v, area_w, area_h);

  // compute the size of the search grid
  unsigned int gridWidth;
  unsigned int gridHeight;
  getGridSize( gridWidth, gridHeight );

  if (graphics) {
    // Display the area were the dot is search
    vpDisplay::displayRectangle(I, area, vpColor::blue, false, thickness);
    //vpDisplay::flush(I);
  }

#ifdef DEBUG
  vpDisplay::displayRectangle(I, area, vpColor::blue);
  vpDisplay::flush(I);
#endif
  // start the search loop; for all points of the search grid,
  // test if the pixel belongs to a valid dot.
  // if it is so eventually add it to the vector of valid dots.
  std::list<vpDot2> badDotsVector;
  std::list<vpDot2>::iterator itnice;
  std::list<vpDot2>::iterator itbad;

  vpDot2* dotToTest = NULL;
  vpDot2 tmpDot;

  unsigned int area_u_min = (unsigned int) area.getLeft();
  unsigned int area_u_max = (unsigned int) area.getRight();
  unsigned int area_v_min = (unsigned int) area.getTop();
  unsigned int area_v_max = (unsigned int) area.getBottom();

  unsigned int u, v;
  vpImagePoint cogTmpDot;

  for( v=area_v_min ; v<area_v_max ; v=v+gridHeight )
  {
    for( u=area_u_min ; u<area_u_max ; u=u+gridWidth )
    {
      // if the pixel we're in doesn't have the right color (outside the
      // graylevel interval), no need to check futher, just get to the
      // next grid intersection.
      if( !hasGoodLevel(I, u, v) ) continue;

      // Test if an other germ is inside the bounding box of a dot previoulsy
      // detected
      bool good_germ = true;

      itnice = niceDots.begin();
      while( itnice != niceDots.end() && good_germ == true) {
        tmpDot = *itnice;

        cogTmpDot = tmpDot.getCog();
        double u0 = cogTmpDot.get_u();
        double v0 = cogTmpDot.get_v();
        double half_w = tmpDot.getWidth()  / 2.;
        double half_h = tmpDot.getHeight() / 2.;

        if ( u >= (u0-half_w) && u <= (u0+half_w) &&
             v >= (v0-half_h) && v <= (v0+half_h) ) {
          // Germ is in a previously detected dot
          good_germ = false;
        }
        ++ itnice;
      }

      if (! good_germ)
        continue;

      // Compute the right border position for this possible germ
      unsigned int border_u;
      unsigned int border_v;
      if(findFirstBorder(I, u, v, border_u, border_v) == false){
        // germ is not good.
        // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
        u = border_u;
        v = border_v;
        continue;
      }

      itbad = badDotsVector.begin();
#define vpBAD_DOT_VALUE (*itbad)
      vpImagePoint cogBadDot;

      while( itbad != badDotsVector.end() && good_germ == true) {
        if( (double)u >= vpBAD_DOT_VALUE.bbox_u_min
            && (double)u <= vpBAD_DOT_VALUE.bbox_u_max &&
            (double)v >= vpBAD_DOT_VALUE.bbox_v_min
            && (double)v <= vpBAD_DOT_VALUE.bbox_v_max){
          std::list<vpImagePoint>::const_iterator it_edges = ip_edges_list.begin();
          while (it_edges != ip_edges_list.end() && good_germ == true){
            // Test if the germ belong to a previously detected dot:
            // - from the germ go right to the border and compare this
            //   position to the list of pixels of previously detected dots
            cogBadDot = *it_edges;
            //if( border_u == cogBadDot.get_u() && v == cogBadDot.get_v()) {
            if( (std::fabs(border_u - cogBadDot.get_u()) <= vpMath::maximum(std::fabs((double)border_u), std::fabs(cogBadDot.get_u()))*std::numeric_limits<double>::epsilon() )
              &&
                  (std::fabs(v - cogBadDot.get_v()) <= vpMath::maximum(std::fabs((double)v), std::fabs(cogBadDot.get_v()))*std::numeric_limits<double>::epsilon() )) {
              good_germ = false;
            }
            ++ it_edges;
          }
        }
        ++itbad;
      }
#undef vpBAD_DOT_VALUE

      if (! good_germ) {
        // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
        u = border_u;
        v = border_v;
        continue;
      }

      vpTRACE(4, "Try germ (%d, %d)", u, v);

      vpImagePoint germ;
      germ.set_u( u );
      germ.set_v( v );

      // otherwise estimate the width, height and surface of the dot we
      // created, and test it.
      if( dotToTest != NULL ) delete dotToTest;
      dotToTest = getInstance();
      dotToTest->setCog( germ );
      dotToTest->setGrayLevelMin ( getGrayLevelMin() );
      dotToTest->setGrayLevelMax ( getGrayLevelMax() );
      dotToTest->setGrayLevelPrecision( getGrayLevelPrecision() );
      dotToTest->setSizePrecision( getSizePrecision() );
      dotToTest->setGraphics( graphics );
      dotToTest->setGraphicsThickness( thickness );
      dotToTest->setComputeMoments( true );
      dotToTest->setArea( area );
      dotToTest->setEllipsoidShapePrecision( ellipsoidShapePrecision );

      // first compute the parameters of the dot.
      // if for some reasons this caused an error tracking
      // (dot partially out of the image...), check the next intersection
      if( dotToTest->computeParameters( I ) == false ) {
        // Jump all the pixels between v,u and v, dotToTest->getFirstBorder_u()
        u = border_u;
        v = border_v;
        continue;
      }
      // if the dot to test is valid,
      if( dotToTest->isValid( I, *this ) )
      {
        vpImagePoint cogDotToTest = dotToTest->getCog();
        // Compute the distance to the center. The center used here is not the
        // area center available by area.getCenter(area_center_u,
        // area_center_v) but the center of the input area which may be
        // partially outside the image.

        double area_center_u = area_u + area_w/2.0 - 0.5;
        double area_center_v = area_v + area_h/2.0 - 0.5;

        double thisDiff_u = cogDotToTest.get_u() - area_center_u;
        double thisDiff_v = cogDotToTest.get_v() - area_center_v;
        double thisDist = sqrt( thisDiff_u*thisDiff_u + thisDiff_v*thisDiff_v);

        bool stopLoop = false;
        itnice = niceDots.begin();

        while( itnice != niceDots.end() &&  stopLoop == false )
        {
          vpDot2 tmpDot = *itnice;

          //double epsilon = 0.001; // detecte +sieurs points
          double epsilon = 3.0;
          // if the center of the dot is the same than the current
          // don't add it, test the next point of the grid
          cogTmpDot = tmpDot.getCog();

          if( fabs( cogTmpDot.get_u() - cogDotToTest.get_u() ) < epsilon &&
              fabs( cogTmpDot.get_v() - cogDotToTest.get_v() ) < epsilon )
          {
            stopLoop = true;
            // Jump all the pixels between v,u and v, tmpDot->getFirstBorder_u()
            u = border_u;
            v = border_v;
            continue;
          }

          double otherDiff_u = cogTmpDot.get_u() - area_center_u;
          double otherDiff_v = cogTmpDot.get_v() - area_center_v;
          double otherDist = sqrt( otherDiff_u*otherDiff_u +
                                   otherDiff_v*otherDiff_v );


          // if the distance of the curent vector element to the center
          // is greater than the distance of this dot to the center,
          // then add this dot before the current vector element.
          if( otherDist > thisDist )
          {
            niceDots.insert(itnice, *dotToTest );
            ++ itnice;
            stopLoop = true;
            // Jump all the pixels between v,u and v, tmpDot->getFirstBorder_u()
            u = border_u;
            v = border_v;
            continue;
          }
          ++itnice;
        }
        vpTRACE(4, "End while (%d, %d)", u, v);

        // if we reached the end of the vector without finding the dot
        // or inserting it, insert it now.
        if( itnice == niceDots.end() && stopLoop == false )
        {
          niceDots.push_back( *dotToTest );
        }
      }
      else {
        // Store bad dots
        badDotsVector.push_front( *dotToTest );
      }
    }
  }
  if( dotToTest != NULL ) delete dotToTest;
}

bool vpDot2::isValid(const vpImage<unsigned char>& I, const vpDot2& wantedDot )
{
  double sizePrecision = wantedDot.getSizePrecision();
  double ellipsoidShapePrecision = wantedDot.getEllipsoidShapePrecision();
  double epsilon = 0.001;

  //
  // First, check the width, height and surface of the dot. Those parameters
  // must be the same.
  //
  //if (   (wantedDot.getWidth()   != 0)
  //  && (wantedDot.getHeight()  != 0)
  //  && (wantedDot.getSurface() != 0) )
  if (   (std::fabs(wantedDot.getWidth()) > std::numeric_limits<double>::epsilon())
    &&
        (std::fabs(wantedDot.getHeight())  > std::numeric_limits<double>::epsilon())
    &&
        (std::fabs(wantedDot.getSurface()) > std::numeric_limits<double>::epsilon()) )
    // if (sizePrecision!=0){
    if (std::fabs(sizePrecision) > std::numeric_limits<double>::epsilon()){
#ifdef DEBUG
         std::cout << "test size precision......................\n";
         std::cout << "wanted dot: " << "w=" << wantedDot.getWidth()
              << " h=" << wantedDot.getHeight()
              << " s=" << wantedDot.getSurface()
              << " precision=" << sizePrecision
              << " epsilon=" << epsilon << std::endl;
         std::cout << "dot found: " << "w=" << getWidth()
              << " h=" << getHeight()
              << " s=" << getSurface() << std::endl;
#endif
    if( ( wantedDot.getWidth()*sizePrecision-epsilon < getWidth() ) == false )
    {
      vpDEBUG_TRACE(3, "Bad width > for dot (%g, %g)",
                    cog.get_u(), cog.get_v());
#ifdef DEBUG
      printf("Bad width > for dot (%g, %g)\n", cog.get_u(), cog.get_v());
#endif
      return false;
    }

    if( ( getWidth() < wantedDot.getWidth()/(sizePrecision+epsilon ) )== false )
    {
      vpDEBUG_TRACE(3, "Bad width > for dot (%g, %g)",
                    cog.get_u(), cog.get_v());
#ifdef DEBUG
      printf("Bad width %g > %g for dot (%g, %g)\n",
             getWidth(), wantedDot.getWidth()/(sizePrecision+epsilon),
                                               cog.get_u(), cog.get_v());
#endif
      return false;
    }

    if( ( wantedDot.getHeight()*sizePrecision-epsilon < getHeight() ) == false )
    {
      vpDEBUG_TRACE(3, "Bad height > for dot (%g, %g)",
                    cog.get_u(), cog.get_v());
#ifdef DEBUG
      printf("Bad height %g > %g for dot (%g, %g)\n",
             wantedDot.getHeight()*sizePrecision-epsilon, getHeight(),
             cog.get_u(), cog.get_v());
#endif
      return false;
    }

    if( ( getHeight() < wantedDot.getHeight()/(sizePrecision+epsilon )) == false )
    {
      vpDEBUG_TRACE(3, "Bad height > for dot (%g, %g)",
                    cog.get_u(), cog.get_v());
#ifdef DEBUG
      printf("Bad height %g > %g for dot (%g, %g)\n",
             getHeight(), wantedDot.getHeight()/(sizePrecision+epsilon),
                                                 cog.get_u(), cog.get_v());
#endif
      return false;
    }

    if( ( wantedDot.getSurface()*(sizePrecision*sizePrecision)-epsilon < getSurface() ) == false )
    {
      vpDEBUG_TRACE(3, "Bad surface > for dot (%g, %g)",
                    cog.get_u(), cog.get_v());
#ifdef DEBUG
      printf("Bad surface %g > %g for dot (%g, %g)\n",
             wantedDot.getSurface()*(sizePrecision*sizePrecision)-epsilon,
             getSurface(),
             cog.get_u(), cog.get_v());
#endif
      return false;
    }

    if( ( getSurface() < wantedDot.getSurface()/(sizePrecision*sizePrecision+epsilon )) == false )
    {
      vpDEBUG_TRACE(3, "Bad surface > for dot (%g, %g)",
                    cog.get_u(), cog.get_v());
#ifdef DEBUG
      printf("Bad surface %g < %g for dot (%g, %g)\n",
             getSurface(), wantedDot.getSurface()/(sizePrecision*sizePrecision+epsilon),
                                                   cog.get_u(), cog.get_v());
#endif
      return false;
    }
  }
  //
  // Now we can proceed to more advanced (and costy) checks.
  // First check there is a white (>level) elipse within dot
  // Then check the dot is surrounded by a black elipse.
  //
  int nb_point_to_test = 20; // Nb points to test on inner and outside ellipsoid
  int nb_bad_points = 0;
  int nb_max_bad_points = (int)(nb_point_to_test*allowedBadPointsPercentage_);
  double step_angle = 2*M_PI / nb_point_to_test;

  //  if (ellipsoidShapePrecision != 0 && compute_moment) {
  if (std::fabs(ellipsoidShapePrecision) > std::numeric_limits<double>::epsilon() && compute_moment) {
    //       std::cout << "test shape precision......................\n";
    // See F. Chaumette. Image moments: a general and useful set of features
    // for visual servoing. IEEE Trans. on Robotics, 20(4):713-723, Ao�t 2004.

    // mu11 = m11 - m00 * xg * yg = m11 - m00 * m10/m00 * m01/m00
    //      = m11 - m10 * m01 / m00
    // mu20 = m20 - m00 * xg^2 = m20 - m00 * m10/m00 * m10/m00
    //      = m20 - m10^2 / m00
    // mu02 = m02 - m01^2 / m00
    // alpha = 1/2 arctan( 2 * mu11 / (mu20 - mu02) )
    //
    // a1^2 = 2 / m00 * (mu02 + mu20 + sqrt( (mu20 - mu02)^2 + 4mu11^2) )
    //
    // a2^2 = 2 / m00 * (mu02 + mu20 - sqrt( (mu20 - mu02)^2 + 4mu11^2) )

    //we compute parameters of the estimated ellipse
    double tmp1 = (m01*m01 -m10*m10)/m00+(m20-m02);
    double tmp2 = m11 -m10*m01/m00 ;
    double Sqrt = sqrt(tmp1*tmp1 + 4*tmp2*tmp2);
    double a1 = sqrt(2/m00*((m20+m02)-(m10*m10+m01*m01)/m00 + Sqrt));
    double a2 = sqrt(2/m00*((m20+m02)-(m10*m10+m01*m01)/m00 - Sqrt));
    double alpha = 0.5*atan2(2*(m11*m00-m10*m01),
                             ((m20-m02)*m00-m10*m10+m01*m01));

    // to be able to track small dots, minorize the ellipsoid radius for the
    // inner test
    a1 -= 1.0;
    a2 -= 1.0;

    double innerCoef =  ellipsoidShapePrecision ;
    unsigned int u, v;
    double cog_u = this->cog.get_u();
    double cog_v = this->cog.get_v();

    vpImagePoint ip;
    nb_bad_points = 0;
    for( double theta = 0. ; theta<2*M_PI ; theta+= step_angle ) {
      u = (unsigned int) (cog_u + innerCoef*(a1*cos(alpha)*cos(theta)-a2*sin(alpha)*sin(theta)));
      v = (unsigned int) (cog_v + innerCoef*(a1*sin(alpha)*cos(theta)+a2*cos(alpha)*sin(theta)));
      if( ! this->hasGoodLevel( I, u, v) ) {
        //  vpTRACE("Inner cercle pixel (%d, %d) has bad level for dot (%g, %g)",
        //      u, v, cog_u, cog_v);
#ifdef DEBUG
        printf("Inner cercle pixel (%d, %d) has bad level for dot (%g, %g): %d not in [%d, %d]\n",
               u, v, cog_u, cog_v, I[v][u], gray_level_min, gray_level_max);
#endif
        //return false;
        nb_bad_points ++;
      }
      if (graphics) {
        for (unsigned int t=0; t< thickness; t++) {
          ip.set_u( u + t );
          ip.set_v( v );
          vpDisplay::displayPoint( I, ip, vpColor::green ) ;
        }
      }
#ifdef DEBUG
      vpDisplay::displayPoint( I, ip, vpColor::green ) ;
      vpDisplay::flush(I);
#endif
    }
    if (nb_bad_points > nb_max_bad_points)
    {
#ifdef DEBUG
        printf("Inner ellipse has %d bad points. Max allowed is %d\n",
               nb_bad_points, nb_max_bad_points);
#endif
      return false;
    }
    // to be able to track small dots, maximize the ellipsoid radius for the
    // inner test
    a1 += 2.0;
    a2 += 2.0;

    double outCoef =  2-ellipsoidShapePrecision;           //1.6;
    nb_bad_points = 0;
    for( double theta=0. ; theta<2*M_PI ; theta+= step_angle ) {
      u = (unsigned int) (cog_u + outCoef*(a1*cos(alpha)*cos(theta)-a2*sin(alpha)*sin(theta)));
      v = (unsigned int) (cog_v + outCoef*(a1*sin(alpha)*cos(theta)+a2*cos(alpha)*sin(theta)));
#ifdef DEBUG
      //vpDisplay::displayRectangle(I, area, vpColor::yellow);
      vpDisplay::displayCross( I, v, u, 7, vpColor::purple ) ;
      vpDisplay::flush(I);
#endif
      // If outside the area, continue
      if ((double)u < area.getLeft() || (double)u > area.getRight()
        || (double)v < area.getTop() || (double)v > area.getBottom()) {
        continue;
      }
      if( ! this->hasReverseLevel( I, u, v ) ) {
        //  vpTRACE("Outside cercle pixel (%d, %d) has bad level for dot (%g, %g)",
        //      u, v, cog_u, cog_v);
#ifdef DEBUG
        printf("Outside cercle pixel (%d, %d) has bad level for dot (%g, %g): %d not in [%d, %d]\n",
               u, v, cog_u, cog_v, I[v][u], gray_level_min, gray_level_max);
#endif
        nb_bad_points ++;
        //return false;
      }
      if (graphics) {
        for(unsigned int t=0; t<thickness; t++) {
          ip.set_u( u + t);
          ip.set_v( v );

          vpDisplay::displayPoint( I, ip, vpColor::green ) ;
        }
      }
    }
  }
  if (nb_bad_points > nb_max_bad_points)
  {
#ifdef DEBUG
      printf("Outside ellipse has %d bad points. Max allowed is %d\n",
             nb_bad_points, nb_max_bad_points);
#endif
    return false;
  }

  return true;
}



bool vpDot2::hasGoodLevel(const vpImage<unsigned char>& I,
                          const unsigned int &u,
                          const unsigned int &v) const
{
  if( !isInArea( u, v ) )
    return false;

  if( I[v][u] >= gray_level_min &&  I[v][u] <= gray_level_max)
  {
    return true;
  }
  else
  {
    return false;
  }
}


bool vpDot2::hasReverseLevel(const vpImage<unsigned char>& I,
                             const unsigned int &u,
                             const unsigned int &v) const
{

  if( !isInArea( u, v ) )
    return false;

  if( I[v][u] < gray_level_min ||  I[v][u] > gray_level_max)
  {
    return true;
  }
  else
  {
    return false;
  }
}


vpDot2* vpDot2::getInstance()
{
  return new vpDot2();
}


#ifdef VISP_BUILD_DEPRECATED_FUNCTIONS

void vpDot2::getFreemanChain(vpList<unsigned int> &freeman_chain)
{
  std::list<unsigned int>::const_iterator it;
  freeman_chain.kill();
  for (it = direction_list.begin(); it != direction_list.end(); ++it) {
    freeman_chain += *it;
  }
}
#endif

void vpDot2::getFreemanChain(std::list<unsigned int> &freeman_chain)
{
  freeman_chain = direction_list;
}



/******************************************************************************
 *
 *      PRIVATE METHODS
 *
 ******************************************************************************/



bool vpDot2::computeParameters(const vpImage<unsigned char> &I,
                               const double &_u,
                               const double &_v)
{
  direction_list.clear();
  ip_edges_list.clear();

  double est_u = _u; // estimated
  double est_v = _v;

  // if u has default value, set it to the actual center value
  //if( est_u == -1.0 )
  if( std::fabs(est_u + 1.0) <= vpMath::maximum(std::fabs(est_u),1.)*std::numeric_limits<double>::epsilon() )
  {
    est_u = this->cog.get_u();
  }

  // if v has default value, set it to the actual center value
  //if( est_v == -1.0 )
  if( std::fabs(est_v + 1.0) <= vpMath::maximum(std::fabs(est_v),1.)*std::numeric_limits<double>::epsilon() )
  {
    est_v = this->cog.get_v();
  }

  // if the estimated position of the dot is out of the image, not need to continue,
  // return an error tracking
  if( !isInArea( (unsigned int) est_u, (unsigned int) est_v ) )
  {
    vpDEBUG_TRACE(3, "Initial pixel coordinates (%d, %d) for dot tracking are not in the area",
                  (int) est_u, (int) est_v) ;
    return false;
  }

  bbox_u_min = (int)I.getWidth();
  bbox_u_max = 0;
  bbox_v_min = (int)I.getHeight();
  bbox_v_max = 0;

  // if the first point doesn't have the right level then there's no point to
  // continue.
  if( !hasGoodLevel( I, (unsigned int) est_u, (unsigned int) est_v ) )
  {
    vpDEBUG_TRACE(3, "Can't find a dot from pixel (%d, %d) coordinates",
                  (int) est_u, (int) est_v) ;
    return false;
  }

  // find the border

  if(!findFirstBorder(I, (unsigned int) est_u, (unsigned int) est_v,
                      this->firstBorder_u, this->firstBorder_v)) {

    vpDEBUG_TRACE(3, "Can't find first border (%d, %d) coordinates",
                  (int) est_u, (int) est_v) ;
    return false;
  }

  unsigned int dir = 6;

  // Determine the first element of the Freeman chain
  computeFreemanChainElement(I, this->firstBorder_u, this->firstBorder_v, dir);
  unsigned int firstDir = dir;

  // if we are now out of the image, return an error tracking
  if( !isInArea( this->firstBorder_u, this->firstBorder_v ) )
  {
    vpDEBUG_TRACE(3, "Border pixel coordinates (%d, %d) of the dot are not in the area",
                  this->firstBorder_u, this->firstBorder_v);
    return false;
  }

  // store the new direction and dot border coordinates.
  direction_list.push_back( dir );
  vpImagePoint ip;
  ip.set_u( this->firstBorder_u );
  ip.set_v( this->firstBorder_v );

  ip_edges_list.push_back( ip );

  int border_u = (int)this->firstBorder_u;
  int border_v = (int)this->firstBorder_v;

  //   vpTRACE("-----------------------------------------");
  //   vpTRACE("first border_u: %d border_v: %d dir: %d",
  //    this->firstBorder_u, this->firstBorder_v,firstDir);
  int du, dv;
  float dS, dMu, dMv, dMuv, dMu2, dMv2;
  m00 = 0.0;
  m10 = 0.0;
  m01 = 0.0;
  m11 = 0.0;
  m20 = 0.0;
  m02 = 0.0;
  // while we didn't come back to the first point, follow the border
  do {
    // if it was asked, show the border
    if (graphics) {
      for(int t=0; t< (int)thickness; t++) {
        ip.set_u ( border_u + t);
        ip.set_v ( border_v );
      
        vpDisplay::displayPoint(I, ip, vpColor::red) ;
      }
      //vpDisplay::flush(I);
    }
#ifdef DEBUG
    vpDisplay::displayPoint(I, border_v, border_u, vpColor::red);
    vpDisplay::flush(I);
#endif
    // Determine the increments for the parameters
    computeFreemanParameters(border_u, border_v, dir, du, dv,
                             dS, // surface
                             dMu, dMv, // first order moments
                             dMuv, dMu2, dMv2); // second order moment

    // Update the parameters
    border_u += du; // Next position on the border
    border_v += dv;
    m00 += dS; // enclosed area
    m10 += dMu; // First order moment along v axis
    m01 += dMv; // First order moment along u axis
    if (compute_moment) {
      m11 += dMuv; // Second order moment
      m20 += dMu2; // Second order moment along v axis
      m02 += dMv2; // Second order moment along u axis
    }
    // if we are now out of the image, return an error tracking
    if( !isInArea( (unsigned int)border_u, (unsigned int)border_v ) )  {

      vpDEBUG_TRACE(3, "Dot (%d, %d) is not in the area", border_u, border_v);
      // Can Occur on a single pixel dot located on the top border
      return false;
    }

    // store the new direction and dot border coordinates.

    direction_list.push_back( dir );

    ip.set_u( border_u );
    ip.set_v( border_v );
    ip_edges_list.push_back( ip );

    // vpDisplay::getClick(I);

    // update the extreme point of the dot.
    if( border_v < bbox_v_min ) bbox_v_min = border_v;
    if( border_v > bbox_v_max ) bbox_v_max = border_v;
    if( border_u < bbox_u_min ) bbox_u_min = border_u;
    if( border_u > bbox_u_max ) bbox_u_max = border_u;

    // move around the tracked entity by following the border.
    if (computeFreemanChainElement(I, (unsigned int)border_u, (unsigned int)border_v, dir) == false) {
      vpDEBUG_TRACE(3, "Can't compute Freeman chain for dot (%d, %d)",
                    border_u, border_v);
      return false;
    }

    //     vpTRACE("border_u: %d border_v: %d dir: %d", border_u, border_v, dir);

  }
  while( (getFirstBorder_u() != (unsigned int)border_u
          || getFirstBorder_v() != (unsigned int)border_v
          || firstDir != dir) &&
         isInArea( (unsigned int)border_u, (unsigned int)border_v ) );

#ifdef VP_DEBUG
#if VP_DEBUG_MODE == 3
  vpDisplay::flush(I);
#endif
#endif

  // if the surface is one or zero , the center of gravity wasn't properly
  // detected. Return an error tracking.
  //if( m00 == 0 || m00 == 1 )
  if( std::fabs(m00) <= std::numeric_limits<double>::epsilon() 
    || std::fabs(m00 - 1.) <= vpMath::maximum(std::fabs(m00), 1.)*std::numeric_limits<double>::epsilon() )
    {
    vpDEBUG_TRACE(3, "The center of gravity of the dot wasn't properly detected");
    return false;
  }
  else // compute the center
  {
    // this magic formula gives the coordinates of the center of gravity
    double tmpCenter_u = m10 / m00;
    double tmpCenter_v = m01 / m00;
    
    //Updates the central moments
    if (compute_moment)
    {
      mu11 = m11 - tmpCenter_u*m01;
      mu02 = m02 - tmpCenter_v*m01;
      mu20 = m20 - tmpCenter_u*m10;
    }


    // check the center is in the image... never know...
    //     if( !hasGoodLevel( I, (unsigned int)tmpCenter_u,
    //             (unsigned int)tmpCenter_v ) )
    //     {
    //       vpDEBUG_TRACE(3, "The center of gravity of the dot (%g, %g) has not a good in level", tmpCenter_u, tmpCenter_v);
    //       return false;
    //     }

    cog.set_u( tmpCenter_u );
    cog.set_v( tmpCenter_v );
  }

  width   = bbox_u_max - bbox_u_min + 1;
  height  = bbox_v_max - bbox_v_min + 1;
  surface = m00;

  computeMeanGrayLevel(I);
  return true;
}


bool
    vpDot2::findFirstBorder(const vpImage<unsigned char> &I,
                            const unsigned int &u,
                            const unsigned int &v,
                            unsigned int &border_u,
                            unsigned int &border_v)
{
  // find the border

  // NOTE:
  // from here we use int and not double. This is because we don't have
  // rounding problems and it's actually more a trouble than smth else to
  // work with double when navigating around the dot.
  border_u = u;
  border_v = v;
  double epsilon =0.001;

#ifdef DEBUG
  std::cout << "gray level: " << gray_level_min << " " << gray_level_max << std::endl;
#endif
  while( hasGoodLevel( I, border_u+1, border_v ) &&
         border_u < area.getRight()/*I.getWidth()*/ )  {
    // if the width of this dot was initialised and we already crossed the dot
    // on more than the max possible width, no need to continue, return an
    // error tracking
    if( getWidth() > 0 && ( border_u - u ) > getWidth()/(getMaxSizeSearchDistancePrecision()+epsilon) ) {
      vpDEBUG_TRACE(3, "The found dot (%d, %d, %d) has a greater width than the required one", u, v, border_u);
      return false;
    }
#ifdef DEBUG
    vpDisplay::displayPoint(I, border_v, border_u+1, vpColor::green);
    vpDisplay::flush(I);
#endif

    border_u++;
  }
  return true;
}


bool
    vpDot2::computeFreemanChainElement(const vpImage<unsigned char> &I,
                                       const unsigned int &u,
                                       const unsigned int &v,
                                       unsigned int &element)
{

  if (hasGoodLevel( I, u, v )) {
    unsigned int _u = u;
    unsigned int _v = v;
    // get the point on the right of the point passed in
    updateFreemanPosition( _u, _v, (element + 2) %8 );
    if (hasGoodLevel( I, _u, _v )) {
      element = (element + 2) % 8;      // turn right
    }
    else {
      unsigned int _u = u;
      unsigned int _v = v;
      updateFreemanPosition( _u, _v, (element + 1) %8 );

      if ( hasGoodLevel( I, _u, _v )) {
        element = (element + 1) % 8;      // turn diag right
      }
      else {
        unsigned int _u = u;
        unsigned int _v = v;
        updateFreemanPosition( _u, _v, element ); // same direction

        if ( hasGoodLevel( I, _u, _v )) {
          //element = element;      // keep same dir
        }
        else {
          unsigned int _u = u;
          unsigned int _v = v;
          updateFreemanPosition( _u, _v, (element + 7) %8 ); // diag left

          if ( hasGoodLevel( I, _u, _v )) {
            element = (element + 7) %8;      // turn diag left
          }
          else {
            unsigned int _u = u;
            unsigned int _v = v;
            updateFreemanPosition( _u, _v, (element + 6) %8 ); // left

            if ( hasGoodLevel( I, _u, _v )) {
              element = (element + 6) %8 ;      // turn left
            }
            else {
              unsigned int _u = u;
              unsigned int _v = v;
              updateFreemanPosition( _u, _v, (element + 5) %8 ); // left

              if ( hasGoodLevel( I, _u, _v )) {
                element = (element + 5) %8 ;      // turn diag down
              }
              else {
                unsigned int _u = u;
                unsigned int _v = v;
                updateFreemanPosition( _u, _v, (element + 4) %8 ); // left

                if ( hasGoodLevel( I, _u, _v )) {
                  element = (element + 4) %8 ;      // turn down
                }
                else {
                  unsigned int _u = u;
                  unsigned int _v = v;
                  updateFreemanPosition( _u, _v, (element + 3) %8 ); // diag

                  if ( hasGoodLevel( I, _u, _v )) {
                    element = (element + 3) %8 ;      // turn diag right down
                  }
                  else {
                    // No neighbor with a good level
                    //
                    return false;
                  }
                }
              }
            }
          }
        }
      }
    }
  }

  else {
    return false;
  }

  return true;

}

void
    vpDot2::computeFreemanParameters(const int &u_p,
                                     const int &v_p,
                                     unsigned int &element,
                                     int &du, int &dv,
                                     float &dS,
                                     float &dMu, float &dMv,
                                     float &dMuv,
                                     float &dMu2, float &dMv2)
{
  du = 0;
  dv = 0;
  dMuv = 0;
  dMu2 = 0;
  dMv2 = 0;

  /*
           3  2  1
            \ | /
             \|/ 
         4 ------- 0
             /|\
            / | \
           5  6  7
  */
  switch(element) {
  case 0: // go right
    du = 1;
    dS = (float) v_p;
    dMu = 0.0;
    dMv = (float)(0.5 * v_p * v_p);
    if (compute_moment) {
      dMuv = (float)(0.25 * v_p * v_p * (2 * u_p + 1));
      dMu2 = 0;
      dMv2 = (float)(1.0/ 3. * v_p * v_p * v_p);
    }
    break;

  case 1: // go right top
    du = 1;
    dv = 1;
    dS = (float)(v_p + 0.5);
    dMu = - (float)(0.5 * u_p * ( u_p + 1 ) + 1.0 / 6.0);
    dMv = (float)(0.5 * v_p * ( v_p + 1 ) + 1.0 / 6.0);
    if (compute_moment) {
      float half_u_p = (float)(0.5*u_p);
      dMuv = (float)(v_p*v_p*(0.25+half_u_p) + v_p*(1./3.+half_u_p) + 1./6.*u_p +0.125);
      dMu2 = (float)(-1./3. * u_p * (u_p * u_p + 1.5 * u_p  + 1.) - 1./12.0);
      dMv2 = (float)( 1./3. * v_p * (v_p * v_p + 1.5 * v_p  + 1.) + 1./12.0);
    }
    break;

  case 2: // go top
    dv = 1;
    dS = 0.0;
    dMu = (float)(- 0.5 * u_p *  u_p);
    dMv = 0.0;
    if (compute_moment) {
      dMuv = 0;
      dMu2 = (float)(-1.0/ 3. * u_p * u_p * u_p);
      dMv2 = 0;
    }
    break;

  case 3:
    du = -1;
    dv = 1;
    dS = (float)(- v_p - 0.5);
    dMu = - (float)(0.5 * u_p * ( u_p - 1 ) + 1.0 / 6.0);
    dMv = - (float)(0.5 * v_p * ( v_p + 1 ) + 1.0 / 6.0);
    if (compute_moment) {
      float half_u_p = (float)(0.5*u_p);
      dMuv = (float)(v_p*v_p*(0.25-half_u_p) + v_p*(1./3.-half_u_p) - 1./6.*u_p +0.125);
      dMu2 = (float)(-1./3. * u_p * (u_p * u_p - 1.5 * u_p  + 1.) - 1./12.0);
      dMv2 = (float)(-1./3. * v_p * (v_p * v_p + 1.5 * v_p  + 1.) - 1./12.0);
    }
    break;

  case 4:
    du = -1;
    dS = (float)(- v_p);
    dMv = (float)(- 0.5 * v_p * v_p);
    dMu = 0.0;
    if (compute_moment) {
      dMuv = (float)(-0.25 * v_p * v_p * (2 * u_p - 1));
      dMu2 = 0;
      dMv2 = (float)(-1.0/ 3. * v_p * v_p * v_p);
    }
    break;

  case 5:
    du = -1;
    dv = -1;
    dS = (float)(- v_p + 0.5);
    dMu = (float)(   0.5 * u_p * ( u_p - 1 ) + 1.0 / 6.0);
    dMv = (float)(- (0.5 * v_p * ( v_p - 1 ) + 1.0 / 6.0));
    if (compute_moment) {
      float half_u_p = (float)(0.5*u_p);
      dMuv = (float)(v_p*v_p*(0.25-half_u_p) - v_p*(1./3.-half_u_p) - 1./6.*u_p +0.125);
      dMu2 = (float)( 1./3. * u_p * (u_p * u_p - 1.5 * u_p  + 1.) - 1./12.0);
      dMv2 = (float)(-1./3. * v_p * (v_p * v_p - 1.5 * v_p  + 1.) - 1./12.0);
    }
    break;

  case 6:
    dv = -1;
    dS = 0.0;
    dMu = (float)(0.5 * u_p *  u_p);
    dMv = 0.0;
    if (compute_moment) {
      dMuv = 0;
      dMu2 = (float)(1.0/ 3. * u_p * u_p * u_p);
      dMv2 = 0;
    }
    break;

  case 7:
    du = 1;
    dv = -1;
    dS = (float)(v_p - 0.5);
    dMu = (float)(0.5 * u_p * ( u_p + 1 ) + 1.0 / 6.0);
    dMv = (float)(0.5 * v_p * ( v_p - 1 ) + 1.0 / 6.0);
    if (compute_moment) {
      float half_u_p = (float)(0.5*u_p);
      dMuv = (float)(v_p*v_p*(0.25+half_u_p) - v_p*(1./3.+half_u_p) + 1./6.*u_p +0.125);
      dMu2 = (float)(1./3. * u_p * (u_p * u_p + 1.5 * u_p  + 1.) + 1./12.0);
      dMv2 = (float)(1./3. * v_p * (v_p * v_p - 1.5 * v_p  + 1.) - 1./12.0);
    }
    break;
  }
}


void vpDot2::updateFreemanPosition( unsigned int& u, unsigned int& v,
                                    const unsigned int &dir )
{
  switch(dir) {
  case 0: u += 1;         break;
  case 1: u += 1; v += 1; break;
  case 2: v += 1;         break;
  case 3: u -= 1; v += 1; break;
  case 4: u -= 1;         break;
  case 5: u -= 1; v -= 1; break;
  case 6: v -= 1;         break;
  case 7: u += 1; v -= 1; break;
  }
}

bool vpDot2::isInImage(const vpImage<unsigned char> &I) const
{
  return isInImage( I, cog);
}

bool vpDot2::isInImage(const vpImage<unsigned char> &I,
                        const vpImagePoint &ip) const
{
  unsigned int height = I.getHeight();
  unsigned int width = I.getWidth();
  double u = ip.get_u();
  double v = ip.get_v();

  if( u < 0 || u >= width ) return false;
  if( v < 0 || v >= height ) return false;
  return true;
}

bool vpDot2::isInArea( const unsigned int &u, const unsigned int &v) const
{
  unsigned int area_u_min = (unsigned int) area.getLeft();
  unsigned int area_u_max = (unsigned int) area.getRight();
  unsigned int area_v_min = (unsigned int) area.getTop();
  unsigned int area_v_max = (unsigned int) area.getBottom();

  if( u < area_u_min || u > area_u_max ) return false;
  if( v < area_v_min || v > area_v_max ) return false;
  return true;
}


void vpDot2::getGridSize( unsigned int &gridWidth, unsigned int &gridHeight )
{
  // first get the research grid width and height Note that
  // 1/sqrt(2)=cos(pi/4). The grid squares should be small enough to be
  // contained in the dot. We gent this here if the dot is a perfect disc.
  // More accurate criterium to define the grid should be implemented if
  // necessary
  gridWidth = (unsigned int) (getWidth() * getMaxSizeSearchDistancePrecision() / sqrt(2.));
  gridHeight = (unsigned int) (getHeight() * getMaxSizeSearchDistancePrecision() / sqrt(2.0));

  if( gridWidth == 0 ) gridWidth = 1;
  if( gridHeight == 0 ) gridHeight = 1;
}



void vpDot2::computeMeanGrayLevel(const vpImage<unsigned char>& I) 
{
  int cog_u = (int)cog.get_u();
  int cog_v = (int)cog.get_v();

  unsigned int sum_value =0;
  unsigned int nb_pixels =0;

  for(unsigned int i=(unsigned int)this->bbox_u_min; i <=(unsigned int)this->bbox_u_max ; i++){
    unsigned int pixel_gray =(unsigned int) I[(unsigned int)cog_v][i];
    if (pixel_gray >= getGrayLevelMin()  && pixel_gray <= getGrayLevelMax()){
      sum_value += pixel_gray;
      nb_pixels ++;
    }
  }
  for(unsigned int i=(unsigned int)this->bbox_v_min; i <=(unsigned int)this->bbox_v_max ; i++){
    unsigned char pixel_gray =I[i][(unsigned int)cog_u];
    if (pixel_gray >= getGrayLevelMin()  && pixel_gray <= getGrayLevelMax()){
      sum_value += pixel_gray;
      nb_pixels ++;
    }
  }
  if(nb_pixels < 10){ //could be good to choose the min nb points from area of dot
    //add diagonals points to have enough point
    int imin,imax;
    if( (cog_u - bbox_u_min) > (cog_v - bbox_v_min)){
      imin=cog_v - bbox_v_min;
    }
    else{ imin = cog_u - bbox_u_min;}
    if( (bbox_u_max - cog_u) > (bbox_v_max - cog_v)){
      imax=bbox_v_max - cog_v;
    }
    else{ imax = bbox_u_max - cog_u;}
    for(int i=-imin; i <=imax ; i++){
      unsigned int pixel_gray =(unsigned int) I[(unsigned int)(cog_v + i)][(unsigned int)(cog_u + i)];
      if (pixel_gray >= getGrayLevelMin()  && pixel_gray <= getGrayLevelMax()){
        sum_value += pixel_gray;
        nb_pixels ++;
      }
    }

    if( (cog_u - bbox_u_min) > (bbox_v_max - cog_v)){
      imin = bbox_v_max - cog_v;
    }
    else{ imin = cog_u - bbox_u_min;}
    if( (bbox_u_max - cog_u) > (cog_v - bbox_v_min)){
      imax = cog_v - bbox_v_min;
    }
    else{ imax = bbox_u_max - cog_u;}

    for(int i=-imin; i <=imax ; i++){
      unsigned char pixel_gray =I[(unsigned int)(cog_v - i)][(unsigned int)(cog_u + i)];
      if (pixel_gray >= getGrayLevelMin()  && pixel_gray <= getGrayLevelMax()){
        sum_value += pixel_gray;
        nb_pixels ++;
      }
    }
  }

  if(nb_pixels== 0){
    //should never happen
    throw(vpTrackingException(vpTrackingException::notEnoughPointError,"No point was found"));
  }
  else{
    mean_gray_level = sum_value/nb_pixels;
  }
}


vpMatrix vpDot2::defineDots(vpDot2 dot[], const unsigned int &n, const std::string &dotFile, vpImage<unsigned char> &I, vpColor col, bool trackDot)
{
    vpMatrix Cogs(n, 2);
    vpImagePoint cog;
    unsigned int i;
    bool fromFile = vpIoTools::checkFilename(dotFile.c_str());
    if(fromFile)
    {
        vpMatrix::loadMatrix(dotFile, Cogs);
        std::cout << Cogs.getRows() << " dots loaded from file " << dotFile << std::endl;
    }

    // test number of cogs in file
    if(Cogs.getRows() < n)
    {
        std::cout << "Dot file has a wrong number of dots : redefining them" << std::endl;
        fromFile = false;
    }

    // read from file and tracks the dots
    if(fromFile)
    {
        try
        {
            for(i=0;i<n;++i)
            {
                cog.set_uv(Cogs[i][0], Cogs[i][1]);
        dot[i].setGraphics(true);
        dot[i].setCog(cog);
                if(trackDot)
                {
                    dot[i].initTracking(I,cog);
                    dot[i].track(I);
                    vpDisplay::displayCross(I, cog, 10, col);
                }
            }
        }
        catch(...)
        {
            std::cout << "Cannot track dots from file" << std::endl;
            fromFile = false;
        }
        vpDisplay::flush(I);

        // check that dots are far away ones from the other
        double d;
        for(i=0;i<n && fromFile;++i)
        {
            d = sqrt(vpMath::sqr(dot[i].getHeight()) + vpMath::sqr(dot[i].getWidth()));
            for(unsigned int j=0;j<n && fromFile;++j)
                if(j!=i)
                    if(dot[i].getDistance(dot[j]) < d)
                    {
        fromFile = false;
        std::cout << "Dots from file seem incoherent" << std::endl;
      }
        }
    }

    if(!fromFile)
    {
        vpDisplay::display(I);
        vpDisplay::flush(I);

        std::cout << "Click on the " << n << " dots clockwise starting from upper/left dot..." << std::endl;
        for (i = 0; i < n; i++)
        {
            if(trackDot)
            {
        dot[i].setGraphics(true);
        dot[i].initTracking(I);
                cog = dot[i].getCog();
            }
            else
            {
                vpDisplay::getClick(I, cog);
                dot[i].setCog(cog);
            }
            Cogs[i][0] = cog.get_u();
            Cogs[i][1] = cog.get_v();
            vpDisplay::displayCross(I, cog, 10, col);
            vpDisplay::flush(I);
        }
    }

    if (!fromFile & (dotFile != ""))
    {
        vpMatrix::saveMatrix(dotFile, Cogs);
        std::cout << Cogs.getRows() << " dots written to file " << dotFile << std::endl;
    }

    // back to non graphic mode
    for(i=0;i<n;++i)
        dot[i].setGraphics(false);

    return Cogs;
}

void vpDot2::trackAndDisplay(vpDot2 dot[], const unsigned int &n, vpImage<unsigned char> &I, std::vector<vpImagePoint> &cogs, vpImagePoint* cogStar)
{
    unsigned int i;
    // tracking
    for(i=0;i<n;++i)
    {
        dot[i].track(I);
        cogs.push_back(dot[i].getCog());
    }
    // trajectories
    for(i=n;i<cogs.size();++i)
        vpDisplay::displayCircle(I,cogs[i],4,vpColor::green,true);
    // initial position
    for(i=0;i<n;++i)
        vpDisplay::displayCircle(I,cogs[i],4,vpColor::blue,true);
    // if exists, desired position
    if(cogStar != NULL)
        for(i=0;i<n;++i)
        {
    vpDisplay::displayDotLine(I,cogStar[i],dot[i].getCog(),vpColor::red);
    vpDisplay::displayCircle(I,cogStar[i],4,vpColor::red,true);
  }
    vpDisplay::flush(I);
}

void vpDot2::display(const vpImage<unsigned char>& I,const vpImagePoint &cog, 
                     const std::list<vpImagePoint> &edges_list, vpColor color,
                     unsigned int thickness)
{
  vpDisplay::displayCross(I, cog, 3*thickness+8, color, thickness);
  std::list<vpImagePoint>::const_iterator it;

  for (it = edges_list.begin(); it != edges_list.end(); ++it)
  {
    vpDisplay::displayPoint(I, *it, color);
  }
}

void vpDot2::display(const vpImage<vpRGBa>& I,const vpImagePoint &cog,
                     const std::list<vpImagePoint> &edges_list, vpColor color,
                     unsigned int thickness)
{
  vpDisplay::displayCross(I, cog, 3*thickness+8, color, thickness);
  std::list<vpImagePoint>::const_iterator it;

  for (it = edges_list.begin(); it != edges_list.end(); ++it)
  {
    vpDisplay::displayPoint(I, *it, color);
  }
}