PCA in PCL

/////////////////////////////////////////////////////////////////////////////////////////
template bool
pcl::PCA::initCompute ()
{
  if(!Base::initCompute ())
  {
    PCL_THROW_EXCEPTION (InitFailedException, "[pcl::PCA::initCompute] failed");
    return (false);
  }
  if(indices_->size () < 3)
  {
    PCL_THROW_EXCEPTION (InitFailedException, "[pcl::PCA::initCompute] number of points < 3");
    return (false);
  }

  // Compute mean
  mean_ = Eigen::Vector4f::Zero ();
  compute3DCentroid (*input_, *indices_, mean_);
  // Compute demeanished cloud
  Eigen::MatrixXf cloud_demean;
  demeanPointCloud (*input_, *indices_, mean_, cloud_demean);
  assert (cloud_demean.cols () == int (indices_->size ()));
  // Compute the product cloud_demean * cloud_demean^T
  Eigen::Matrix3f alpha = cloud_demean.topRows<3> () * cloud_demean.topRows<3> ().transpose ();

  // Compute eigen vectors and values
  Eigen::SelfAdjointEigenSolver evd (alpha);
  // Organize eigenvectors and eigenvalues in ascendent order
  for (int i = 0; i < 3; ++i)
  {
    eigenvalues_[i] = evd.eigenvalues () [2-i];
    eigenvectors_.col (i) = evd.eigenvectors ().col (2-i);
  }
  // If not basis only then compute the coefficients

  if (!basis_only_)
    coefficients_ = eigenvectors_.transpose() * cloud_demean.topRows<3> ();
  compute_done_ = true;
  return (true);
}



from /opt/ros/fuerte/include/pcl-1.5/pcl/common/impl/pca.hpp

Eigenvalues of rotation matrix : 0~180 degrees

Eigenvalue의 의미를 보여주는 그래프. y축은 imaginary axis.

추가 1)

When an n×n rotation matrix, Q, does not include −1 as an eigenvalue, so that none of the planar rotations of which it is composed are 180° rotations, then Q+I is an invertible matrix. Most rotation matrices fit this description.

http://en.wikipedia.org/wiki/Rotation_matrix