vpMbtFaceDepthNormal.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:
 * Manage depth normal features for a particular face.
 *
 *****************************************************************************/

#include <visp3/core/vpCPUFeatures.h>
#include <visp3/mbt/vpMbtFaceDepthNormal.h>
#include <visp3/mbt/vpMbtTukeyEstimator.h>

#ifdef VISP_HAVE_PCL
#include <pcl/common/centroid.h>
#include <pcl/filters/extract_indices.h>
#include <pcl/segmentation/sac_segmentation.h>
#endif

#if defined __SSE2__ || defined _M_X64 || (defined _M_IX86_FP && _M_IX86_FP >= 2)
#include <emmintrin.h>
#define VISP_HAVE_SSE2 1
#endif

#define USE_SSE_CODE 1
#if VISP_HAVE_SSE2 && USE_SSE_CODE
#define USE_SSE 1
#else
#define USE_SSE 0
#endif

vpMbtFaceDepthNormal::vpMbtFaceDepthNormal()
  : m_cam(), m_clippingFlag(vpPolygon3D::NO_CLIPPING), m_distFarClip(100), m_distNearClip(0.001), m_hiddenFace(NULL),
    m_planeObject(), m_polygon(NULL), m_useScanLine(false), m_faceActivated(false),
    m_faceCentroidMethod(GEOMETRIC_CENTROID), m_faceDesiredCentroid(), m_faceDesiredNormal(),
    m_featureEstimationMethod(ROBUST_FEATURE_ESTIMATION), m_isTrackedDepthNormalFace(true), m_isVisible(false),
    m_listOfFaceLines(), m_planeCamera(),
    m_pclPlaneEstimationMethod(2), // SAC_MSAC, see pcl/sample_consensus/method_types.h
    m_pclPlaneEstimationRansacMaxIter(200), m_pclPlaneEstimationRansacThreshold(0.001), m_polygonLines()
{
}

vpMbtFaceDepthNormal::~vpMbtFaceDepthNormal()
{
  for (size_t i = 0; i < m_listOfFaceLines.size(); i++) {
    delete m_listOfFaceLines[i];
  }
}

void vpMbtFaceDepthNormal::addLine(vpPoint &P1, vpPoint &P2, vpMbHiddenFaces<vpMbtPolygon> *const faces, int polygon,
                                   std::string name)
{
  // Build a PolygonLine to be able to easily display the lines model
  PolygonLine polygon_line;

  // Add polygon
  polygon_line.m_poly.setNbPoint(2);
  polygon_line.m_poly.addPoint(0, P1);
  polygon_line.m_poly.addPoint(1, P2);

  polygon_line.m_poly.setClipping(m_clippingFlag);
  polygon_line.m_poly.setNearClippingDistance(m_distNearClip);
  polygon_line.m_poly.setFarClippingDistance(m_distFarClip);

  polygon_line.m_p1 = &polygon_line.m_poly.p[0];
  polygon_line.m_p2 = &polygon_line.m_poly.p[1];

  m_polygonLines.push_back(polygon_line);

  // suppress line already in the model
  bool already_here = false;
  vpMbtDistanceLine *l;

  for (std::vector<vpMbtDistanceLine *>::const_iterator it = m_listOfFaceLines.begin(); it != m_listOfFaceLines.end();
       ++it) {
    l = *it;
    if ((samePoint(*(l->p1), P1) && samePoint(*(l->p2), P2)) || (samePoint(*(l->p1), P2) && samePoint(*(l->p2), P1))) {
      already_here = true;
      l->addPolygon(polygon);
      l->hiddenface = faces;
      l->useScanLine = m_useScanLine;
    }
  }

  if (!already_here) {
    l = new vpMbtDistanceLine;

    l->setCameraParameters(m_cam);
    l->buildFrom(P1, P2);
    l->addPolygon(polygon);
    l->hiddenface = faces;
    l->useScanLine = m_useScanLine;

    l->setIndex((unsigned int)m_listOfFaceLines.size());
    l->setName(name);

    if (m_clippingFlag != vpPolygon3D::NO_CLIPPING)
      l->getPolygon().setClipping(m_clippingFlag);

    if ((m_clippingFlag & vpPolygon3D::NEAR_CLIPPING) == vpPolygon3D::NEAR_CLIPPING)
      l->getPolygon().setNearClippingDistance(m_distNearClip);

    if ((m_clippingFlag & vpPolygon3D::FAR_CLIPPING) == vpPolygon3D::FAR_CLIPPING)
      l->getPolygon().setFarClippingDistance(m_distFarClip);

    m_listOfFaceLines.push_back(l);
  }
}

#ifdef VISP_HAVE_PCL
bool vpMbtFaceDepthNormal::computeDesiredFeatures(const vpHomogeneousMatrix &cMo, const unsigned int width,
                                                  const unsigned int height,
                                                  const pcl::PointCloud<pcl::PointXYZ>::ConstPtr &point_cloud,
                                                  vpColVector &desired_features, const unsigned int stepX,
                                                  const unsigned int stepY
#if DEBUG_DISPLAY_DEPTH_NORMAL
                                                  ,
                                                  vpImage<unsigned char> &debugImage,
                                                  std::vector<std::vector<vpImagePoint> > &roiPts_vec
#endif
                                                  , const vpImage<bool> *mask
)
{
  m_faceActivated = false;

  if (width == 0 || height == 0)
    return false;

  std::vector<vpImagePoint> roiPts;
  vpColVector desired_normal(3);

  computeROI(cMo, width, height, roiPts
#if DEBUG_DISPLAY_DEPTH_NORMAL
             ,
             roiPts_vec
#endif
  );

  if (roiPts.size() <= 2) {
#ifndef NDEBUG
    std::cerr << "Error: roiPts.size() <= 2 in computeDesiredFeatures" << std::endl;
#endif
    return false;
  }

  vpPolygon polygon_2d(roiPts);
  vpRect bb = polygon_2d.getBoundingBox();

  unsigned int top = (unsigned int)std::max(0.0, bb.getTop());
  unsigned int bottom = (unsigned int)std::min((double)height, std::max(0.0, bb.getBottom()));
  unsigned int left = (unsigned int)std::max(0.0, bb.getLeft());
  unsigned int right = (unsigned int)std::min((double)width, std::max(0.0, bb.getRight()));

  bb.setTop(top);
  bb.setBottom(bottom);
  bb.setLeft(left);
  bb.setRight(right);

  // Keep only 3D points inside the projected polygon face
  pcl::PointCloud<pcl::PointXYZ>::Ptr point_cloud_face(new pcl::PointCloud<pcl::PointXYZ>);
  std::vector<double> point_cloud_face_vec, point_cloud_face_custom;

  if (m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
    point_cloud_face_custom.reserve((size_t)(3 * bb.getWidth() * bb.getHeight()));
    point_cloud_face_vec.reserve((size_t)(3 * bb.getWidth() * bb.getHeight()));
  } else if (m_featureEstimationMethod == ROBUST_SVD_PLANE_ESTIMATION) {
    point_cloud_face_vec.reserve((size_t)(3 * bb.getWidth() * bb.getHeight()));
  } else if (m_featureEstimationMethod == PCL_PLANE_ESTIMATION) {
    point_cloud_face->reserve((size_t)(bb.getWidth() * bb.getHeight()));
  }

  bool checkSSE2 = vpCPUFeatures::checkSSE2();
#if !USE_SSE
  checkSSE2 = false;
#else
  bool push = false;
  double prev_x, prev_y, prev_z;
#endif

  double x = 0.0, y = 0.0;
  for (unsigned int i = top; i < bottom; i += stepY) {
    for (unsigned int j = left; j < right; j += stepX) {
      if (vpMeTracker::inMask(mask, i, j) && pcl::isFinite((*point_cloud)(j, i)) && (*point_cloud)(j, i).z > 0 &&
          (m_useScanLine ? (i < m_hiddenFace->getMbScanLineRenderer().getPrimitiveIDs().getHeight() &&
                            j < m_hiddenFace->getMbScanLineRenderer().getPrimitiveIDs().getWidth() &&
                            m_hiddenFace->getMbScanLineRenderer().getPrimitiveIDs()[i][j] == m_polygon->getIndex())
                         : polygon_2d.isInside(vpImagePoint(i, j)))) {

        if (m_featureEstimationMethod == PCL_PLANE_ESTIMATION) {
          point_cloud_face->push_back((*point_cloud)(j, i));
        } else if (m_featureEstimationMethod == ROBUST_SVD_PLANE_ESTIMATION ||
                   m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
          point_cloud_face_vec.push_back((*point_cloud)(j, i).x);
          point_cloud_face_vec.push_back((*point_cloud)(j, i).y);
          point_cloud_face_vec.push_back((*point_cloud)(j, i).z);

          if (m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
            // Add point for custom method for plane equation estimation
            vpPixelMeterConversion::convertPoint(m_cam, j, i, x, y);

            if (checkSSE2) {
#if USE_SSE
              if (!push) {
                push = true;
                prev_x = x;
                prev_y = y;
                prev_z = (*point_cloud)(j, i).z;
              } else {
                push = false;
                point_cloud_face_custom.push_back(prev_x);
                point_cloud_face_custom.push_back(x);

                point_cloud_face_custom.push_back(prev_y);
                point_cloud_face_custom.push_back(y);

                point_cloud_face_custom.push_back(prev_z);
                point_cloud_face_custom.push_back((*point_cloud)(j, i).z);
              }
#endif
            } else {
              point_cloud_face_custom.push_back(x);
              point_cloud_face_custom.push_back(y);
              point_cloud_face_custom.push_back((*point_cloud)(j, i).z);
            }
          }
        }

#if DEBUG_DISPLAY_DEPTH_NORMAL
        debugImage[i][j] = 255;
#endif
      }
    }
  }

#if USE_SSE
  if (checkSSE2 && push) {
    point_cloud_face_custom.push_back(prev_x);
    point_cloud_face_custom.push_back(prev_y);
    point_cloud_face_custom.push_back(prev_z);
  }
#endif

  if (point_cloud_face->empty() && point_cloud_face_custom.empty() && point_cloud_face_vec.empty()) {
    return false;
  }

  // Face centroid computed by the different methods
  vpColVector centroid_point(3);

  if (m_featureEstimationMethod == PCL_PLANE_ESTIMATION) {
    if (!computeDesiredFeaturesPCL(point_cloud_face, desired_features, desired_normal, centroid_point)) {
      return false;
    }
  } else if (m_featureEstimationMethod == ROBUST_SVD_PLANE_ESTIMATION) {
    computeDesiredFeaturesSVD(point_cloud_face_vec, cMo, desired_features, desired_normal, centroid_point);
  } else if (m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
    computeDesiredFeaturesRobustFeatures(point_cloud_face_custom, point_cloud_face_vec, cMo, desired_features,
                                         desired_normal, centroid_point);
  } else {
    throw vpException(vpException::badValue, "Unknown feature estimation method!");
  }

  computeDesiredNormalAndCentroid(cMo, desired_normal, centroid_point);

  m_faceActivated = true;

  return true;
}
#endif

bool vpMbtFaceDepthNormal::computeDesiredFeatures(const vpHomogeneousMatrix &cMo, const unsigned int width,
                                                  const unsigned int height,
                                                  const std::vector<vpColVector> &point_cloud,
                                                  vpColVector &desired_features, const unsigned int stepX,
                                                  const unsigned int stepY
#if DEBUG_DISPLAY_DEPTH_NORMAL
                                                  ,
                                                  vpImage<unsigned char> &debugImage,
                                                  std::vector<std::vector<vpImagePoint> > &roiPts_vec
#endif
                                                  , const vpImage<bool> *mask
)
{
  m_faceActivated = false;

  if (width == 0 || height == 0)
    return false;

  std::vector<vpImagePoint> roiPts;
  vpColVector desired_normal(3);

  computeROI(cMo, width, height, roiPts
#if DEBUG_DISPLAY_DEPTH_NORMAL
             ,
             roiPts_vec
#endif
  );

  if (roiPts.size() <= 2) {
#ifndef NDEBUG
    std::cerr << "Error: roiPts.size() <= 2 in computeDesiredFeatures" << std::endl;
#endif
    return false;
  }

  vpPolygon polygon_2d(roiPts);
  vpRect bb = polygon_2d.getBoundingBox();

  unsigned int top = (unsigned int)std::max(0.0, bb.getTop());
  unsigned int bottom = (unsigned int)std::min((double)height, std::max(0.0, bb.getBottom()));
  unsigned int left = (unsigned int)std::max(0.0, bb.getLeft());
  unsigned int right = (unsigned int)std::min((double)width, std::max(0.0, bb.getRight()));

  bb.setTop(top);
  bb.setBottom(bottom);
  bb.setLeft(left);
  bb.setRight(right);

  // Keep only 3D points inside the projected polygon face
  std::vector<double> point_cloud_face, point_cloud_face_custom;

  point_cloud_face.reserve((size_t)(3 * bb.getWidth() * bb.getHeight()));
  if (m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
    point_cloud_face_custom.reserve((size_t)(3 * bb.getWidth() * bb.getHeight()));
  }

  bool checkSSE2 = vpCPUFeatures::checkSSE2();
#if !USE_SSE
  checkSSE2 = false;
#else
  bool push = false;
  double prev_x, prev_y, prev_z;
#endif

  double x = 0.0, y = 0.0;
  for (unsigned int i = top; i < bottom; i += stepY) {
    for (unsigned int j = left; j < right; j += stepX) {
      if (vpMeTracker::inMask(mask, i, j) && point_cloud[i * width + j][2] > 0 &&
          (m_useScanLine ? (i < m_hiddenFace->getMbScanLineRenderer().getPrimitiveIDs().getHeight() &&
                            j < m_hiddenFace->getMbScanLineRenderer().getPrimitiveIDs().getWidth() &&
                            m_hiddenFace->getMbScanLineRenderer().getPrimitiveIDs()[i][j] == m_polygon->getIndex())
                         : polygon_2d.isInside(vpImagePoint(i, j)))) {
        // Add point
        point_cloud_face.push_back(point_cloud[i * width + j][0]);
        point_cloud_face.push_back(point_cloud[i * width + j][1]);
        point_cloud_face.push_back(point_cloud[i * width + j][2]);

        if (m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
          // Add point for custom method for plane equation estimation
          vpPixelMeterConversion::convertPoint(m_cam, j, i, x, y);

          if (checkSSE2) {
#if USE_SSE
            if (!push) {
              push = true;
              prev_x = x;
              prev_y = y;
              prev_z = point_cloud[i * width + j][2];
            } else {
              push = false;
              point_cloud_face_custom.push_back(prev_x);
              point_cloud_face_custom.push_back(x);

              point_cloud_face_custom.push_back(prev_y);
              point_cloud_face_custom.push_back(y);

              point_cloud_face_custom.push_back(prev_z);
              point_cloud_face_custom.push_back(point_cloud[i * width + j][2]);
            }
#endif
          } else {
            point_cloud_face_custom.push_back(x);
            point_cloud_face_custom.push_back(y);
            point_cloud_face_custom.push_back(point_cloud[i * width + j][2]);
          }
        }

#if DEBUG_DISPLAY_DEPTH_NORMAL
        debugImage[i][j] = 255;
#endif
      }
    }
  }

#if USE_SSE
  if (checkSSE2 && push) {
    point_cloud_face_custom.push_back(prev_x);
    point_cloud_face_custom.push_back(prev_y);
    point_cloud_face_custom.push_back(prev_z);
  }
#endif

  if (point_cloud_face.empty() && point_cloud_face_custom.empty()) {
    return false;
  }

  // Face centroid computed by the different methods
  vpColVector centroid_point(3);

#ifdef VISP_HAVE_PCL
  if (m_featureEstimationMethod == PCL_PLANE_ESTIMATION) {
    pcl::PointCloud<pcl::PointXYZ>::Ptr point_cloud_face_pcl(new pcl::PointCloud<pcl::PointXYZ>);
    point_cloud_face_pcl->reserve(point_cloud_face.size() / 3);

    for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
      point_cloud_face_pcl->push_back(
          pcl::PointXYZ(point_cloud_face[3 * i], point_cloud_face[3 * i + 1], point_cloud_face[3 * i + 2]));
    }

    computeDesiredFeaturesPCL(point_cloud_face_pcl, desired_features, desired_normal, centroid_point);
  } else
#endif
      if (m_featureEstimationMethod == ROBUST_SVD_PLANE_ESTIMATION) {
    computeDesiredFeaturesSVD(point_cloud_face, cMo, desired_features, desired_normal, centroid_point);
  } else if (m_featureEstimationMethod == ROBUST_FEATURE_ESTIMATION) {
    computeDesiredFeaturesRobustFeatures(point_cloud_face_custom, point_cloud_face, cMo, desired_features,
                                         desired_normal, centroid_point);
  } else {
    throw vpException(vpException::badValue, "Unknown feature estimation method!");
  }

  computeDesiredNormalAndCentroid(cMo, desired_normal, centroid_point);

  m_faceActivated = true;

  return true;
}

#ifdef VISP_HAVE_PCL
bool vpMbtFaceDepthNormal::computeDesiredFeaturesPCL(const pcl::PointCloud<pcl::PointXYZ>::ConstPtr &point_cloud_face,
                                                     vpColVector &desired_features, vpColVector &desired_normal,
                                                     vpColVector &centroid_point)
{
  try {
    // Compute plane equation for this subset of point cloud
    pcl::ModelCoefficients::Ptr coefficients(new pcl::ModelCoefficients);
    pcl::PointIndices::Ptr inliers(new pcl::PointIndices);
    // Create the segmentation object
    pcl::SACSegmentation<pcl::PointXYZ> seg;
    // Optional
    seg.setOptimizeCoefficients(true);
    // Mandatory
    seg.setModelType(pcl::SACMODEL_PLANE);
    seg.setMethodType(m_pclPlaneEstimationMethod);
    seg.setDistanceThreshold(m_pclPlaneEstimationRansacThreshold);
    seg.setMaxIterations(m_pclPlaneEstimationRansacMaxIter);

    seg.setInputCloud(point_cloud_face);
    seg.segment(*inliers, *coefficients);

    pcl::PointCloud<pcl::PointXYZ>::Ptr point_cloud_face_extracted(new pcl::PointCloud<pcl::PointXYZ>);
    // Create the filtering object
    pcl::ExtractIndices<pcl::PointXYZ> extract;

    // Extract the inliers
    extract.setInputCloud(point_cloud_face);
    extract.setIndices(inliers);
    extract.setNegative(false);
    extract.filter(*point_cloud_face_extracted);

    pcl::PointXYZ centroid_point_pcl;
    if (pcl::computeCentroid(*point_cloud_face_extracted, centroid_point_pcl)) {
      pcl::PointXYZ face_normal;
      computeNormalVisibility(coefficients->values[0], coefficients->values[1], coefficients->values[2],
                              centroid_point_pcl, face_normal);

      desired_features.resize(3, false);
      desired_features[0] = -coefficients->values[0] / coefficients->values[3];
      desired_features[1] = -coefficients->values[1] / coefficients->values[3];
      desired_features[2] = -coefficients->values[2] / coefficients->values[3];

      desired_normal[0] = face_normal.x;
      desired_normal[1] = face_normal.y;
      desired_normal[2] = face_normal.z;

      centroid_point[0] = centroid_point_pcl.x;
      centroid_point[1] = centroid_point_pcl.y;
      centroid_point[2] = centroid_point_pcl.z;
    } else {
      std::cerr << "Cannot compute centroid!" << std::endl;
      return false;
    }
  } catch (const pcl::PCLException &e) {
    std::cerr << "Catch a PCL exception: " << e.what() << std::endl;
    throw;
  }

  return true;
}
#endif

void vpMbtFaceDepthNormal::computeDesiredFeaturesRobustFeatures(const std::vector<double> &point_cloud_face_custom,
                                                                const std::vector<double> &point_cloud_face,
                                                                const vpHomogeneousMatrix &cMo,
                                                                vpColVector &desired_features,
                                                                vpColVector &desired_normal,
                                                                vpColVector &centroid_point)
{
  std::vector<double> weights;
  double den = 0.0;
  estimateFeatures(point_cloud_face_custom, cMo, desired_features, weights);

  // Compute face centroid
  for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
    centroid_point[0] += weights[i] * point_cloud_face[3 * i];
    centroid_point[1] += weights[i] * point_cloud_face[3 * i + 1];
    centroid_point[2] += weights[i] * point_cloud_face[3 * i + 2];

    den += weights[i];
  }

  centroid_point[0] /= den;
  centroid_point[1] /= den;
  centroid_point[2] /= den;

  computeNormalVisibility(-desired_features[0], -desired_features[1], -desired_features[2], centroid_point,
                          desired_normal);
}

void vpMbtFaceDepthNormal::computeDesiredFeaturesSVD(const std::vector<double> &point_cloud_face,
                                                     const vpHomogeneousMatrix &cMo, vpColVector &desired_features,
                                                     vpColVector &desired_normal, vpColVector &centroid_point)
{
  vpColVector plane_equation_SVD;
  estimatePlaneEquationSVD(point_cloud_face, cMo, plane_equation_SVD, centroid_point);

  desired_features.resize(3, false);
  desired_features[0] = -plane_equation_SVD[0] / plane_equation_SVD[3];
  desired_features[1] = -plane_equation_SVD[1] / plane_equation_SVD[3];
  desired_features[2] = -plane_equation_SVD[2] / plane_equation_SVD[3];

  computeNormalVisibility(-desired_features[0], -desired_features[1], -desired_features[2], centroid_point,
                          desired_normal);
}

void vpMbtFaceDepthNormal::computeDesiredNormalAndCentroid(const vpHomogeneousMatrix &cMo,
                                                           const vpColVector &desired_normal,
                                                           const vpColVector &centroid_point)
{
  // Compute desired centroid in the object frame
  vpColVector centroid_cam(4);
  centroid_cam[0] = centroid_point[0];
  centroid_cam[1] = centroid_point[1];
  centroid_cam[2] = centroid_point[2];
  centroid_cam[3] = 1;

  vpColVector centroid_obj = cMo.inverse() * centroid_cam;
  m_faceDesiredCentroid.setWorldCoordinates(centroid_obj[0], centroid_obj[1], centroid_obj[2]);

  // Compute desired face normal in the object frame
  vpColVector face_normal_cam(4);
  face_normal_cam[0] = desired_normal[0];
  face_normal_cam[1] = desired_normal[1];
  face_normal_cam[2] = desired_normal[2];
  face_normal_cam[3] = 1;

  vpColVector face_normal_obj = cMo.inverse() * face_normal_cam;
  m_faceDesiredNormal.setWorldCoordinates(face_normal_obj[0], face_normal_obj[1], face_normal_obj[2]);
}

bool vpMbtFaceDepthNormal::computePolygonCentroid(const std::vector<vpPoint> &points_, vpPoint &centroid)
{
  if (points_.empty()) {
    return false;
  }

  if (points_.size() < 2) {
    centroid = points_[0];
    return true;
  }

  std::vector<vpPoint> points = points_;
  points.push_back(points_.front());

  double A1 = 0.0, A2 = 0.0, c_x1 = 0.0, c_x2 = 0.0, c_y = 0.0, c_z = 0.0;

  for (size_t i = 0; i < points.size() - 1; i++) {
    // projection onto xy plane
    c_x1 += (points[i].get_X() + points[i + 1].get_X()) *
            (points[i].get_X() * points[i + 1].get_Y() - points[i + 1].get_X() * points[i].get_Y());
    c_y += (points[i].get_Y() + points[i + 1].get_Y()) *
           (points[i].get_X() * points[i + 1].get_Y() - points[i + 1].get_X() * points[i].get_Y());
    A1 += points[i].get_X() * points[i + 1].get_Y() - points[i + 1].get_X() * points[i].get_Y();

    // projection onto xz plane
    c_x2 += (points[i].get_X() + points[i + 1].get_X()) *
            (points[i].get_X() * points[i + 1].get_Z() - points[i + 1].get_X() * points[i].get_Z());
    c_z += (points[i].get_Z() + points[i + 1].get_Z()) *
           (points[i].get_X() * points[i + 1].get_Z() - points[i + 1].get_X() * points[i].get_Z());
    A2 += points[i].get_X() * points[i + 1].get_Z() - points[i + 1].get_X() * points[i].get_Z();
  }

  c_x1 /= 3.0 * A1;
  c_y /= 3.0 * A1;
  c_x2 /= 3.0 * A2;
  c_z /= 3.0 * A2;

  if (A1 > A2) {
    centroid.set_X(c_x1);
  } else {
    centroid.set_X(c_x2);
  }

  centroid.set_Y(c_y);
  centroid.set_Z(c_z);

  return true;
}

void vpMbtFaceDepthNormal::computeROI(const vpHomogeneousMatrix &cMo, const unsigned int width,
                                      const unsigned int height, std::vector<vpImagePoint> &roiPts
#if DEBUG_DISPLAY_DEPTH_NORMAL
                                      ,
                                      std::vector<std::vector<vpImagePoint> > &roiPts_vec
#endif
)
{
  if (m_useScanLine || m_clippingFlag > 2)
    m_cam.computeFov(width, height);

  if (m_useScanLine) {
    for (std::vector<PolygonLine>::iterator it = m_polygonLines.begin(); it != m_polygonLines.end(); ++it) {
      it->m_p1->changeFrame(cMo);
      it->m_p2->changeFrame(cMo);

      vpImagePoint ip1, ip2;

      it->m_poly.changeFrame(cMo);
      it->m_poly.computePolygonClipped(m_cam);

      if (it->m_poly.polyClipped.size() == 2 &&
          ((it->m_poly.polyClipped[1].second & it->m_poly.polyClipped[0].second & vpPolygon3D::NEAR_CLIPPING) == 0) &&
          ((it->m_poly.polyClipped[1].second & it->m_poly.polyClipped[0].second & vpPolygon3D::FAR_CLIPPING) == 0) &&
          ((it->m_poly.polyClipped[1].second & it->m_poly.polyClipped[0].second & vpPolygon3D::DOWN_CLIPPING) == 0) &&
          ((it->m_poly.polyClipped[1].second & it->m_poly.polyClipped[0].second & vpPolygon3D::UP_CLIPPING) == 0) &&
          ((it->m_poly.polyClipped[1].second & it->m_poly.polyClipped[0].second & vpPolygon3D::LEFT_CLIPPING) == 0) &&
          ((it->m_poly.polyClipped[1].second & it->m_poly.polyClipped[0].second & vpPolygon3D::RIGHT_CLIPPING) == 0)) {

        std::vector<std::pair<vpPoint, vpPoint> > linesLst;
        m_hiddenFace->computeScanLineQuery(it->m_poly.polyClipped[0].first, it->m_poly.polyClipped[1].first, linesLst,
                                           true);

        for (unsigned int i = 0; i < linesLst.size(); i++) {
          linesLst[i].first.project();
          linesLst[i].second.project();

          vpMeterPixelConversion::convertPoint(m_cam, linesLst[i].first.get_x(), linesLst[i].first.get_y(), ip1);
          vpMeterPixelConversion::convertPoint(m_cam, linesLst[i].second.get_x(), linesLst[i].second.get_y(), ip2);

          it->m_imPt1 = ip1;
          it->m_imPt2 = ip2;

          roiPts.push_back(ip1);
          roiPts.push_back(ip2);

#if DEBUG_DISPLAY_DEPTH_NORMAL
          std::vector<vpImagePoint> roiPts_;
          roiPts_.push_back(ip1);
          roiPts_.push_back(ip2);
          roiPts_vec.push_back(roiPts_);
#endif
        }
      }
    }
  } else {
    // Get polygon clipped
    m_polygon->getRoiClipped(m_cam, roiPts, cMo);

#if DEBUG_DISPLAY_DEPTH_NORMAL
    roiPts_vec.push_back(roiPts);
#endif
  }
}

void vpMbtFaceDepthNormal::computeVisibility() { m_isVisible = m_polygon->isVisible(); }

void vpMbtFaceDepthNormal::computeVisibilityDisplay()
{
  // Compute lines visibility, only for display
  vpMbtDistanceLine *line;
  for (std::vector<vpMbtDistanceLine *>::const_iterator it = m_listOfFaceLines.begin(); it != m_listOfFaceLines.end();
       ++it) {
    line = *it;
    bool isvisible = false;

    for (std::list<int>::const_iterator itindex = line->Lindex_polygon.begin(); itindex != line->Lindex_polygon.end();
         ++itindex) {
      int index = *itindex;
      if (index == -1) {
        isvisible = true;
      } else {
        if (line->hiddenface->isVisible((unsigned int)index)) {
          isvisible = true;
        }
      }
    }

    // Si la ligne n'appartient a aucune face elle est tout le temps visible
    if (line->Lindex_polygon.empty())
      isvisible = true; // Not sure that this can occur

    if (isvisible) {
      line->setVisible(true);
    } else {
      line->setVisible(false);
    }
  }
}

void vpMbtFaceDepthNormal::computeNormalVisibility(const double nx, const double ny, const double nz,
                                                   const vpHomogeneousMatrix &cMo, const vpCameraParameters &camera,
                                                   vpColVector &correct_normal, vpPoint &centroid)
{
  vpColVector faceNormal(3);
  faceNormal[0] = nx;
  faceNormal[1] = ny;
  faceNormal[2] = nz;
  faceNormal.normalize();

  // Get polygon clipped
  std::vector<vpImagePoint> roiPts;
  m_polygon->getRoiClipped(camera, roiPts, cMo);

  std::vector<vpPoint> polyPts;
  m_polygon->getPolygonClipped(polyPts);

  vpColVector e4(3);
  if (m_faceCentroidMethod == GEOMETRIC_CENTROID) {
    computePolygonCentroid(polyPts, centroid);
    centroid.project();

    e4[0] = -centroid.get_X();
    e4[1] = -centroid.get_Y();
    e4[2] = -centroid.get_Z();
    e4.normalize();
  } else {
    double centroid_x = 0.0;
    double centroid_y = 0.0;
    double centroid_z = 0.0;

    for (size_t i = 0; i < polyPts.size(); i++) {
      centroid_x += polyPts[i].get_X();
      centroid_y += polyPts[i].get_Y();
      centroid_z += polyPts[i].get_Z();
    }

    centroid_x /= polyPts.size();
    centroid_y /= polyPts.size();
    centroid_z /= polyPts.size();

    e4[0] = -centroid_x;
    e4[1] = -centroid_y;
    e4[2] = -centroid_z;
    e4.normalize();

    centroid.set_X(centroid_x);
    centroid.set_Y(centroid_y);
    centroid.set_Z(centroid_z);
  }

  correct_normal.resize(3, false);
  double angle = acos(vpColVector::dotProd(e4, faceNormal));
  if (angle < M_PI_2) {
    correct_normal = faceNormal;
  } else {
    correct_normal[0] = -faceNormal[0];
    correct_normal[1] = -faceNormal[1];
    correct_normal[2] = -faceNormal[2];
  }
}

#ifdef VISP_HAVE_PCL
void vpMbtFaceDepthNormal::computeNormalVisibility(const float nx, const float ny, const float nz,
                                                   const pcl::PointXYZ &centroid_point, pcl::PointXYZ &face_normal)
{
  vpColVector faceNormal(3);
  faceNormal[0] = nx;
  faceNormal[1] = ny;
  faceNormal[2] = nz;
  faceNormal.normalize();

  vpColVector e4(3);
  e4[0] = -centroid_point.x;
  e4[1] = -centroid_point.y;
  e4[2] = -centroid_point.z;
  e4.normalize();

  double angle = acos(vpColVector::dotProd(e4, faceNormal));
  if (angle < M_PI_2) {
    face_normal = pcl::PointXYZ(faceNormal[0], faceNormal[1], faceNormal[2]);
  } else {
    face_normal = pcl::PointXYZ(-faceNormal[0], -faceNormal[1], -faceNormal[2]);
  }
}
#endif

void vpMbtFaceDepthNormal::computeNormalVisibility(const double nx, const double ny, const double nz,
                                                   const vpColVector &centroid_point, vpColVector &face_normal)
{
  face_normal.resize(3, false);
  face_normal[0] = nx;
  face_normal[1] = ny;
  face_normal[2] = nz;
  face_normal.normalize();

  vpColVector e4 = -centroid_point;
  e4.normalize();

  double angle = acos(vpColVector::dotProd(e4, face_normal));
  if (angle >= M_PI_2) {
    face_normal[0] = -face_normal[0];
    face_normal[1] = -face_normal[1];
    face_normal[2] = -face_normal[2];
  }
}

void vpMbtFaceDepthNormal::computeInteractionMatrix(const vpHomogeneousMatrix &cMo, vpMatrix &L, vpColVector &features)
{
  L.resize(3, 6, false, false);

  // Transform the plane equation for the current pose
  m_planeCamera = m_planeObject;
  m_planeCamera.changeFrame(cMo);

  double ux = m_planeCamera.getA();
  double uy = m_planeCamera.getB();
  double uz = m_planeCamera.getC();
  double D = m_planeCamera.getD();
  double D2 = D * D;

  // Features
  features.resize(3, false);
  features[0] = -ux / D;
  features[1] = -uy / D;
  features[2] = -uz / D;

  // L_A
  L[0][0] = ux * ux / D2;
  L[0][1] = ux * uy / D2;
  L[0][2] = ux * uz / D2;
  L[0][3] = 0.0;
  L[0][4] = uz / D;
  L[0][5] = -uy / D;

  // L_B
  L[1][0] = ux * uy / D2;
  L[1][1] = uy * uy / D2;
  L[1][2] = uy * uz / D2;
  L[1][3] = -uz / D;
  L[1][4] = 0.0;
  L[1][5] = ux / D;

  // L_C
  L[2][0] = ux * uz / D2;
  L[2][1] = uy * uz / D2;
  L[2][2] = uz * uz / D2;
  L[2][3] = uy / D;
  L[2][4] = -ux / D;
  L[2][5] = 0.0;
}

void vpMbtFaceDepthNormal::display(const vpImage<unsigned char> &I, const vpHomogeneousMatrix &cMo,
                                   const vpCameraParameters &cam, const vpColor &col, const unsigned int thickness,
                                   const bool displayFullModel)
{
  if ((m_polygon->isVisible() && m_isTrackedDepthNormalFace) || displayFullModel) {
    computeVisibilityDisplay();

    for (std::vector<vpMbtDistanceLine *>::const_iterator it = m_listOfFaceLines.begin(); it != m_listOfFaceLines.end();
         ++it) {
      vpMbtDistanceLine *line = *it;
      line->display(I, cMo, cam, col, thickness, displayFullModel);
    }
  }
}

void vpMbtFaceDepthNormal::display(const vpImage<vpRGBa> &I, const vpHomogeneousMatrix &cMo,
                                   const vpCameraParameters &cam, const vpColor &col, const unsigned int thickness,
                                   const bool displayFullModel)
{
  if ((m_polygon->isVisible() && m_isTrackedDepthNormalFace) || displayFullModel) {
    computeVisibilityDisplay();

    for (std::vector<vpMbtDistanceLine *>::const_iterator it = m_listOfFaceLines.begin(); it != m_listOfFaceLines.end();
         ++it) {
      vpMbtDistanceLine *line = *it;
      line->display(I, cMo, cam, col, thickness, displayFullModel);
    }
  }
}

void vpMbtFaceDepthNormal::displayFeature(const vpImage<unsigned char> &I, const vpHomogeneousMatrix &cMo,
                                          const vpCameraParameters &cam, const double scale,
                                          const unsigned int thickness)
{
  if (m_faceActivated && m_isTrackedDepthNormalFace && m_isVisible) {
    // Desired feature
    vpPoint pt_centroid = m_faceDesiredCentroid;
    pt_centroid.changeFrame(cMo);
    pt_centroid.project();

    vpImagePoint im_centroid;
    vpMeterPixelConversion::convertPoint(cam, pt_centroid.get_x(), pt_centroid.get_y(), im_centroid);

    vpPoint pt_normal = m_faceDesiredNormal;
    pt_normal.changeFrame(cMo);
    pt_normal.project();

    vpPoint pt_extremity;
    pt_extremity.set_X(pt_centroid.get_X() + pt_normal.get_X() * scale);
    pt_extremity.set_Y(pt_centroid.get_Y() + pt_normal.get_Y() * scale);
    pt_extremity.set_Z(pt_centroid.get_Z() + pt_normal.get_Z() * scale);
    pt_extremity.project();

    vpImagePoint im_extremity;
    vpMeterPixelConversion::convertPoint(cam, pt_extremity.get_x(), pt_extremity.get_y(), im_extremity);

    vpDisplay::displayArrow(I, im_centroid, im_extremity, vpColor::blue, 4, 2, thickness);

    // Current feature
    // Transform the plane equation for the current pose
    m_planeCamera = m_planeObject;
    m_planeCamera.changeFrame(cMo);

    double ux = m_planeCamera.getA();
    double uy = m_planeCamera.getB();
    double uz = m_planeCamera.getC();

    vpColVector correct_normal;
    vpCameraParameters cam_copy = cam;
    cam_copy.computeFov(I.getWidth(), I.getHeight());
    computeNormalVisibility(ux, uy, uz, cMo, cam_copy, correct_normal, pt_centroid);

    pt_centroid.project();
    vpMeterPixelConversion::convertPoint(cam_copy, pt_centroid.get_x(), pt_centroid.get_y(), im_centroid);

    pt_extremity.set_X(pt_centroid.get_X() + correct_normal[0] * scale);
    pt_extremity.set_Y(pt_centroid.get_Y() + correct_normal[1] * scale);
    pt_extremity.set_Z(pt_centroid.get_Z() + correct_normal[2] * scale);
    pt_extremity.project();

    vpMeterPixelConversion::convertPoint(cam_copy, pt_extremity.get_x(), pt_extremity.get_y(), im_extremity);

    vpDisplay::displayArrow(I, im_centroid, im_extremity, vpColor::red, 4, 2, thickness);
  }
}

void vpMbtFaceDepthNormal::displayFeature(const vpImage<vpRGBa> &I, const vpHomogeneousMatrix &cMo,
                                          const vpCameraParameters &cam, const double scale,
                                          const unsigned int thickness)
{
  if (m_faceActivated && m_isTrackedDepthNormalFace && m_isVisible) {
    // Desired feature
    vpPoint pt_centroid = m_faceDesiredCentroid;
    pt_centroid.changeFrame(cMo);
    pt_centroid.project();

    vpImagePoint im_centroid;
    vpMeterPixelConversion::convertPoint(cam, pt_centroid.get_x(), pt_centroid.get_y(), im_centroid);

    vpPoint pt_normal = m_faceDesiredNormal;
    pt_normal.changeFrame(cMo);
    pt_normal.project();

    vpPoint pt_extremity;
    pt_extremity.set_X(pt_centroid.get_X() + pt_normal.get_X() * scale);
    pt_extremity.set_Y(pt_centroid.get_Y() + pt_normal.get_Y() * scale);
    pt_extremity.set_Z(pt_centroid.get_Z() + pt_normal.get_Z() * scale);
    pt_extremity.project();

    vpImagePoint im_extremity;
    vpMeterPixelConversion::convertPoint(cam, pt_extremity.get_x(), pt_extremity.get_y(), im_extremity);

    vpDisplay::displayArrow(I, im_centroid, im_extremity, vpColor::blue, 4, 2, thickness);

    // Current feature
    // Transform the plane equation for the current pose
    m_planeCamera = m_planeObject;
    m_planeCamera.changeFrame(cMo);

    double ux = m_planeCamera.getA();
    double uy = m_planeCamera.getB();
    double uz = m_planeCamera.getC();

    vpColVector correct_normal;
    vpCameraParameters cam_copy = cam;
    cam_copy.computeFov(I.getWidth(), I.getHeight());
    computeNormalVisibility(ux, uy, uz, cMo, cam_copy, correct_normal, pt_centroid);

    pt_centroid.project();
    vpMeterPixelConversion::convertPoint(cam_copy, pt_centroid.get_x(), pt_centroid.get_y(), im_centroid);

    pt_extremity.set_X(pt_centroid.get_X() + correct_normal[0] * scale);
    pt_extremity.set_Y(pt_centroid.get_Y() + correct_normal[1] * scale);
    pt_extremity.set_Z(pt_centroid.get_Z() + correct_normal[2] * scale);
    pt_extremity.project();

    vpMeterPixelConversion::convertPoint(cam_copy, pt_extremity.get_x(), pt_extremity.get_y(), im_extremity);

    vpDisplay::displayArrow(I, im_centroid, im_extremity, vpColor::red, 4, 2, thickness);
  }
}

void vpMbtFaceDepthNormal::estimateFeatures(const std::vector<double> &point_cloud_face, const vpHomogeneousMatrix &cMo,
                                            vpColVector &x_estimated, std::vector<double> &w)
{
  vpMbtTukeyEstimator<double> tukey_robust;
  std::vector<double> residues(point_cloud_face.size() / 3);

  w.resize(point_cloud_face.size() / 3, 1.0);

  unsigned int max_iter = 30, iter = 0;
  double error = 0.0, prev_error = -1.0;
  double A = 0.0, B = 0.0, C = 0.0;

  Mat33<double> ATA_3x3;

  bool checkSSE2 = vpCPUFeatures::checkSSE2();
#if !USE_SSE
  checkSSE2 = false;
#endif

  if (checkSSE2) {
#if USE_SSE
    while (std::fabs(error - prev_error) > 1e-6 && (iter < max_iter)) {
      if (iter == 0) {
        // Transform the plane equation for the current pose
        m_planeCamera = m_planeObject;
        m_planeCamera.changeFrame(cMo);

        double ux = m_planeCamera.getA();
        double uy = m_planeCamera.getB();
        double uz = m_planeCamera.getC();
        double D = m_planeCamera.getD();

        // Features
        A = -ux / D;
        B = -uy / D;
        C = -uz / D;

        size_t cpt = 0;
        if (point_cloud_face.size() / 3 >= 2) {
          const double *ptr_point_cloud = &point_cloud_face[0];
          const __m128d vA = _mm_set1_pd(A);
          const __m128d vB = _mm_set1_pd(B);
          const __m128d vC = _mm_set1_pd(C);
          const __m128d vones = _mm_set1_pd(1.0);

          double *ptr_residues = &residues[0];

          for (; cpt <= point_cloud_face.size() - 6; cpt += 6, ptr_point_cloud += 6, ptr_residues += 2) {
            const __m128d vxi = _mm_loadu_pd(ptr_point_cloud);
            const __m128d vyi = _mm_loadu_pd(ptr_point_cloud + 2);
            const __m128d vZi = _mm_loadu_pd(ptr_point_cloud + 4);
            const __m128d vinvZi = _mm_div_pd(vones, vZi);

            const __m128d tmp =
                _mm_add_pd(_mm_add_pd(_mm_mul_pd(vA, vxi), _mm_mul_pd(vB, vyi)), _mm_sub_pd(vC, vinvZi));
            _mm_storeu_pd(ptr_residues, tmp);
          }
        }

        for (; cpt < point_cloud_face.size(); cpt += 3) {
          double xi = point_cloud_face[cpt];
          double yi = point_cloud_face[cpt + 1];
          double Zi = point_cloud_face[cpt + 2];

          residues[cpt / 3] = (A * xi + B * yi + C - 1 / Zi);
        }
      }

      tukey_robust.MEstimator(residues, w, 1e-2);

      __m128d vsum_wi2_xi2 = _mm_setzero_pd();
      __m128d vsum_wi2_yi2 = _mm_setzero_pd();
      __m128d vsum_wi2 = _mm_setzero_pd();
      __m128d vsum_wi2_xi_yi = _mm_setzero_pd();
      __m128d vsum_wi2_xi = _mm_setzero_pd();
      __m128d vsum_wi2_yi = _mm_setzero_pd();

      __m128d vsum_wi2_xi_Zi = _mm_setzero_pd();
      __m128d vsum_wi2_yi_Zi = _mm_setzero_pd();
      __m128d vsum_wi2_Zi = _mm_setzero_pd();

      // Estimate A, B, C
      size_t cpt = 0;
      if (point_cloud_face.size() / 3 >= 2) {
        const double *ptr_point_cloud = &point_cloud_face[0];
        double *ptr_w = &w[0];

        const __m128d vones = _mm_set1_pd(1.0);

        for (; cpt <= point_cloud_face.size() - 6; cpt += 6, ptr_point_cloud += 6, ptr_w += 2) {
          const __m128d vwi2 = _mm_mul_pd(_mm_loadu_pd(ptr_w), _mm_loadu_pd(ptr_w));

          const __m128d vxi = _mm_loadu_pd(ptr_point_cloud);
          const __m128d vyi = _mm_loadu_pd(ptr_point_cloud + 2);
          const __m128d vZi = _mm_loadu_pd(ptr_point_cloud + 4);
          const __m128d vinvZi = _mm_div_pd(vones, vZi);

          vsum_wi2_xi2 = _mm_add_pd(vsum_wi2_xi2, _mm_mul_pd(vwi2, _mm_mul_pd(vxi, vxi)));
          vsum_wi2_yi2 = _mm_add_pd(vsum_wi2_yi2, _mm_mul_pd(vwi2, _mm_mul_pd(vyi, vyi)));
          vsum_wi2 = _mm_add_pd(vsum_wi2, vwi2);
          vsum_wi2_xi_yi = _mm_add_pd(vsum_wi2_xi_yi, _mm_mul_pd(vwi2, _mm_mul_pd(vxi, vyi)));
          vsum_wi2_xi = _mm_add_pd(vsum_wi2_xi, _mm_mul_pd(vwi2, vxi));
          vsum_wi2_yi = _mm_add_pd(vsum_wi2_yi, _mm_mul_pd(vwi2, vyi));

          const __m128d vwi2_invZi = _mm_mul_pd(vwi2, vinvZi);
          vsum_wi2_xi_Zi = _mm_add_pd(vsum_wi2_xi_Zi, _mm_mul_pd(vxi, vwi2_invZi));
          vsum_wi2_yi_Zi = _mm_add_pd(vsum_wi2_yi_Zi, _mm_mul_pd(vyi, vwi2_invZi));
          vsum_wi2_Zi = _mm_add_pd(vsum_wi2_Zi, vwi2_invZi);
        }
      }

      double vtmp[2];
      _mm_storeu_pd(vtmp, vsum_wi2_xi2);
      double sum_wi2_xi2 = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_yi2);
      double sum_wi2_yi2 = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2);
      double sum_wi2 = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_xi_yi);
      double sum_wi2_xi_yi = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_xi);
      double sum_wi2_xi = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_yi);
      double sum_wi2_yi = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_xi_Zi);
      double sum_wi2_xi_Zi = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_yi_Zi);
      double sum_wi2_yi_Zi = vtmp[0] + vtmp[1];

      _mm_storeu_pd(vtmp, vsum_wi2_Zi);
      double sum_wi2_Zi = vtmp[0] + vtmp[1];

      for (; cpt < point_cloud_face.size(); cpt += 3) {
        double wi2 = w[cpt / 3] * w[cpt / 3];

        double xi = point_cloud_face[cpt];
        double yi = point_cloud_face[cpt + 1];
        double Zi = point_cloud_face[cpt + 2];
        double invZi = 1.0 / Zi;

        sum_wi2_xi2 += wi2 * xi * xi;
        sum_wi2_yi2 += wi2 * yi * yi;
        sum_wi2 += wi2;
        sum_wi2_xi_yi += wi2 * xi * yi;
        sum_wi2_xi += wi2 * xi;
        sum_wi2_yi += wi2 * yi;

        sum_wi2_xi_Zi += wi2 * xi * invZi;
        sum_wi2_yi_Zi += wi2 * yi * invZi;
        sum_wi2_Zi += wi2 * invZi;
      }

      ATA_3x3[0] = sum_wi2_xi2;
      ATA_3x3[1] = sum_wi2_xi_yi;
      ATA_3x3[2] = sum_wi2_xi;
      ATA_3x3[3] = sum_wi2_xi_yi;
      ATA_3x3[4] = sum_wi2_yi2;
      ATA_3x3[5] = sum_wi2_yi;
      ATA_3x3[6] = sum_wi2_xi;
      ATA_3x3[7] = sum_wi2_yi;
      ATA_3x3[8] = sum_wi2;

      Mat33<double> minv = ATA_3x3.inverse();

      A = minv[0] * sum_wi2_xi_Zi + minv[1] * sum_wi2_yi_Zi + minv[2] * sum_wi2_Zi;
      B = minv[3] * sum_wi2_xi_Zi + minv[4] * sum_wi2_yi_Zi + minv[5] * sum_wi2_Zi;
      C = minv[6] * sum_wi2_xi_Zi + minv[7] * sum_wi2_yi_Zi + minv[8] * sum_wi2_Zi;

      cpt = 0;

      // Compute error
      prev_error = error;
      error = 0.0;

      __m128d verror = _mm_set1_pd(0.0);
      if (point_cloud_face.size() / 3 >= 2) {
        const double *ptr_point_cloud = &point_cloud_face[0];
        const __m128d vA = _mm_set1_pd(A);
        const __m128d vB = _mm_set1_pd(B);
        const __m128d vC = _mm_set1_pd(C);
        const __m128d vones = _mm_set1_pd(1.0);

        double *ptr_residues = &residues[0];

        for (; cpt <= point_cloud_face.size() - 6; cpt += 6, ptr_point_cloud += 6, ptr_residues += 2) {
          const __m128d vxi = _mm_loadu_pd(ptr_point_cloud);
          const __m128d vyi = _mm_loadu_pd(ptr_point_cloud + 2);
          const __m128d vZi = _mm_loadu_pd(ptr_point_cloud + 4);
          const __m128d vinvZi = _mm_div_pd(vones, vZi);

          const __m128d tmp = _mm_add_pd(_mm_add_pd(_mm_mul_pd(vA, vxi), _mm_mul_pd(vB, vyi)), _mm_sub_pd(vC, vinvZi));
          verror = _mm_add_pd(verror, _mm_mul_pd(tmp, tmp));

          _mm_storeu_pd(ptr_residues, tmp);
        }
      }

      _mm_storeu_pd(vtmp, verror);
      error = vtmp[0] + vtmp[1];

      for (size_t idx = cpt; idx < point_cloud_face.size(); idx += 3) {
        double xi = point_cloud_face[idx];
        double yi = point_cloud_face[idx + 1];
        double Zi = point_cloud_face[idx + 2];

        error += vpMath::sqr(A * xi + B * yi + C - 1 / Zi);
        residues[idx / 3] = (A * xi + B * yi + C - 1 / Zi);
      }

      error /= point_cloud_face.size() / 3;

      iter++;
    } // while ( std::fabs(error - prev_error) > 1e-6 && (iter < max_iter) )
#endif
  } else {
    while (std::fabs(error - prev_error) > 1e-6 && (iter < max_iter)) {
      if (iter == 0) {
        // Transform the plane equation for the current pose
        m_planeCamera = m_planeObject;
        m_planeCamera.changeFrame(cMo);

        double ux = m_planeCamera.getA();
        double uy = m_planeCamera.getB();
        double uz = m_planeCamera.getC();
        double D = m_planeCamera.getD();

        // Features
        A = -ux / D;
        B = -uy / D;
        C = -uz / D;

        for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
          double xi = point_cloud_face[3 * i];
          double yi = point_cloud_face[3 * i + 1];
          double Zi = point_cloud_face[3 * i + 2];

          residues[i] = (A * xi + B * yi + C - 1 / Zi);
        }
      }

      tukey_robust.MEstimator(residues, w, 1e-2);

      // Estimate A, B, C
      double sum_wi2_xi2 = 0.0, sum_wi2_yi2 = 0.0, sum_wi2 = 0.0;
      double sum_wi2_xi_yi = 0.0, sum_wi2_xi = 0.0, sum_wi2_yi = 0.0;

      double sum_wi2_xi_Zi = 0.0, sum_wi2_yi_Zi = 0.0, sum_wi2_Zi = 0.0;

      for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
        double wi2 = w[i] * w[i];

        double xi = point_cloud_face[3 * i];
        double yi = point_cloud_face[3 * i + 1];
        double Zi = point_cloud_face[3 * i + 2];
        double invZi = 1 / Zi;

        sum_wi2_xi2 += wi2 * xi * xi;
        sum_wi2_yi2 += wi2 * yi * yi;
        sum_wi2 += wi2;
        sum_wi2_xi_yi += wi2 * xi * yi;
        sum_wi2_xi += wi2 * xi;
        sum_wi2_yi += wi2 * yi;

        sum_wi2_xi_Zi += wi2 * xi * invZi;
        sum_wi2_yi_Zi += wi2 * yi * invZi;
        sum_wi2_Zi += wi2 * invZi;
      }

      ATA_3x3[0] = sum_wi2_xi2;
      ATA_3x3[1] = sum_wi2_xi_yi;
      ATA_3x3[2] = sum_wi2_xi;
      ATA_3x3[3] = sum_wi2_xi_yi;
      ATA_3x3[4] = sum_wi2_yi2;
      ATA_3x3[5] = sum_wi2_yi;
      ATA_3x3[6] = sum_wi2_xi;
      ATA_3x3[7] = sum_wi2_yi;
      ATA_3x3[8] = sum_wi2;

      Mat33<double> minv = ATA_3x3.inverse();

      A = minv[0] * sum_wi2_xi_Zi + minv[1] * sum_wi2_yi_Zi + minv[2] * sum_wi2_Zi;
      B = minv[3] * sum_wi2_xi_Zi + minv[4] * sum_wi2_yi_Zi + minv[5] * sum_wi2_Zi;
      C = minv[6] * sum_wi2_xi_Zi + minv[7] * sum_wi2_yi_Zi + minv[8] * sum_wi2_Zi;

      prev_error = error;
      error = 0.0;

      // Compute error
      for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
        double xi = point_cloud_face[3 * i];
        double yi = point_cloud_face[3 * i + 1];
        double Zi = point_cloud_face[3 * i + 2];

        error += vpMath::sqr(A * xi + B * yi + C - 1 / Zi);
        residues[i] = (A * xi + B * yi + C - 1 / Zi);
      }

      error /= point_cloud_face.size() / 3;

      iter++;
    } // while ( std::fabs(error - prev_error) > 1e-6 && (iter < max_iter) )
  }

  x_estimated.resize(3, false);
  x_estimated[0] = A;
  x_estimated[1] = B;
  x_estimated[2] = C;
}

void vpMbtFaceDepthNormal::estimatePlaneEquationSVD(const std::vector<double> &point_cloud_face,
                                                    const vpHomogeneousMatrix &cMo,
                                                    vpColVector &plane_equation_estimated, vpColVector &centroid)
{
  const unsigned int max_iter = 10;
  double prev_error = 1e3;
  double error = 1e3 - 1;

  std::vector<double> weights(point_cloud_face.size() / 3, 1.0);
  std::vector<double> residues(point_cloud_face.size() / 3);
  vpMatrix M((unsigned int)(point_cloud_face.size() / 3), 3);
  vpMbtTukeyEstimator<double> tukey;
  vpColVector normal;

  for (unsigned int iter = 0; iter < max_iter && std::fabs(error - prev_error) > 1e-6; iter++) {
    if (iter != 0) {
      tukey.MEstimator(residues, weights, 1e-4);
    } else {
      // Transform the plane equation for the current pose
      m_planeCamera = m_planeObject;
      m_planeCamera.changeFrame(cMo);

      double A = m_planeCamera.getA();
      double B = m_planeCamera.getB();
      double C = m_planeCamera.getC();
      double D = m_planeCamera.getD();

      // Compute distance point to estimated plane
      for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
        residues[i] = std::fabs(A * point_cloud_face[3 * i] + B * point_cloud_face[3 * i + 1] +
                                C * point_cloud_face[3 * i + 2] + D) /
                      sqrt(A * A + B * B + C * C);
      }

      tukey.MEstimator(residues, weights, 1e-4);
      plane_equation_estimated.resize(4, false);
    }

    // Compute centroid
    double centroid_x = 0.0, centroid_y = 0.0, centroid_z = 0.0;
    double total_w = 0.0;

    for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
      centroid_x += weights[i] * point_cloud_face[3 * i];
      centroid_y += weights[i] * point_cloud_face[3 * i + 1];
      centroid_z += weights[i] * point_cloud_face[3 * i + 2];
      total_w += weights[i];
    }

    centroid_x /= total_w;
    centroid_y /= total_w;
    centroid_z /= total_w;

    // Minimization
    for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
      M[(unsigned int)i][0] = weights[i] * (point_cloud_face[3 * i] - centroid_x);
      M[(unsigned int)i][1] = weights[i] * (point_cloud_face[3 * i + 1] - centroid_y);
      M[(unsigned int)i][2] = weights[i] * (point_cloud_face[3 * i + 2] - centroid_z);
    }

    vpMatrix J = M.t() * M;

    vpColVector W;
    vpMatrix V;
    J.svd(W, V);

    double smallestSv = W[0];
    unsigned int indexSmallestSv = 0;
    for (unsigned int i = 1; i < W.size(); i++) {
      if (W[i] < smallestSv) {
        smallestSv = W[i];
        indexSmallestSv = i;
      }
    }

    normal = V.getCol(indexSmallestSv);

    // Compute plane equation
    double A = normal[0], B = normal[1], C = normal[2];
    double D = -(A * centroid_x + B * centroid_y + C * centroid_z);

    // Update plane equation
    plane_equation_estimated[0] = A;
    plane_equation_estimated[1] = B;
    plane_equation_estimated[2] = C;
    plane_equation_estimated[3] = D;

    // Compute error points to estimated plane
    prev_error = error;
    error = 0.0;
    for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
      residues[i] = std::fabs(A * point_cloud_face[3 * i] + B * point_cloud_face[3 * i + 1] +
                              C * point_cloud_face[3 * i + 2] + D) /
                    sqrt(A * A + B * B + C * C);
      error += residues[i] * residues[i];
    }
    error /= sqrt(error / total_w);
  }

  // Update final weights
  tukey.MEstimator(residues, weights, 1e-4);

  // Update final centroid
  centroid.resize(3, false);
  double total_w = 0.0;

  for (size_t i = 0; i < point_cloud_face.size() / 3; i++) {
    centroid[0] += weights[i] * point_cloud_face[3 * i];
    centroid[1] += weights[i] * point_cloud_face[3 * i + 1];
    centroid[2] += weights[i] * point_cloud_face[3 * i + 2];
    total_w += weights[i];
  }

  centroid[0] /= total_w;
  centroid[1] /= total_w;
  centroid[2] /= total_w;

  // Compute final plane equation
  double A = normal[0], B = normal[1], C = normal[2];
  double D = -(A * centroid[0] + B * centroid[1] + C * centroid[2]);

  // Update final plane equation
  plane_equation_estimated[0] = A;
  plane_equation_estimated[1] = B;
  plane_equation_estimated[2] = C;
  plane_equation_estimated[3] = D;
}

bool vpMbtFaceDepthNormal::samePoint(const vpPoint &P1, const vpPoint &P2) const
{
  double dx = fabs(P1.get_oX() - P2.get_oX());
  double dy = fabs(P1.get_oY() - P2.get_oY());
  double dz = fabs(P1.get_oZ() - P2.get_oZ());

  if (dx <= std::numeric_limits<double>::epsilon() && dy <= std::numeric_limits<double>::epsilon() &&
      dz <= std::numeric_limits<double>::epsilon())
    return true;
  else
    return false;
}

void vpMbtFaceDepthNormal::setCameraParameters(const vpCameraParameters &camera)
{
  m_cam = camera;

  for (std::vector<vpMbtDistanceLine *>::const_iterator it = m_listOfFaceLines.begin(); it != m_listOfFaceLines.end();
       ++it) {
    (*it)->setCameraParameters(camera);
  }
}

void vpMbtFaceDepthNormal::setScanLineVisibilityTest(const bool v)
{
  m_useScanLine = v;

  for (std::vector<vpMbtDistanceLine *>::const_iterator it = m_listOfFaceLines.begin(); it != m_listOfFaceLines.end();
       ++it) {
    (*it)->useScanLine = v;
  }
}