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*
* $Id: vpHomography.h 4574 2014-01-09 08:48:51Z fspindle $
*
* This file is part of the ViSP software.
* Copyright (C) 2005 - 2014 by INRIA. All rights reserved.
*
* This software is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* ("GPL") version 2 as published by the Free Software Foundation.
* See the file LICENSE.txt at the root directory of this source
* distribution for additional information about the GNU GPL.
*
* For using ViSP with software that can not be combined with the GNU
* GPL, please contact INRIA about acquiring a ViSP Professional
* Edition License.
*
* See http://www.irisa.fr/lagadic/visp/visp.html for more information.
*
* This software was developed at:
* INRIA Rennes - Bretagne Atlantique
* Campus Universitaire de Beaulieu
* 35042 Rennes Cedex
* France
* http://www.irisa.fr/lagadic
*
* If you have questions regarding the use of this file, please contact
* INRIA at visp@inria.fr
*
* This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
* WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
*
* Description:
* Homography transformation.
*
* Authors:
* Muriel Pressigout
* Fabien Spindler
*
*****************************************************************************/
/*!
\file vpHomography.h
This file defines an homography transformation. This class aims to provide some
tools for homography computation.
*/
#ifndef vpHomography_hh
#define vpHomography_hh
#include <list>
#include <vector>
#include <visp/vpCameraParameters.h>
#include <visp/vpImagePoint.h>
#include <visp/vpHomogeneousMatrix.h>
#include <visp/vpPlane.h>
#ifdef VISP_BUILD_DEPRECATED_FUNCTIONS
# include <visp/vpList.h>
#endif
/*!
\class vpHomography
\ingroup Homography HomographyTransformation
\brief This class aims to compute the homography wrt.two images.
These two images are both described by a set of points. The 2 sets (one per
image) are sets of corresponding points : for a point in a image, there is
the corresponding point (image of the same 3D point) in the other image
points set. These 2 sets are the only data needed to compute the
homography. One method used is the one introduced by Ezio Malis during his
PhD \cite TheseMalis. A normalization is carried out on this points in order to improve the
conditioning of the problem, what leads to improve the stability of the
result.
Store and compute the homography such that
\f[
^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}
\f]
with
\f[ ^a{\bf H}_b = ^a{\bf R}_b + \frac{^a{\bf t}_b}{^bd}
{ ^b{\bf n}^T}
\f]
The \ref tutorial-homography explains how to use this class.
The example below shows also how to manipulate this class to first
compute a ground truth homography from camera poses, project pixel
coordinates points using an homography and lastly estimate an
homography from a subset of 4 matched points in frame a and frame b
respectively.
\code
#include <visp/vpHomogeneousMatrix.h>
#include <visp/vpHomography.h>
#include <visp/vpMath.h>
#include <visp/vpMeterPixelConversion.h>
int main()
{
// Initialize in the object frame the coordinates in meters of 4 points that
// belong to a planar object
vpPoint Po[4];
Po[0].setWorldCoordinates(-0.1, -0.1, 0);
Po[1].setWorldCoordinates( 0.2, -0.1, 0);
Po[2].setWorldCoordinates( 0.1, 0.1, 0);
Po[3].setWorldCoordinates(-0.1, 0.3, 0);
// Initialize the pose between camera frame a and object frame o
vpHomogeneousMatrix aMo(0, 0, 1, 0, 0, 0); // Camera is 1 meter far
// Initialize the pose between camera frame a and camera frame
// b. These two frames correspond for example to two successive
// camera positions
vpHomogeneousMatrix aMb(0.2, 0.1, 0, 0, 0, vpMath::rad(2));
// Compute the pose between camera frame b and object frame
vpHomogeneousMatrix bMo = aMb.inverse() * aMo;
// Initialize camera intrinsic parameters
vpCameraParameters cam;
// Compute the coordinates in pixels of the 4 object points in the
// camera frame a
vpPoint Pa[4];
std::vector<double> xa(4), ya(4); // Coordinates in pixels of the points in frame a
for(int i=0 ; i < 4 ; i++) {
Pa[i] = Po[i];
Pa[i].project(aMo); // Project the points from object frame to
// camera frame a
vpMeterPixelConversion::convertPoint(cam,
Pa[i].get_x(), Pa[i].get_y(),
xa[i], ya[i]);
}
// Compute the coordinates in pixels of the 4 object points in the
// camera frame b
vpPoint Pb[4];
std::vector<double> xb(4), yb(4); // Coordinates in pixels of the points in frame b
for(int i=0 ; i < 4 ; i++) {
Pb[i] = Po[i];
Pb[i].project(bMo); // Project the points from object frame to
// camera frame a
}
// Compute equation of the 3D plane containing the points in camera frame b
vpPlane bP(Pb[0], Pb[1], Pb[2]);
// Compute the corresponding ground truth homography
vpHomography aHb(aMb, bP);
std::cout << "Ground truth homography aHb: \n" << aHb<< std::endl;
// Compute the coordinates of the points in frame b using the ground
// truth homography and the coordinates of the points in frame a
vpHomography bHa = aHb.inverse();
for(int i = 0; i < 4 ; i++){
double inv_z = 1. / (bHa[2][0] * xa[i] + bHa[2][1] * ya[i] + bHa[2][2]);
xb[i] = (bHa[0][0] * xa[i] + bHa[0][1] * ya[i] + bHa[0][2]) * inv_z;
yb[i] = (bHa[1][0] * xa[i] + bHa[1][1] * ya[i] + bHa[1][2]) * inv_z;
}
// Estimate the homography from 4 points coordinates expressed in pixels
vpHomography::DLT(xb, yb, xa, ya, aHb, true);
aHb /= aHb[2][2]; // Apply a scale factor to have aHb[2][2] = 1
std::cout << "Estimated homography aHb: \n" << aHb<< std::endl;
}
\endcode
*/
class VISP_EXPORT vpHomography
{
public:
//! Data array
double *data;
private:
static const double sing_threshold; // = 0.0001;
static const double threshold_rotation;
static const double threshold_displacement;
vpHomogeneousMatrix aMb ;
// bool isplanar;
//! reference plane coordinates expressed in Rb
vpPlane bP ;
private:
//! build the homography from aMb and Rb
void build() ;
//! insert a rotation matrix
void insert(const vpHomogeneousMatrix &aRb) ;
//! insert a rotation matrix
void insert(const vpRotationMatrix &aRb) ;
//! insert a theta u vector (transformation into a rotation matrix)
void insert(const vpThetaUVector &tu) ;
//! insert a translation vector
void insert(const vpTranslationVector &atb) ;
//! insert a translation vector
void insert(const vpPlane &bP) ;
static void initRansac(unsigned int n,
double *xb, double *yb,
double *xa, double *ya,
vpColVector &x) ;
public:
vpHomography() ;
vpHomography(const vpHomography &H) ;
//! Construction from Translation and rotation and a plane
vpHomography(const vpHomogeneousMatrix &aMb,
const vpPlane &bP) ;
//! Construction from Translation and rotation and a plane
vpHomography(const vpRotationMatrix &aRb,
const vpTranslationVector &atb,
const vpPlane &bP) ;
//! Construction from Translation and rotation and a plane
vpHomography(const vpThetaUVector &tu,
const vpTranslationVector &atb,
const vpPlane &bP) ;
//! Construction from Translation and rotation and a plane
vpHomography(const vpPoseVector &arb,
const vpPlane &bP) ;
virtual ~vpHomography();
//! Construction from Translation and rotation and a plane
void buildFrom(const vpRotationMatrix &aRb,
const vpTranslationVector &atb,
const vpPlane &bP) ;
//! Construction from Translation and rotation and a plane
void buildFrom(const vpThetaUVector &tu,
const vpTranslationVector &atb,
const vpPlane &bP) ;
//! Construction from Translation and rotation and a plane
void buildFrom(const vpPoseVector &arb,
const vpPlane &bP) ;
//! Construction from homogeneous matrix and a plane
void buildFrom(const vpHomogeneousMatrix &aMb,
const vpPlane &bP) ;
void computeDisplacement(vpRotationMatrix &aRb,
vpTranslationVector &atb,
vpColVector &n) ;
void computeDisplacement(const vpColVector& nd,
vpRotationMatrix &aRb,
vpTranslationVector &atb,
vpColVector &n) ;
//! Return the number of rows of the homography matrix.
inline unsigned int getRows() const { return 3;}
//! Return the number of columns of the homography matrix.
inline unsigned int getCols() const { return 3; }
//! invert the homography
vpHomography inverse() const ;
//! invert the homography
void inverse(vpHomography &Hi) const;
//! Load an homography from a file
void load(std::ifstream &f) ;
//! Write elements Hij (usage : H[i][j] = x )
inline double *operator[](unsigned int i) { return &data[i*3]; }
//! Read elements Hij (usage : x = H[i][j] )
inline double *operator[](unsigned int i) const {return &data[i*3];}
// Multiplication by an homography
vpHomography operator*(const vpHomography &H) const;
// Multiplication by a scalar
vpHomography operator*(const double &v) const;
vpColVector operator*(const vpColVector &b) const;
// Division by a scalar
vpHomography operator/(const double &v) const;
vpHomography & operator/=(double v);
vpHomography & operator=(const vpHomography &H);
vpHomography & operator=(const vpMatrix &H);
//! Save an homography in a file
void save(std::ofstream &f) const ;
void setIdentity();
friend VISP_EXPORT std::ostream &operator << (std::ostream &s,const vpHomography &H);
static void DLT(const std::vector<double> &xb, const std::vector<double> &yb,
const std::vector<double> &xa, const std::vector<double> &ya ,
vpHomography &aHb,
bool normalization=true);
static void HLM(const std::vector<double> &xb, const std::vector<double> &yb,
const std::vector<double> &xa, const std::vector<double> &ya,
bool isplanar,
vpHomography &aHb) ;
static bool ransac(const std::vector<double> &xb, const std::vector<double> &yb,
const std::vector<double> &xa, const std::vector<double> &ya,
vpHomography &aHb,
std::vector<bool> &inliers,
double &residual,
unsigned int nbInliersConsensus,
double threshold,
bool normalization=true);
static vpImagePoint project(const vpCameraParameters &cam, const vpHomography &bHa, const vpImagePoint &iPa);
static vpPoint project(const vpHomography &bHa, const vpPoint &Pa);
static void robust(const std::vector<double> &xb, const std::vector<double> &yb,
const std::vector<double> &xa, const std::vector<double> &ya,
vpHomography &aHb,
std::vector<bool> &inlier,
double &residual,
double weights_threshold=0.4,
unsigned int niter=4,
bool normalization=true);
#ifndef DOXYGEN_SHOULD_SKIP_THIS
//! build the homography from aMb and Rb
static void build(vpHomography &aHb,
const vpHomogeneousMatrix &aMb,
const vpPlane &bP) ;
static void computeDisplacement(const vpHomography &aHb,
const vpColVector& nd,
vpRotationMatrix &aRb,
vpTranslationVector &atb,
vpColVector &n) ;
static void computeDisplacement (const vpHomography &aHb,
vpRotationMatrix &aRb,
vpTranslationVector &atb,
vpColVector &n) ;
static void computeDisplacement(const vpMatrix &H,
const double x,
const double y,
std::list<vpRotationMatrix> & vR,
std::list<vpTranslationVector> & vT,
std::list<vpColVector> & vN) ;
static double computeDisplacement(unsigned int nbpoint,
vpPoint *c1P,
vpPoint *c2P,
vpPlane &oN,
vpHomogeneousMatrix &c2Mc1,
vpHomogeneousMatrix &c1Mo,
int userobust
) ;
static double computeDisplacement(unsigned int nbpoint,
vpPoint *c1P,
vpPoint *c2P,
vpPlane *oN,
vpHomogeneousMatrix &c2Mc1,
vpHomogeneousMatrix &c1Mo,
int userobust
) ;
static double computeResidual(vpColVector &x, vpColVector &M, vpColVector &d);
// VVS
static double computeRotation(unsigned int nbpoint,
vpPoint *c1P,
vpPoint *c2P,
vpHomogeneousMatrix &c2Mc1,
int userobust) ;
static void computeTransformation(vpColVector &x,unsigned int *ind, vpColVector &M) ;
static bool degenerateConfiguration(vpColVector &x,unsigned int *ind) ;
static bool degenerateConfiguration(vpColVector &x,unsigned int *ind, double threshold_area);
static bool degenerateConfiguration(const std::vector<double> &xb, const std::vector<double> &yb,
const std::vector<double> &xa, const std::vector<double> &ya);
static void HartleyNormalization(unsigned int n,
const double *x, const double *y,
double *xn, double *yn,
double &xg, double &yg,
double &coef);
static void HartleyNormalization(const std::vector<double> &x, const std::vector<double> &y,
std::vector<double> &xn, std::vector<double> &yn,
double &xg, double &yg, double &coef);
static void HartleyDenormalization(vpHomography &aHbn,
vpHomography &aHb,
double xg1, double yg1, double coef1,
double xg2, double yg2, double coef2 ) ;
#endif // DOXYGEN_SHOULD_SKIP_THIS
#ifdef VISP_BUILD_DEPRECATED_FUNCTIONS
/*!
@name Deprecated functions
*/
vp_deprecated static void computeDisplacement(const vpMatrix H,
const double x,
const double y,
vpList<vpRotationMatrix> & vR,
vpList<vpTranslationVector> & vT,
vpList<vpColVector> & vN);
static void DLT(unsigned int n,
double *xb, double *yb ,
double *xa, double *ya,
vpHomography &aHb) ;
vp_deprecated static void HartleyDLT(unsigned int n,
double *xb, double *yb ,
double *xa, double *ya,
vpHomography &aHb) ;
static void HLM(unsigned int n,
double *xb, double *yb,
double *xa, double *ya ,
bool isplan,
vpHomography &aHb) ;
//! Print the matrix
vp_deprecated void print() ;
vp_deprecated static bool ransac(unsigned int n,
double *xb, double *yb,
double *xa, double *ya ,
vpHomography &aHb,
int consensus = 1000,
double threshold = 1e-6) ;
vp_deprecated static bool ransac(unsigned int n,
double *xb, double *yb,
double *xa, double *ya ,
vpHomography &aHb,
vpColVector& inliers,
double residual = 0.1, // Not used
int consensus = 1000,
double threshold = 1e-6,
double areaThreshold = 0.0);
#endif // VISP_BUILD_DEPRECATED_FUNCTIONS
} ;
#endif
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