Homography33.h

Go to the documentation of this file.

//-*-c++-*-

#ifndef HOMOGRAPHY33_H
#define HOMOGRAPHY33_H

#include <utility>

#include "Shared/fmat.h"

//! Compute 3x3 homography using Direct Linear Transform
/*
 *  y = Hx (y = image coordinates in homogeneous coordinates, H = 3x3
 *  homography matrix, x = homogeneous 2D world coordinates)
 *
 *  For each point correspondence, constrain y x Hx = 0 (where x is
 *  cross product). This means that they have the same direction, and
 *  ignores scale factor.
 *
 *  We rewrite this as Ah = 0, where h is the 9x1 column vector of the
 *  elements of H. Each point correspondence gives us 3 equations of
 *  rank 2. The solution h is the minimum right eigenvector of A,
 *  which we can obtain via SVD, USV' = A. h is the right-most column
 *  of V'.
 *
 *  We will actually maintain A'A internally, which is 9x9 regardless
 *  of how many correspondences we're given, and has the same
 *  eigenvectors as A.
 */
class Homography33 {
public:
  //! Constructor
  Homography33(const std::pair<float,float> &opticalCenter);

  //! Note that the returned H matrix does not reflect cxy.
  fmat::Matrix<3,3>& getH();

  const std::pair<float,float> getCXY() const { return cxy; }

  void addCorrespondence(float worldx, float worldy, float imagex, float imagey);

  void compute();

  std::pair<float,float> project(float worldx, float worldy);

private:
  std::pair<float,float> cxy;
  fmat::Matrix<9,9> fA;
  fmat::Matrix<3,3> H;
  bool valid;
};

#endif