mlesac.cpp

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/*
 * Copyright (c) 2008 Radu Bogdan Rusu <rusu -=- cs.tum.edu>
 *
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#include <cfloat>
#include <limits>
#include <door_handle_detector/sample_consensus/mlesac.h>
#include <door_handle_detector/geometry/statistics.h>

namespace sample_consensus
{

  MLESAC::MLESAC (SACModel *model, double threshold) : SAC (model)
  {
    this->threshold_      = threshold;
    // Desired probability of choosing at least one sample free from outliers
    this->probability_    = 0.99;
    // Maximum number of trials before we give up.
    this->max_iterations_ = 10000;

    // Max number of EM (Expectation Maximization) iterations
    this->iterations_EM_  = 3;
    this->iterations_     = 0;
  }


  MLESAC::MLESAC (SACModel* model) : SAC (model) { }


  bool
    MLESAC::computeModel (int debug)
  {
    iterations_ = 0;
    double d_best_penalty = DBL_MAX;

    double k = 1.0;

    std::vector<int> best_model;
    std::vector<int> best_inliers, inliers;
    std::vector<int> selection;
    std::vector<double> distances;

    int n_inliers_count = 0;

    // Compute sigma - remember to set threshold_ correctly !
    sigma_ = cloud_geometry::statistics::computeMedianAbsoluteDeviation (*sac_model_->getCloud (), *sac_model_->getIndices (), threshold_);
    if (debug)
      std::cerr << "[MLESAC::computeModel] Estimated sigma value : " << sigma_ << "." << std::endl;

    // Compute the bounding box diagonal: V = sqrt (sum (max(pointCloud) - min(pointCloud)^2))
    geometry_msgs::Point32 min_pt, max_pt;
    cloud_geometry::statistics::getMinMax (*sac_model_->getCloud (), *sac_model_->getIndices (), min_pt, max_pt);

    double v = sqrt ( (max_pt.x - min_pt.x) * (max_pt.x - min_pt.x) +
                      (max_pt.y - min_pt.y) * (max_pt.y - min_pt.y) +
                      (max_pt.z - min_pt.z) * (max_pt.z - min_pt.z)
                    );


    // Iterate
    while (iterations_ < k)
    {
      // Get X samples which satisfy the model criteria
      sac_model_->getSamples (iterations_, selection);

      if (selection.size () == 0) break;

      // Search for inliers in the point cloud for the current plane model M
      sac_model_->computeModelCoefficients (selection);

      // Iterate through the 3d points and calculate the distances from them to the model
      sac_model_->getDistancesToModel (sac_model_->getModelCoefficients (), distances);
      if (distances.size () == 0 && k != 1.0)
      {
        iterations_ += 1;
        continue;
      }

      // Use Expectiation-Maximization to find out the right value for d_cur_penalty
      // ---[ Initial estimate for the gamma mixing parameter = 1/2
      double gamma = 0.5;
      double p_outlier_prob = 0;

      std::vector<double> p_inlier_prob (sac_model_->getIndices ()->size ());
      for (int j = 0; j < iterations_EM_; j++)
      {
        // Likelihood of a datum given that it is an inlier
        for (unsigned int i = 0; i < sac_model_->getIndices ()->size (); i++)
          p_inlier_prob[i] = gamma * exp (- (distances.at (i) * distances.at (i) ) / 2 * (sigma_ * sigma_) ) /
                             (sqrt (2 * M_PI) * sigma_);

        // Likelihood of a datum given that it is an outlier
        p_outlier_prob = (1 - gamma) / v;

        gamma = 0;
        for (unsigned int i = 0; i < sac_model_->getIndices ()->size (); i++)
          gamma += p_inlier_prob [i] / (p_inlier_prob[i] + p_outlier_prob);
        gamma /= sac_model_->getIndices ()->size ();
      }

      // Find the log likelihood of the model -L = -sum [log (pInlierProb + pOutlierProb)]
      double d_cur_penalty = 0;
      for (unsigned int i = 0; i < sac_model_->getIndices ()->size (); i++)
        d_cur_penalty += log (p_inlier_prob[i] + p_outlier_prob);
      d_cur_penalty = - d_cur_penalty;

      // Better match ?
      if (d_cur_penalty < d_best_penalty)
      {
        d_best_penalty = d_cur_penalty;
        best_model = selection;

        // Save the inliers
        best_inliers.resize (sac_model_->getIndices ()->size ());
        n_inliers_count = 0;
        for (unsigned int i = 0; i < sac_model_->getIndices ()->size (); i++)
        {
          if (distances[i] <= 2 * sigma_)
          {
            best_inliers[n_inliers_count] = sac_model_->getIndices ()->at (i);
            n_inliers_count++;
          }
        }
        best_inliers.resize (n_inliers_count);

        // Compute the k parameter (k=log(z)/log(1-w^n))
        double w = (double)((double)n_inliers_count / (double)sac_model_->getIndices ()->size ());
        double p_no_outliers = 1 - pow (w, (double)selection.size ());
        p_no_outliers = std::max (std::numeric_limits<double>::epsilon (), p_no_outliers);       // Avoid division by -Inf
        p_no_outliers = std::min (1 - std::numeric_limits<double>::epsilon (), p_no_outliers);   // Avoid division by 0
        k = log (1 - probability_) / log (p_no_outliers);
      }

      iterations_ += 1;
      if (debug > 1)
        std::cerr << "[MLESAC::computeModel] Trial " << iterations_ << " out of " << ceil (k) << ": best number of inliers so far is " << best_inliers.size () << "." << std::endl;
      if (iterations_ > max_iterations_)
      {
        if (debug > 0)
          std::cerr << "[MLESAC::computeModel] MSAC reached the maximum number of trials." << std::endl;
        break;
      }
    }

    if (best_model.size () != 0)
    {
      if (debug > 0)
        std::cerr << "[MLESAC::computeModel] Model found: " << best_inliers.size () << " inliers." << std::endl;
      sac_model_->setBestModel (best_model);
      sac_model_->setBestInliers (best_inliers);
      return (true);
    }
    else
      if (debug > 0)
        std::cerr << "[MLESAC::computeModel] Unable to find a solution!" << std::endl;
    return (false);
  }
}