sac_model_sphere.hpp

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#ifndef PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_SPHERE_H_
#define PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_SPHERE_H_
 
#include <unsupported/Eigen/NonLinearOptimization> // for LevenbergMarquardt
#include <pcl/sample_consensus/sac_model_sphere.h>
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelSphere<PointT>::isSampleGood (const Indices &samples) const
{
  if (samples.size () != sample_size_)
  {
    PCL_ERROR ("[pcl::SampleConsensusModelSphere::isSampleGood] Wrong number of samples (is %lu, should be %lu)!\n", samples.size (), sample_size_);
    return (false);
  }
  return (true);
}
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelSphere<PointT>::computeModelCoefficients (
      const Indices &samples, Eigen::VectorXf &model_coefficients) const
{
  // Need 4 samples
  if (samples.size () != sample_size_)
  {
    PCL_ERROR ("[pcl::SampleConsensusModelSphere::computeModelCoefficients] Invalid set of samples given (%lu)!\n", samples.size ());
    return (false);
  }
 
  // TODO maybe find a more stable algorithm for this?
  Eigen::Matrix4d temp;
  for (int i = 0; i < 4; i++)
  {
    temp (i, 0) = (*input_)[samples[i]].x;
    temp (i, 1) = (*input_)[samples[i]].y;
    temp (i, 2) = (*input_)[samples[i]].z;
    temp (i, 3) = 1;
  }
  const double m11 = temp.determinant ();
  if (m11 == 0)
  {
    return (false);             // the points don't define a sphere!
  }
 
  for (int i = 0; i < 4; ++i)
  {
    temp (i, 0) = ((*input_)[samples[i]].x) * ((*input_)[samples[i]].x) +
                  ((*input_)[samples[i]].y) * ((*input_)[samples[i]].y) +
                  ((*input_)[samples[i]].z) * ((*input_)[samples[i]].z);
  }
  const double m12 = temp.determinant ();
 
  for (int i = 0; i < 4; ++i)
  {
    temp (i, 1) = temp (i, 0);
    temp (i, 0) = (*input_)[samples[i]].x;
  }
  const double m13 = temp.determinant ();
 
  for (int i = 0; i < 4; ++i)
  {
    temp (i, 2) = temp (i, 1);
    temp (i, 1) = (*input_)[samples[i]].y;
  }
  const double m14 = temp.determinant ();
 
  for (int i = 0; i < 4; ++i)
  {
    temp (i, 0) = temp (i, 2);
    temp (i, 1) = (*input_)[samples[i]].x;
    temp (i, 2) = (*input_)[samples[i]].y;
    temp (i, 3) = (*input_)[samples[i]].z;
  }
  const double m15 = temp.determinant ();
 
  // Center (x , y, z)
  model_coefficients.resize (model_size_);
  model_coefficients[0] = 0.5f * m12 / m11;
  model_coefficients[1] = 0.5f * m13 / m11;
  model_coefficients[2] = 0.5f * m14 / m11;
  // Radius
  model_coefficients[3] = std::sqrt (model_coefficients[0] * model_coefficients[0] +
                                     model_coefficients[1] * model_coefficients[1] +
                                     model_coefficients[2] * model_coefficients[2] - m15 / m11);
 
  PCL_DEBUG ("[pcl::SampleConsensusModelSphere::computeModelCoefficients] Model is (%g,%g,%g,%g)\n",
             model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3]);
  return (true);
}
 
#define AT(POS) ((*input_)[(*indices_)[(POS)]])
 
#ifdef __AVX__
// This function computes the squared distances (i.e. the distances without the square root) of 8 points to the center of the sphere
template <typename PointT> inline __m256 pcl::SampleConsensusModelSphere<PointT>::sqr_dist8 (const std::size_t i, const __m256 a_vec, const __m256 b_vec, const __m256 c_vec) const
{
  const __m256 tmp1 = _mm256_sub_ps (_mm256_set_ps (AT(i  ).x, AT(i+1).x, AT(i+2).x, AT(i+3).x, AT(i+4).x, AT(i+5).x, AT(i+6).x, AT(i+7).x), a_vec);
  const __m256 tmp2 = _mm256_sub_ps (_mm256_set_ps (AT(i  ).y, AT(i+1).y, AT(i+2).y, AT(i+3).y, AT(i+4).y, AT(i+5).y, AT(i+6).y, AT(i+7).y), b_vec);
  const __m256 tmp3 = _mm256_sub_ps (_mm256_set_ps (AT(i  ).z, AT(i+1).z, AT(i+2).z, AT(i+3).z, AT(i+4).z, AT(i+5).z, AT(i+6).z, AT(i+7).z), c_vec);
  return _mm256_add_ps (_mm256_add_ps (_mm256_mul_ps (tmp1, tmp1), _mm256_mul_ps (tmp2, tmp2)), _mm256_mul_ps(tmp3, tmp3));
}
#endif // ifdef __AVX__
 
#ifdef __SSE__
// This function computes the squared distances (i.e. the distances without the square root) of 4 points to the center of the sphere
template <typename PointT> inline __m128 pcl::SampleConsensusModelSphere<PointT>::sqr_dist4 (const std::size_t i, const __m128 a_vec, const __m128 b_vec, const __m128 c_vec) const
{
  const __m128 tmp1 = _mm_sub_ps (_mm_set_ps (AT(i  ).x, AT(i+1).x, AT(i+2).x, AT(i+3).x), a_vec);
  const __m128 tmp2 = _mm_sub_ps (_mm_set_ps (AT(i  ).y, AT(i+1).y, AT(i+2).y, AT(i+3).y), b_vec);
  const __m128 tmp3 = _mm_sub_ps (_mm_set_ps (AT(i  ).z, AT(i+1).z, AT(i+2).z, AT(i+3).z), c_vec);
  return _mm_add_ps (_mm_add_ps (_mm_mul_ps (tmp1, tmp1), _mm_mul_ps (tmp2, tmp2)), _mm_mul_ps(tmp3, tmp3));
}
#endif // ifdef __SSE__
 
#undef AT
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelSphere<PointT>::getDistancesToModel (
      const Eigen::VectorXf &model_coefficients, std::vector<double> &distances) const
{
  // Check if the model is valid given the user constraints
  if (!isModelValid (model_coefficients))
  {
    distances.clear ();
    return;
  }
  distances.resize (indices_->size ());
 
  const Eigen::Vector3f center (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
  // Iterate through the 3d points and calculate the distances from them to the sphere
  for (std::size_t i = 0; i < indices_->size (); ++i)
  {
    // Calculate the distance from the point to the sphere as the difference between
    //dist(point,sphere_origin) and sphere_radius
    distances[i] = std::abs (((*input_)[(*indices_)[i]].getVector3fMap () - center).norm () - model_coefficients[3]);
  }
}
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelSphere<PointT>::selectWithinDistance (
      const Eigen::VectorXf &model_coefficients, const double threshold, Indices &inliers)
{
  // Check if the model is valid given the user constraints
  if (!isModelValid (model_coefficients))
  {
    inliers.clear ();
    return;
  }
 
  inliers.clear ();
  error_sqr_dists_.clear ();
  inliers.reserve (indices_->size ());
  error_sqr_dists_.reserve (indices_->size ());
 
  const float sqr_inner_radius = (model_coefficients[3] <= threshold ? 0.0f : (model_coefficients[3] - threshold) * (model_coefficients[3] - threshold));
  const float sqr_outer_radius = (model_coefficients[3] + threshold) * (model_coefficients[3] + threshold);
  const Eigen::Vector3f center (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
  // Iterate through the 3d points and calculate the distances from them to the sphere
  for (std::size_t i = 0; i < indices_->size (); ++i)
  {
    // To avoid sqrt computation: consider one larger sphere (radius + threshold) and one smaller sphere (radius - threshold).
    // Valid if point is in larger sphere, but not in smaller sphere.
    const float sqr_dist = ((*input_)[(*indices_)[i]].getVector3fMap () - center).squaredNorm ();
    if ((sqr_dist <= sqr_outer_radius) && (sqr_dist >= sqr_inner_radius))
    {
      // Returns the indices of the points whose distances are smaller than the threshold
      inliers.push_back ((*indices_)[i]);
      // Only compute exact distance if necessary (if point is inlier)
      error_sqr_dists_.push_back (static_cast<double> (std::abs (std::sqrt (sqr_dist) - model_coefficients[3])));
    }
  }
}
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> std::size_t
pcl::SampleConsensusModelSphere<PointT>::countWithinDistance (
      const Eigen::VectorXf &model_coefficients, const double threshold) const
{
  // Check if the model is valid given the user constraints
  if (!isModelValid (model_coefficients))
    return (0);
 
#if defined (__AVX__) && defined (__AVX2__)
  return countWithinDistanceAVX (model_coefficients, threshold);
#elif defined (__SSE__) && defined (__SSE2__) && defined (__SSE4_1__)
  return countWithinDistanceSSE (model_coefficients, threshold);
#else
  return countWithinDistanceStandard (model_coefficients, threshold);
#endif
}
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> std::size_t
pcl::SampleConsensusModelSphere<PointT>::countWithinDistanceStandard (
      const Eigen::VectorXf &model_coefficients, const double threshold, std::size_t i) const
{
  std::size_t nr_p = 0;
  const float sqr_inner_radius = (model_coefficients[3] <= threshold ? 0.0f : (model_coefficients[3] - threshold) * (model_coefficients[3] - threshold));
  const float sqr_outer_radius = (model_coefficients[3] + threshold) * (model_coefficients[3] + threshold);
  const Eigen::Vector3f center (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
  // Iterate through the 3d points and calculate the distances from them to the sphere
  for (; i < indices_->size (); ++i)
  {
    // To avoid sqrt computation: consider one larger sphere (radius + threshold) and one smaller sphere (radius - threshold).
    // Valid if point is in larger sphere, but not in smaller sphere.
    const float sqr_dist = ((*input_)[(*indices_)[i]].getVector3fMap () - center).squaredNorm ();
    if ((sqr_dist <= sqr_outer_radius) && (sqr_dist >= sqr_inner_radius))
      nr_p++;
  }
  return (nr_p);
}
 
//////////////////////////////////////////////////////////////////////////
#if defined (__SSE__) && defined (__SSE2__) && defined (__SSE4_1__)
template <typename PointT> std::size_t
pcl::SampleConsensusModelSphere<PointT>::countWithinDistanceSSE (
      const Eigen::VectorXf &model_coefficients, const double threshold, std::size_t i) const
{
  std::size_t nr_p = 0;
  const __m128 a_vec = _mm_set1_ps (model_coefficients[0]);
  const __m128 b_vec = _mm_set1_ps (model_coefficients[1]);
  const __m128 c_vec = _mm_set1_ps (model_coefficients[2]);
  // To avoid sqrt computation: consider one larger sphere (radius + threshold) and one smaller sphere (radius - threshold). Valid if point is in larger sphere, but not in smaller sphere.
  const __m128 sqr_inner_radius = _mm_set1_ps ((model_coefficients[3] <= threshold ? 0.0 : (model_coefficients[3]-threshold)*(model_coefficients[3]-threshold)));
  const __m128 sqr_outer_radius = _mm_set1_ps ((model_coefficients[3]+threshold)*(model_coefficients[3]+threshold));
  __m128i res = _mm_set1_epi32(0); // This corresponds to nr_p: 4 32bit integers that, summed together, hold the number of inliers
  for (; (i + 4) <= indices_->size (); i += 4)
  {
    const __m128 sqr_dist = sqr_dist4 (i, a_vec, b_vec, c_vec);
    const __m128 mask = _mm_and_ps (_mm_cmplt_ps (sqr_inner_radius, sqr_dist), _mm_cmplt_ps (sqr_dist, sqr_outer_radius)); // The mask contains 1 bits if the corresponding points are inliers, else 0 bits
    res = _mm_add_epi32 (res, _mm_and_si128 (_mm_set1_epi32 (1), _mm_castps_si128 (mask))); // The latter part creates a vector with ones (as 32bit integers) where the points are inliers
    //const int res = _mm_movemask_ps (mask);
    //if (res & 1) nr_p++;
    //if (res & 2) nr_p++;
    //if (res & 4) nr_p++;
    //if (res & 8) nr_p++;
  }
  nr_p += _mm_extract_epi32 (res, 0);
  nr_p += _mm_extract_epi32 (res, 1);
  nr_p += _mm_extract_epi32 (res, 2);
  nr_p += _mm_extract_epi32 (res, 3);
 
  // Process the remaining points (at most 3)
  nr_p += countWithinDistanceStandard (model_coefficients, threshold, i);
  return (nr_p);
}
#endif
 
//////////////////////////////////////////////////////////////////////////
#if defined (__AVX__) && defined (__AVX2__)
template <typename PointT> std::size_t
pcl::SampleConsensusModelSphere<PointT>::countWithinDistanceAVX (
      const Eigen::VectorXf &model_coefficients, const double threshold, std::size_t i) const
{
  std::size_t nr_p = 0;
  const __m256 a_vec = _mm256_set1_ps (model_coefficients[0]);
  const __m256 b_vec = _mm256_set1_ps (model_coefficients[1]);
  const __m256 c_vec = _mm256_set1_ps (model_coefficients[2]);
  // To avoid sqrt computation: consider one larger sphere (radius + threshold) and one smaller sphere (radius - threshold). Valid if point is in larger sphere, but not in smaller sphere.
  const __m256 sqr_inner_radius = _mm256_set1_ps ((model_coefficients[3] <= threshold ? 0.0 : (model_coefficients[3]-threshold)*(model_coefficients[3]-threshold)));
  const __m256 sqr_outer_radius = _mm256_set1_ps ((model_coefficients[3]+threshold)*(model_coefficients[3]+threshold));
  __m256i res = _mm256_set1_epi32(0); // This corresponds to nr_p: 8 32bit integers that, summed together, hold the number of inliers
  for (; (i + 8) <= indices_->size (); i += 8)
  {
    const __m256 sqr_dist = sqr_dist8 (i, a_vec, b_vec, c_vec);
    const __m256 mask = _mm256_and_ps (_mm256_cmp_ps (sqr_inner_radius, sqr_dist, _CMP_LT_OQ), _mm256_cmp_ps (sqr_dist, sqr_outer_radius, _CMP_LT_OQ)); // The mask contains 1 bits if the corresponding points are inliers, else 0 bits
    res = _mm256_add_epi32 (res, _mm256_and_si256 (_mm256_set1_epi32 (1), _mm256_castps_si256 (mask))); // The latter part creates a vector with ones (as 32bit integers) where the points are inliers
    //const int res = _mm256_movemask_ps (mask);
    //if (res &   1) nr_p++;
    //if (res &   2) nr_p++;
    //if (res &   4) nr_p++;
    //if (res &   8) nr_p++;
    //if (res &  16) nr_p++;
    //if (res &  32) nr_p++;
    //if (res &  64) nr_p++;
    //if (res & 128) nr_p++;
  }
  nr_p += _mm256_extract_epi32 (res, 0);
  nr_p += _mm256_extract_epi32 (res, 1);
  nr_p += _mm256_extract_epi32 (res, 2);
  nr_p += _mm256_extract_epi32 (res, 3);
  nr_p += _mm256_extract_epi32 (res, 4);
  nr_p += _mm256_extract_epi32 (res, 5);
  nr_p += _mm256_extract_epi32 (res, 6);
  nr_p += _mm256_extract_epi32 (res, 7);
 
  // Process the remaining points (at most 7)
  nr_p += countWithinDistanceStandard (model_coefficients, threshold, i);
  return (nr_p);
}
#endif
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelSphere<PointT>::optimizeModelCoefficients (
      const Indices &inliers, const Eigen::VectorXf &model_coefficients, Eigen::VectorXf &optimized_coefficients) const
{
  optimized_coefficients = model_coefficients;
 
  // Needs a set of valid model coefficients
  if (!isModelValid (model_coefficients))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelSphere::optimizeModelCoefficients] Given model is invalid!\n");
    return;
  }
 
  // Need more than the minimum sample size to make a difference
  if (inliers.size () <= sample_size_)
  {
    PCL_ERROR ("[pcl::SampleConsensusModelSphere::optimizeModelCoefficients] Not enough inliers to refine/optimize the model's coefficients (%lu)! Returning the same coefficients.\n", inliers.size ());
    return;
  }
 
  OptimizationFunctor functor (this, inliers);
  Eigen::NumericalDiff<OptimizationFunctor> num_diff (functor);
  Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctor>, float> lm (num_diff);
  int info = lm.minimize (optimized_coefficients);
 
  // Compute the L2 norm of the residuals
  PCL_DEBUG ("[pcl::SampleConsensusModelSphere::optimizeModelCoefficients] LM solver finished with exit code %i, having a residual norm of %g. \nInitial solution: %g %g %g %g \nFinal solution: %g %g %g %g\n",
             info, lm.fvec.norm (), model_coefficients[0], model_coefficients[1], model_coefficients[2], model_coefficients[3], optimized_coefficients[0], optimized_coefficients[1], optimized_coefficients[2], optimized_coefficients[3]);
}
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> void
pcl::SampleConsensusModelSphere<PointT>::projectPoints (
      const Indices &inliers, const Eigen::VectorXf &model_coefficients, PointCloud &projected_points, bool copy_data_fields) const
{
  // Needs a valid set of model coefficients
  if (!isModelValid (model_coefficients))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelSphere::projectPoints] Given model is invalid!\n");
    return;
  }
 
  projected_points.header   = input_->header;
  projected_points.is_dense = input_->is_dense;
 
  // C : sphere center
  const Eigen::Vector3d C (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
  // r : radius
  const double r = model_coefficients[3];
 
  // Copy all the data fields from the input cloud to the projected one?
  if (copy_data_fields)
  {
    // Allocate enough space and copy the basics
    projected_points.resize (input_->size ());
    projected_points.width    = input_->width;
    projected_points.height   = input_->height;
 
    using FieldList = typename pcl::traits::fieldList<PointT>::type;
    // Iterate over each point
    for (std::size_t i = 0; i < projected_points.points.size (); ++i)
      // Iterate over each dimension
      pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> (input_->points[i], projected_points.points[i]));
 
    // Iterate through the 3d points and calculate the distances from them to the sphere
    for (const auto& inlier : inliers)
    {
      // what i have:
      // P : Sample Point
      const Eigen::Vector3d P (input_->points[inlier].x, input_->points[inlier].y, input_->points[inlier].z);
 
      const Eigen::Vector3d direction = (P - C).normalized();
 
      // K : Point on Sphere
      const Eigen::Vector3d K = C + r * direction;
 
      projected_points.points[inlier].x = static_cast<float> (K[0]);
      projected_points.points[inlier].y = static_cast<float> (K[1]);
      projected_points.points[inlier].z = static_cast<float> (K[2]);
    }
  }
  else
  {
    // Allocate enough space and copy the basics
    projected_points.resize (inliers.size ());
    projected_points.width    = static_cast<uint32_t> (inliers.size ());
    projected_points.height   = 1;
 
    using FieldList = typename pcl::traits::fieldList<PointT>::type;
    // Iterate over each point
    for (std::size_t i = 0; i < inliers.size (); ++i)
      // Iterate over each dimension
      pcl::for_each_type <FieldList> (NdConcatenateFunctor <PointT, PointT> (input_->points[inliers[i]], projected_points.points[i]));
 
    // Iterate through the 3d points and calculate the distances from them to the plane
    for (std::size_t i = 0; i < inliers.size (); ++i)
    {
      // what i have:
      // P : Sample Point
      const Eigen::Vector3d P (input_->points[inliers[i]].x, input_->points[inliers[i]].y, input_->points[inliers[i]].z);
 
      const Eigen::Vector3d direction = (P - C).normalized();
 
      // K : Point on Sphere
      const Eigen::Vector3d K = C + r * direction;
 
      projected_points.points[i].x = static_cast<float> (K[0]);
      projected_points.points[i].y = static_cast<float> (K[1]);
      projected_points.points[i].z = static_cast<float> (K[2]);
    }
  }
}
 
//////////////////////////////////////////////////////////////////////////
template <typename PointT> bool
pcl::SampleConsensusModelSphere<PointT>::doSamplesVerifyModel (
      const std::set<index_t> &indices, const Eigen::VectorXf &model_coefficients, const double threshold) const
{
  // Needs a valid model coefficients
  if (!isModelValid (model_coefficients))
  {
    PCL_ERROR ("[pcl::SampleConsensusModelSphere::doSamplesVerifyModel] Given model is invalid!\n");
    return (false);
  }
 
  const float sqr_inner_radius = (model_coefficients[3] <= threshold ? 0.0f : (model_coefficients[3] - threshold) * (model_coefficients[3] - threshold));
  const float sqr_outer_radius = (model_coefficients[3] + threshold) * (model_coefficients[3] + threshold);
  const Eigen::Vector3f center (model_coefficients[0], model_coefficients[1], model_coefficients[2]);
  for (const auto &index : indices)
  {
    // To avoid sqrt computation: consider one larger sphere (radius + threshold) and one smaller sphere (radius - threshold).
    // Valid if point is in larger sphere, but not in smaller sphere.
    const float sqr_dist = ((*input_)[index].getVector3fMap () - center).squaredNorm ();
    if ((sqr_dist > sqr_outer_radius) || (sqr_dist < sqr_inner_radius))
    {
      return (false);
    }
  }
 
  return (true);
}
 
#define PCL_INSTANTIATE_SampleConsensusModelSphere(T) template class PCL_EXPORTS pcl::SampleConsensusModelSphere<T>;
 
#endif    // PCL_SAMPLE_CONSENSUS_IMPL_SAC_MODEL_SPHERE_H_