geometric_alignment.h

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/**
 *  \file IMP/algebra/geometric_alignment.h
 *  \brief align sets of points.
 *
 *  Copyright 2007-2022 IMP Inventors. All rights reserved.
 */

#ifndef IMPALGEBRA_GEOMETRIC_ALIGNMENT_H
#define IMPALGEBRA_GEOMETRIC_ALIGNMENT_H

#include <IMP/algebra/algebra_config.h>
#include "Vector3D.h"
#include "SphereD.h"
#include "Rotation3D.h"
#include "Transformation3D.h"
#include "Transformation2D.h"
#include <IMP/check_macros.h>
#include <IMP/log.h>
#include <IMP/log_macros.h>

IMPALGEBRA_BEGIN_NAMESPACE

//! Compute the rigid transform bringing the first point set to the second
/** The points are assumed to be corresponding (that is, from[0] is aligned
    to to[0] etc.). The alignment computed is that which minimizes the
    sum of squared distances between corresponding points. This uses the
    Kabsch algorithm.

    \return the
    \f[ \textit{argmin}_T
    \sum \left|T\left(f\left[i\right]\right)-t[i]\right|^2 \f]

    If the point sets lie in a 1 or 2 dimensional subspace,
    the alignment algorithm
    is unstable and not guaranteed to work. A warning is printed in this
    case.

    \genericgeometry

    \see Transformation3D
    \see Vector3D
 */
template <class Vector3DsOrXYZs0, class Vector3DsOrXYZs1>
inline IMP::algebra::Transformation3D
get_transformation_aligning_first_to_second(const Vector3DsOrXYZs0& source,
                                            const Vector3DsOrXYZs1& target) {
  using algebra::get_vector_geometry;
  IMP_INTERNAL_CHECK(source.size() == target.size(), "sizes don't match");
  IMP_INTERNAL_CHECK(source.size() > 0, "Points are needed");
  // compute the centroid of the points and transform
  // point sets so that their centroids coincide

  Vector3D center_source(0, 0, 0), center_target(0, 0, 0);
  for (unsigned int i = 0; i < source.size(); ++i) {
    // double x= p_it->x();
    center_source += get_vector_geometry(source[i]);
    center_target += get_vector_geometry(target[i]);
    IMP_LOG_VERBOSE(i << ": (" << get_vector_geometry(source[i]) << ") ("
                      << get_vector_geometry(target[i]) << ")\n");
  }
  center_source = center_source / source.size();
  center_target = center_target / target.size();

  IMP_LOG_VERBOSE("Centers are (" << center_source << ") (" << center_target
                                  << ")\n");
  Vector3Ds shifted_source(source.size()), shifted_target(target.size());
  for (unsigned int i = 0; i < source.size(); ++i) {
    shifted_source[i] = get_vector_geometry(source[i]) - center_source;
    shifted_target[i] = get_vector_geometry(target[i]) - center_target;
  }

  // covariance matrix
  Eigen::Matrix3d H;
  for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 3; j++) {
      H(i, j) = 0;
    }
  }
  for (unsigned int i = 0; i < source.size(); i++) {
    for (int j = 0; j < 3; j++) {
      for (int k = 0; k < 3; k++) {
        H(j, k) += shifted_source[i][j] * shifted_target[i][k];
      }
    }
  }

  IMP_LOG_VERBOSE("H is " << H << std::endl);
  Eigen::JacobiSVD<Eigen::Matrix3d> svd =
      H.jacobiSvd(Eigen::ComputeFullV | Eigen::ComputeFullU);
  Eigen::Matrix3d U = svd.matrixU(), V = svd.matrixV();
  Eigen::Vector3d SV = svd.singularValues();
  IMP_LOG_VERBOSE("SVD is " << U << std::endl << V << std::endl);

  double det = SV[0] * SV[1] * SV[2];
  IMP_IF_CHECK(USAGE) {
    if (det < .00001) {
      IMP_LOG_TERSE("SOURCE:\n");
      for (unsigned int i = 0; i < source.size(); ++i) {
        IMP_LOG_TERSE(source[i] << std::endl);
      }
      IMP_LOG_TERSE("TO:\n");
      for (unsigned int i = 0; i < target.size(); ++i) {
        IMP_LOG_TERSE(target[i] << std::endl);
      }
      IMP_LOG_TERSE(H);
      IMP_WARN("Degenerate point set. I may not be able to align them."
               << std::endl);
    }
  }

  IMP_IF_LOG(VERBOSE) {
    Eigen::Matrix3d Sigma = Eigen::Matrix3d::Zero();

    for (int i = 0; i < 3; ++i) {
      Sigma(i, i) = SV[i];
    }

    IMP_LOG_VERBOSE("Reconstructed is " << U * Sigma * V.transpose()
                                        << std::endl);
  }

  // the rotation matrix is R = VU^T
  Eigen::Matrix3d rot = V * U.transpose();

  // check for reflection
  if (rot.determinant() < 0) {
    IMP_LOG_VERBOSE("Flipping matrix" << std::endl);
    Eigen::Matrix3d S = Eigen::Matrix3d::Zero();
    S(0, 0) = S(1, 1) = 1;
    S(2, 2) = -1;
    rot = V * S * U.transpose();
  }

  IMP_LOG_VERBOSE("Rotation matrix is " << rot << std::endl);

  Rotation3D rotation = get_rotation_from_matrix(rot);
  IMP_LOG_VERBOSE("Rotation is " << rotation << std::endl);
  Vector3D translation = center_target - rotation.get_rotated(center_source);

  Transformation3D ret(rotation, translation);
  return ret;
}

//! Builds the transformation required to obtain a set of points from
//! the first one
/**
  \note The function assumes that the relative distances between points
  are conserved.
**/
IMPALGEBRAEXPORT Transformation2D
    get_transformation_aligning_pair(const Vector2Ds& set_from,
                                     const Vector2Ds& set_to);

// implemented in Transformation2D

IMPALGEBRA_END_NAMESPACE

#endif /* IMPALGEBRA_GEOMETRIC_ALIGNMENT_H */