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vpHomography Class Reference
vision: Computer vision module » Homography estimation

#include <visp3/vision/vpHomography.h>

+ Inheritance diagram for vpHomography:

Public Member Functions

 vpHomography ()
 
 vpHomography (const vpHomography &H)
 
 vpHomography (const vpHomogeneousMatrix &aMb, const vpPlane &bP)
 
 vpHomography (const vpRotationMatrix &aRb, const vpTranslationVector &atb, const vpPlane &bP)
 
 vpHomography (const vpThetaUVector &tu, const vpTranslationVector &atb, const vpPlane &bP)
 
 vpHomography (const vpPoseVector &arb, const vpPlane &bP)
 
virtual ~vpHomography ()
 
void buildFrom (const vpRotationMatrix &aRb, const vpTranslationVector &atb, const vpPlane &bP)
 
void buildFrom (const vpThetaUVector &tu, const vpTranslationVector &atb, const vpPlane &bP)
 
void buildFrom (const vpPoseVector &arb, const vpPlane &bP)
 
void buildFrom (const vpHomogeneousMatrix &aMb, const vpPlane &bP)
 
vpHomography collineation2homography (const vpCameraParameters &cam) const
 
vpMatrix convert () const
 
void computeDisplacement (vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)
 
void computeDisplacement (const vpColVector &nd, vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)
 
double det () const
 
void eye ()
 
vpHomography homography2collineation (const vpCameraParameters &cam) const
 
vpHomography inverse (double sv_threshold=1e-16, unsigned int *rank=NULL) const
 
void inverse (vpHomography &Hi) const
 
void load (std::ifstream &f)
 
vpHomography operator* (const vpHomography &H) const
 
vpHomography operator* (const double &v) const
 
vpColVector operator* (const vpColVector &b) const
 
vpPoint operator* (const vpPoint &H) const
 
vpHomography operator/ (const double &v) const
 
vpHomography & operator/= (double v)
 
vpHomography & operator= (const vpHomography &H)
 
vpHomography & operator= (const vpMatrix &H)
 
vpImagePoint projection (const vpImagePoint &p)
 
void resize (unsigned int nrows, unsigned int ncols, bool flagNullify=true)
 
void save (std::ofstream &f) const
 
void setIdentity ()
 
bool operator== (const vpArray2D< float > &A) const
 
Inherited functionalities from vpArray2D
unsigned int getCols () const
 
double getMaxValue () const
 
double getMinValue () const
 
unsigned int getRows () const
 
unsigned int size () const
 
void resize (unsigned int nrows, unsigned int ncols, bool flagNullify=true, bool recopy_=true)
 
void reshape (unsigned int nrows, unsigned int ncols)
 
bool operator== (const vpArray2D< double > &A) const
 
bool operator!= (const vpArray2D< double > &A) const
 
double * operator[] (unsigned int i)
 
double * operator[] (unsigned int i) const
 
vpArray2D< double > hadamard (const vpArray2D< double > &m) const
 

Static Public Member Functions

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)
 
Inherited I/O from vpArray2D with Static Public Member Functions
static bool load (const std::string &filename, vpArray2D< double > &A, bool binary=false, char *header=NULL)
 
static bool loadYAML (const std::string &filename, vpArray2D< double > &A, char *header=NULL)
 
static bool save (const std::string &filename, const vpArray2D< double > &A, bool binary=false, const char *header="")
 
static bool saveYAML (const std::string &filename, const vpArray2D< double > &A, const char *header="")
 

Public Attributes

double * data
 

Protected Attributes

unsigned int rowNum
 
unsigned int colNum
 
double ** rowPtrs
 
unsigned int dsize
 

Related Functions

(Note that these are not member functions.)

enum  vpGEMMmethod
 
bool operator== (const vpArray2D< double > &A) const
 
void vpGEMM (const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0)
 

Detailed Description

Implementation of an homography and operations on homographies.

This class aims to compute the homography wrt. two images [33].

The vpHomography class is derived from vpArray2D<double>.

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 [27]. 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

\[ ^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p} \]

with

\[ ^a{\bf H}_b = ^a{\bf R}_b + \frac{^a{\bf t}_b}{^bd} { ^b{\bf n}^T} \]

The Tutorial: Homography estimation from points 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.

#include <visp3/core/vpHomogeneousMatrix.h>
#include <visp3/core/vpMath.h>
#include <visp3/core/vpMeterPixelConversion.h>
#include <visp3/vision/vpHomography.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;
}
vpCameraParameters
Generic class defining intrinsic camera parameters.
Definition: vpCameraParameters.h:259
vpHomogeneousMatrix
Implementation of an homogeneous matrix and operations on such kind of matrices.
Definition: vpHomogeneousMatrix.h:158
vpHomogeneousMatrix::inverse
vpHomogeneousMatrix inverse() const
Definition: vpHomogeneousMatrix.cpp:860
vpHomography
Implementation of an homography and operations on homographies.
Definition: vpHomography.h:175
vpHomography::inverse
vpHomography inverse(double sv_threshold=1e-16, unsigned int *rank=NULL) const
invert the homography
Definition: vpHomography.cpp:171
vpHomography::DLT
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)
Definition: vpHomographyDLT.cpp:250
vpMath::rad
static double rad(double deg)
Definition: vpMath.h:121
vpMeterPixelConversion::convertPoint
static void convertPoint(const vpCameraParameters &cam, const double &x, const double &y, double &u, double &v)
Definition: vpMeterPixelConversion.h:111
vpPlane
This class defines the container for a plane geometrical structure.
Definition: vpPlane.h:59
vpPoint
Class that defines a 3D point in the object frame and allows forward projection of a 3D point in the ...
Definition: vpPoint.h:82
vpPoint::setWorldCoordinates
void setWorldCoordinates(double oX, double oY, double oZ)
Definition: vpPoint.cpp:113
Examples
homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyHartleyDLT2DObject.cpp, homographyRansac2DObject.cpp, planarObjectDetector.cpp, testDisplacement.cpp, tutorial-homography-from-points.cpp, tutorial-matching-keypoint-homography.cpp, tutorial-matching-surf-homography-deprecated.cpp, and tutorial-template-tracker.cpp.

Definition at line 174 of file vpHomography.h.

Constructor & Destructor Documentation

◆ vpHomography() [1/6]

vpHomography::vpHomography ( )

initialize an homography as Identity

Definition at line 60 of file vpHomography.cpp.

References eye().

◆ vpHomography() [2/6]

vpHomography::vpHomography ( const vpHomography &  H)

initialize an homography from another homography

Definition at line 66 of file vpHomography.cpp.

◆ vpHomography() [3/6]

vpHomography::vpHomography ( const vpHomogeneousMatrix &  aMb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

initialize an homography from another homography

Definition at line 71 of file vpHomography.cpp.

References buildFrom().

◆ vpHomography() [4/6]

vpHomography::vpHomography ( const vpRotationMatrix &  aRb,
const vpTranslationVector &  atb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

Definition at line 82 of file vpHomography.cpp.

References buildFrom().

◆ vpHomography() [5/6]

vpHomography::vpHomography ( const vpThetaUVector &  tu,
const vpTranslationVector &  atb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

Definition at line 76 of file vpHomography.cpp.

References buildFrom().

◆ vpHomography() [6/6]

vpHomography::vpHomography ( const vpPoseVector &  arb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

Definition at line 88 of file vpHomography.cpp.

References buildFrom().

◆ ~vpHomography()

virtual vpHomography::~vpHomography ( )
inlinevirtual

Definition at line 213 of file vpHomography.h.

Member Function Documentation

◆ buildFrom() [1/4]

void vpHomography::buildFrom ( const vpHomogeneousMatrix &  aMb,
const vpPlane &  bP 
)

Construction from homogeneous matrix and a plane.

Definition at line 93 of file vpHomography.cpp.

◆ buildFrom() [2/4]

void vpHomography::buildFrom ( const vpPoseVector &  arb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

Definition at line 116 of file vpHomography.cpp.

References vpHomogeneousMatrix::buildFrom().

◆ buildFrom() [3/4]

void vpHomography::buildFrom ( const vpRotationMatrix &  aRb,
const vpTranslationVector &  atb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

Examples
testDisplacement.cpp.

Definition at line 108 of file vpHomography.cpp.

Referenced by vpHomography().

◆ buildFrom() [4/4]

void vpHomography::buildFrom ( const vpThetaUVector &  tu,
const vpTranslationVector &  atb,
const vpPlane &  bP 
)

Construction from Translation and rotation and a plane.

Definition at line 100 of file vpHomography.cpp.

◆ collineation2homography()

vpHomography vpHomography::collineation2homography ( const vpCameraParameters &  cam) const

Transform an homography from pixel space to calibrated domain.

Given homography $\bf G$ corresponding to the collineation matrix in the pixel space, compute the homography matrix $\bf H$ in the Euclidian space or calibrated domain using:

\[ {\bf H} = {\bf K}^{-1} {\bf G} {\bf K} \]

Parameters
[in]cam: Camera parameters used to fill ${\bf K}$ matrix such as

\[{\bf K} = \left[ \begin{array}{ccc} p_x & 0 & u_0 \\ 0 & p_y & v_0 \\ 0 & 0 & 1 \end{array}\right] \]

Returns
The corresponding homography matrix $\bf H$ in the Euclidian space or calibrated domain.
See also
homography2collineation()

Definition at line 786 of file vpHomography.cpp.

References vpCameraParameters::get_px(), vpCameraParameters::get_px_inverse(), vpCameraParameters::get_py(), vpCameraParameters::get_py_inverse(), vpCameraParameters::get_u0(), and vpCameraParameters::get_v0().

◆ computeDisplacement() [1/2]

void vpHomography::computeDisplacement ( const vpColVector &  nd,
vpRotationMatrix &  aRb,
vpTranslationVector &  atb,
vpColVector &  n 
)

Compute the camera displacement between two images from the homography $ {^a}{\bf H}_b $ which is here an implicit parameter (*this).

Camera displacement between $ {^a}{\bf p} $ and $ {^a}{\bf p} $ is represented as a rotation matrix $ {^a}{\bf R}_b $ and a translation vector $ ^a{\bf t}_b $ from which an homogeneous matrix can be build (vpHomogeneousMatrix).

Parameters
nd: Input normal vector to the plane used to compar with the normal vector n extracted from the homography.
aRb: Rotation matrix as an output $ {^a}{\bf R}_b $.
atb: Translation vector as an output $ ^a{\bf t}_b $.
n: Normal vector to the plane as an output.

Definition at line 92 of file vpHomographyExtract.cpp.

References computeDisplacement().

◆ computeDisplacement() [2/2]

void vpHomography::computeDisplacement ( vpRotationMatrix &  aRb,
vpTranslationVector &  atb,
vpColVector &  n 
)

Compute the camera displacement between two images from the homography $ {^a}{\bf H}_b $ which is here an implicit parameter (*this).

Parameters
aRb: Rotation matrix as an output $ {^a}{\bf R}_b $.
atb: Translation vector as an output $ ^a{\bf t}_b $.
n: Normal vector to the plane as an output.
Examples
homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, homographyHartleyDLT2DObject.cpp, testDisplacement.cpp, and tutorial-homography-from-points.cpp.

Definition at line 61 of file vpHomographyExtract.cpp.

Referenced by computeDisplacement().

◆ convert()

vpMatrix vpHomography::convert ( ) const

Converts an homography to a matrix.

Returns
The 3x3 matrix corresponding to the homography.

Definition at line 758 of file vpHomography.cpp.

Referenced by vpMbtDistanceKltPoints::computeHomography().

◆ det()

double vpHomography::det ( ) const

Return homography determinant.

Definition at line 476 of file vpHomography.cpp.

◆ DLT()

void vpHomography::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

From couples of matched points $^a{\bf p}=(x_a,y_a,1)$ in image a and $^b{\bf p}=(x_b,y_b,1)$ in image b with homogeneous coordinates, computes the homography matrix by resolving $^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$ using the DLT (Direct Linear Transform) algorithm.

At least 4 couples of points are needed.

To do so, we use the DLT algorithm on the data, ie we resolve the linear system by SDV : $\bf{Ah} =0$ where $\bf{h}$ is the vector with the terms of $^a{\bf H}_b$ and $\mathbf{A}$ depends on the points coordinates.

For each point, in homogeneous coordinates we have:

\[ ^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p} \]

which is equivalent to:

\[ ^a{\bf p} \times {^a{\bf H}_b \; ^b{\bf p}} =0 \]

If we note $\mathbf{h}_j^T$ the $j^{\textrm{th}}$ line of $^a{\bf H}_b$, we can write:

\[ ^a{\bf H}_b \; ^b{\bf p} = \left( \begin{array}{c}\mathbf{h}_1^T \;^b{\bf p} \\\mathbf{h}_2^T \; ^b{\bf p} \\\mathbf{h}_3^T \;^b{\bf p} \end{array}\right) \]

Setting $^a{\bf p}=(x_{a},y_{a},w_{a})$, the cross product can be rewritten by:

\[ ^a{\bf p} \times ^a{\bf H}_b \; ^b{\bf p} =\left( \begin{array}{c}y_{a}\mathbf{h}_3^T \; ^b{\bf p}-w_{a}\mathbf{h}_2^T \; ^b{\bf p} \\w_{a}\mathbf{h}_1^T \; ^b{\bf p} -x_{a}\mathbf{h}_3^T \; ^b{\bf p} \\x_{a}\mathbf{h}_2^T \; ^b{\bf p}- y_{a}\mathbf{h}_1^T \; ^b{\bf p}\end{array}\right) \]

\[ \underbrace{\left( \begin{array}{ccc}\mathbf{0}^T & -w_{a} \; ^b{\bf p}^T & y_{a} \; ^b{\bf p}^T \\ w_{a} \; ^b{\bf p}^T&\mathbf{0}^T & -x_{a} \; ^b{\bf p}^T \\ -y_{a} \; ^b{\bf p}^T & x_{a} \; ^b{\bf p}^T & \mathbf{0}^T\end{array}\right)}_{\mathbf{A}_i (3\times 9)} \underbrace{\left( \begin{array}{c}\mathbf{h}_{1}^{T} \\ \mathbf{h}_{2}^{T}\\\mathbf{h}_{3}^{T}\end{array}\right)}_{\mathbf{h} (9\times 1)}=0 \]

leading to an homogeneous system to be solved: $\mathbf{A}\mathbf{h}=0$ with $\mathbf{A}=\left(\mathbf{A}_1^T, ..., \mathbf{A}_i^T, ..., \mathbf{A}_n^T \right)^T$.

It can be solved using an SVD decomposition:

\[\bf A = UDV^T \]

h is the column of V associated with the smalest singular value of A

Parameters
xb,yb: Coordinates vector of matched points in image b. These coordinates are expressed in meters.
xa,ya: Coordinates vector of matched points in image a. These coordinates are expressed in meters.
aHb: Estimated homography that relies the transformation from image a to image b.
normalization: When set to true, the coordinates of the points are normalized. The normalization carried out is the one preconized by Hartley.
Exceptions
vpMatrixException::rankDeficient: When the rank of the matrix that should be 8 is deficient.
Examples
homographyHartleyDLT2DObject.cpp, and tutorial-homography-from-points.cpp.

Definition at line 250 of file vpHomographyDLT.cpp.

References vpException::dimensionError, vpException::fatalError, vpMatrix::getCol(), vpMatrixException::rankDeficient, vpArray2D< Type >::resize(), vpMatrix::svd(), vpERROR_TRACE, and vpTRACE.

Referenced by ransac().

◆ eye()

void vpHomography::eye ( )

Set the homography as identity transformation by setting the diagonal to 1 and all other values to 0.

Examples
testDisplacement.cpp.

Definition at line 487 of file vpHomography.cpp.

Referenced by setIdentity(), and vpHomography().

◆ getCols()

unsigned int vpArray2D< double >::getCols ( ) const
inlineinherited

Return the number of columns of the 2D array.

See also
getRows(), size()
Examples
servoViper850Point2DArtVelocity-jointAvoidance-basic.cpp, testAprilTag.cpp, testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 278 of file vpArray2D.h.

◆ getMaxValue()

double vpArray2D< double >::getMaxValue
inherited

Return the array max value.

Examples
servoMomentImage.cpp.

Definition at line 280 of file vpArray2D.h.

◆ getMinValue()

double vpArray2D< double >::getMinValue
inherited

Return the array min value.

Examples
servoMomentImage.cpp.

Definition at line 282 of file vpArray2D.h.

◆ getRows()

unsigned int vpArray2D< double >::getRows ( ) const
inlineinherited

Return the number of rows of the 2D array.

See also
getCols(), size()
Examples
mbtGenericTrackingDepth.cpp, mbtGenericTrackingDepthOnly.cpp, testAprilTag.cpp, testColVector.cpp, testDisplacement.cpp, testGenericTracker.cpp, testGenericTrackerDepth.cpp, testMatrix.cpp, testMatrixConditionNumber.cpp, testMatrixConvolution.cpp, testMatrixDeterminant.cpp, testMatrixInitialization.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, testPoseVector.cpp, testRowVector.cpp, testSvd.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 288 of file vpArray2D.h.

◆ hadamard()

vpArray2D< double > vpArray2D< double >::hadamard ( const vpArray2D< Type > &  m) const
inherited

Compute the Hadamard product (element wise matrix multiplication).

Parameters
m: Second matrix;
Returns
m1.hadamard(m2) The Hadamard product : $ m1 \circ m2 = (m1 \circ m2)_{i,j} = (m1)_{i,j} (m2)_{i,j} $

Definition at line 516 of file vpArray2D.h.

◆ HLM()

void vpHomography::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

From couples of matched points $^a{\bf p}=(x_a,y_a,1)$ in image a and $^b{\bf p}=(x_b,y_b,1)$ in image b with homogeneous coordinates, computes the homography matrix by resolving $^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$ using Ezio Malis linear method (HLM) [26].

This method can consider points that are planar or non planar. The algorithm for planar scene implemented in this file is described in Ezio Malis PhD thesis [27].

Parameters
xb,yb: Coordinates vector of matched points in image b. These coordinates are expressed in meters.
xa,ya: Coordinates vector of matched points in image a. These coordinates are expressed in meters.
isplanar: If true the points are assumed to be in a plane, otherwise there are assumed to be non planar.
aHb: Estimated homography that relies the transformation from image a to image b.

If the boolean isplanar is true the points are assumed to be in a plane otherwise there are assumed to be non planar.

See also
DLT() when the scene is planar.
Examples
homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, and tutorial-homography-from-points.cpp.

Definition at line 622 of file vpHomographyMalis.cpp.

References vpException::dimensionError, and vpException::fatalError.

Referenced by vpPose::poseFromRectangle().

◆ homography2collineation()

vpHomography vpHomography::homography2collineation ( const vpCameraParameters &  cam) const

Transform an homography from calibrated domain to pixel space.

Given homography $\bf H$ in the Euclidian space or in the calibrated domain, compute the homography $\bf G$ corresponding to the collineation matrix in the pixel space using:

\[ {\bf G} = {\bf K} {\bf H} {\bf K}^{-1} \]

Parameters
[in]cam: Camera parameters used to fill ${\bf K}$ matrix such as

\[{\bf K} = \left[ \begin{array}{ccc} p_x & 0 & u_0 \\ 0 & p_y & v_0 \\ 0 & 0 & 1 \end{array}\right] \]

Returns
The corresponding collineation matrix $\bf G$ in the pixel space.
See also
collineation2homography()

Definition at line 842 of file vpHomography.cpp.

References vpCameraParameters::get_px(), vpCameraParameters::get_px_inverse(), vpCameraParameters::get_py(), vpCameraParameters::get_py_inverse(), vpCameraParameters::get_u0(), and vpCameraParameters::get_v0().

Referenced by project().

◆ inverse() [1/2]

vpHomography vpHomography::inverse ( double  sv_threshold = 1e-16,
unsigned int *  rank = NULL 
) const

invert the homography

Return inverted homography.

Parameters
[in]sv_threshold: Threshold used to test the singular values. If a singular value is lower than this threshold we consider that the homography is not full rank.
[out]rank: Rank of the homography that should be 3.
Returns
$\bf H^{-1}$

Definition at line 171 of file vpHomography.cpp.

References vpMatrix::pseudoInverse().

Referenced by inverse().

◆ inverse() [2/2]

void vpHomography::inverse ( vpHomography &  bHa) const

invert the homography

Invert the homography.

Parameters
bHa: $\bf H^{-1}$ with H = *this.

Definition at line 194 of file vpHomography.cpp.

References inverse().

◆ load() [1/2]

static bool vpArray2D< double >::load ( const std::string &  filename,
vpArray2D< Type > &  A,
bool  binary = false,
char *  header = NULL 
)
inlinestaticinherited

Load a matrix from a file.

Parameters
filename: Absolute file name.
A: Array to be loaded
binary: If true the matrix is loaded from a binary file, else from a text file.
header: Header of the file is loaded in this parameter.
Returns
Returns true if success.
See also
save()

Definition at line 538 of file vpArray2D.h.

◆ load() [2/2]

void vpHomography::load ( std::ifstream &  f)

Load an homography from a file.

Read an homography in a file, verify if it is really an homogeneous matrix.

Parameters
f: the file. This file has to be written using save().
See also
save()

Definition at line 400 of file vpHomography.cpp.

References vpException::ioError.

◆ loadYAML()

static bool vpArray2D< double >::loadYAML ( const std::string &  filename,
vpArray2D< Type > &  A,
char *  header = NULL 
)
inlinestaticinherited

Load an array from a YAML-formatted file.

Parameters
filename: absolute file name.
A: array to be loaded from the file.
header: header of the file is loaded in this parameter.
Returns
Returns true on success.
See also
saveYAML()
Examples
servoFlirPtuIBVS.cpp, servoFrankaIBVS.cpp, servoFrankaPBVS.cpp, servoUniversalRobotsIBVS.cpp, servoUniversalRobotsPBVS.cpp, tutorial-flir-ptu-ibvs.cpp, and tutorial-hand-eye-calibration.cpp.

Definition at line 649 of file vpArray2D.h.

◆ operator!=()

bool vpArray2D< double >::operator!= ( const vpArray2D< Type > &  A) const
inherited

Not equal to comparison operator of a 2D array.

Definition at line 408 of file vpArray2D.h.

◆ operator*() [1/4]

vpHomography vpHomography::operator* ( const double &  v) const

Multiply an homography by a scalar.

Parameters
v: Value of the scalar.
double v = 1.1;
vpHomography aHb;
// Initialize aHb
vpHomography H = aHb * v;

Definition at line 275 of file vpHomography.cpp.

References vpArray2D< double >::data, and vpArray2D< Type >::data.

◆ operator*() [2/4]

vpColVector vpHomography::operator* ( const vpColVector &  b) const

Operation a = aHb * b.

Parameters
b: 3 dimension vector.

Definition at line 245 of file vpHomography.cpp.

References vpException::dimensionError, and vpArray2D< Type >::size().

◆ operator*() [3/4]

vpHomography vpHomography::operator* ( const vpHomography &  H) const

Multiplication by an homography.

Parameters
H: Homography to multiply with.
vpHomography aHb, bHc;
// Initialize aHb and bHc homographies
vpHomography aHc = aHb * bHc;

Definition at line 225 of file vpHomography.cpp.

◆ operator*() [4/4]

vpPoint vpHomography::operator* ( const vpPoint &  b_P) const

From the coordinates of the point in image plane b and the homography between image a and b computes the coordinates of the point in image plane a.

Parameters
b_P: 2D coordinates of the point in the image plane b.
Returns
A point with 2D coordinates in the image plane a.

Definition at line 295 of file vpHomography.cpp.

References vpPoint::get_w(), vpPoint::get_x(), vpPoint::get_y(), vpPoint::set_w(), vpPoint::set_x(), and vpPoint::set_y().

◆ operator/()

vpHomography vpHomography::operator/ ( const double &  v) const

Divide an homography by a scalar.

Parameters
v: Value of the scalar.
vpHomography aHb;
// Initialize aHb
vpHomography H = aHb / aHb[2][2];

Definition at line 328 of file vpHomography.cpp.

References vpArray2D< double >::data, vpArray2D< Type >::data, and vpException::divideByZeroError.

◆ operator/=()

vpHomography & vpHomography::operator/= ( double  v)

Divide all the element of the homography matrix by v : Hij = Hij / v.

Definition at line 344 of file vpHomography.cpp.

References vpArray2D< double >::data, and vpException::divideByZeroError.

◆ operator=() [1/2]

vpHomography & vpHomography::operator= ( const vpHomography &  H)

Copy operator. Allow operation such as aHb = H

Parameters
H: Homography matrix to be copied.

Definition at line 364 of file vpHomography.cpp.

◆ operator=() [2/2]

vpHomography & vpHomography::operator= ( const vpMatrix &  H)

Copy operator. Allow operation such as aHb = H

Parameters
H: Matrix to be copied.

Definition at line 380 of file vpHomography.cpp.

References vpException::dimensionError, vpArray2D< Type >::getCols(), and vpArray2D< Type >::getRows().

◆ operator==() [1/2]

bool vpArray2D< double >::operator== ( const vpArray2D< Type > &  A) const
inherited

Equal to comparison operator of a 2D array.

Definition at line 404 of file vpArray2D.h.

◆ operator==() [2/2]

bool vpArray2D< float >::operator== ( const vpArray2D< float > &  A) const
inlineinherited

Definition at line 973 of file vpArray2D.h.

◆ operator[]() [1/2]

double * vpArray2D< double >::operator[] ( unsigned int  i)
inlineinherited

Set element $A_{ij} = x$ using A[i][j] = x.

Definition at line 482 of file vpArray2D.h.

◆ operator[]() [2/2]

double * vpArray2D< double >::operator[] ( unsigned int  i) const
inlineinherited

Get element $x = A_{ij}$ using x = A[i][j].

Definition at line 484 of file vpArray2D.h.

◆ project() [1/2]

vpImagePoint vpHomography::project ( const vpCameraParameters &  cam,
const vpHomography &  bHa,
const vpImagePoint &  iPa 
)
static

Given iPa a pixel with coordinates $(u_a,v_a)$ in image a, and the homography bHa in the Euclidian space or calibrated domain that links image a and b, computes the coordinates of the pixel $(u_b,v_b)$ in the image b using the camera parameters matrix $\bf K$.

Compute $^b{\bf p} = {\bf K} \; {^b}{\bf H}_a \; {\bf K}^{-1} {^a}{\bf p}$ with $^a{\bf p}=(u_a,v_a,1)$ and $^b{\bf p}=(u_b,v_b,1)$

Returns
The coordinates in pixel of the point with coordinates $(u_b,v_b)$.
Examples
tutorial-homography-from-points.cpp, tutorial-matching-keypoint-homography.cpp, and tutorial-matching-surf-homography-deprecated.cpp.

Definition at line 519 of file vpHomography.cpp.

References vpImagePoint::get_u(), vpImagePoint::get_v(), and homography2collineation().

◆ project() [2/2]

vpPoint vpHomography::project ( const vpHomography &  bHa,
const vpPoint &  Pa 
)
static

Given Pa a point with normalized coordinates $(x_a,y_a,1)$ in the image plane a, and the homography bHa in the Euclidian space that links image a and b, computes the normalized coordinates of the point $(x_b,y_b,1)$ in the image plane b.

Compute $^b{\bf p} = {^b}{\bf H}_a \; {^a}{\bf p}$ with $^a{\bf p}=(x_a,y_a,1)$ and $^b{\bf p}=(x_b,y_b,1)$

Returns
The coordinates in meter of the point with coordinates $(x_b,y_b)$.

Definition at line 545 of file vpHomography.cpp.

References vpPoint::get_x(), vpPoint::get_y(), vpPoint::set_x(), and vpPoint::set_y().

◆ projection()

vpImagePoint vpHomography::projection ( const vpImagePoint &  ipb)

Project the current image point (in frame b) into the frame a using the homography aHb.

Parameters
ipb: Homography defining the relation between frame a and frame b.
Returns
The projected image point in the frame a.

Definition at line 736 of file vpHomography.cpp.

References vpImagePoint::get_u(), vpImagePoint::get_v(), vpImagePoint::set_u(), and vpImagePoint::set_v().

◆ ransac()

bool vpHomography::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

From couples of matched points $^a{\bf p}=(x_a,y_a,1)$ in image a and $^b{\bf p}=(x_b,y_b,1)$ in image b with homogeneous coordinates, computes the homography matrix by resolving $^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$ using Ransac algorithm.

Parameters
xb,yb: Coordinates vector of matched points in image b. These coordinates are expressed in meters.
xa,ya: Coordinates vector of matched points in image a. These coordinates are expressed in meters.
aHb: Estimated homography that relies the transformation from image a to image b.
inliers: Vector that indicates if a matched point is an inlier (true) or an outlier (false).
residual: Global residual computed as $r = \sqrt{1/n \sum_{inliers} {\| {^a{\bf p} - {\hat{^a{\bf H}_b}} {^b{\bf p}}} \|}^{2}}$ with $n$ the number of inliers.
nbInliersConsensus: Minimal number of points requested to fit the estimated homography.
threshold: Threshold for outlier removing. A point is considered as an outlier if the reprojection error $\| {^a{\bf p} - {\hat{^a{\bf H}_b}} {^b{\bf p}}} \|$ is greater than this threshold.
normalization: When set to true, the coordinates of the points are normalized. The normalization carried out is the one preconized by Hartley.
Returns
true if the homography could be computed, false otherwise.
Examples
homographyRansac2DObject.cpp, tutorial-matching-keypoint-homography.cpp, and tutorial-matching-surf-homography-deprecated.cpp.

Definition at line 318 of file vpHomographyRansac.cpp.

References vpException::dimensionError, DLT(), vpException::fatalError, and vpERROR_TRACE.

◆ reshape()

void vpArray2D< double >::reshape ( unsigned int  nrows,
unsigned int  ncols 
)
inlineinherited
Examples
testMatrixInitialization.cpp.

Definition at line 378 of file vpArray2D.h.

◆ resize() [1/2]

void vpHomography::resize ( unsigned int  nrows,
unsigned int  ncols,
bool  flagNullify = true 
)
inline

This function is not applicable to an homography that is always a 3-by-3 matrix.

Exceptions
vpException::fatalErrorWhen this function is called.

Definition at line 266 of file vpHomography.h.

References vpException::fatalError.

Referenced by robust().

◆ resize() [2/2]

void vpArray2D< double >::resize ( unsigned int  nrows,
unsigned int  ncols,
bool  flagNullify = true,
bool  recopy_ = true 
)
inlineinherited

Set the size of the array and initialize all the values to zero.

Parameters
nrows: number of rows.
ncols: number of column.
flagNullify: if true, then the array is re-initialized to 0 after resize. If false, the initial values from the common part of the array (common part between old and new version of the array) are kept. Default value is true.
recopy_: if true, will perform an explicit recopy of the old data.
Examples
testArray2D.cpp, testMatrix.cpp, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 303 of file vpArray2D.h.

◆ robust()

void vpHomography::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 > &  inliers,
double &  residual,
double  weights_threshold = 0.4,
unsigned int  niter = 4,
bool  normalization = true 
)
static

From couples of matched points $^a{\bf p}=(x_a,y_a,1)$ in image a and $^b{\bf p}=(x_b,y_b,1)$ in image b with homogeneous coordinates, computes the homography matrix by resolving $^a{\bf p} = ^a{\bf H}_b\; ^b{\bf p}$ using a robust estimation scheme.

This method is to compare to DLT() except that here a robust estimator is used to reject couples of points that are considered as outliers.

At least 4 couples of points are needed.

Parameters
xb,yb: Coordinates vector of matched points in image b. These coordinates are expressed in meters.
xa,ya: Coordinates vector of matched points in image a. These coordinates are expressed in meters.
aHb: Estimated homography that relies the transformation from image a to image b.
inliers: Vector that indicates if a matched point is an inlier (true) or an outlier (false).
residual: Global residual computed as $r = \sqrt{1/n \sum_{inliers} {\| {^a{\bf p} - {\hat{^a{\bf H}_b}} {^b{\bf p}}} \|}^{2}}$ with $n$ the number of inliers.
weights_threshold: Threshold applied on the weights updated during the robust estimation and used to consider if a point is an outlier or an inlier. Values should be in [0:1]. A couple of matched points that have a weight lower than this threshold is considered as an outlier. A value equal to zero indicates that all the points are inliers.
niter: Number of iterations of the estimation process.
normalization: When set to true, the coordinates of the points are normalized. The normalization carried out is the one preconized by Hartley.
See also
DLT(), ransac()
Examples
tutorial-matching-keypoint-homography.cpp, and tutorial-matching-surf-homography-deprecated.cpp.

Definition at line 593 of file vpHomography.cpp.

References vpArray2D< Type >::data, vpException::dimensionError, vpException::fatalError, vpRobust::MEstimator(), vpMatrix::pseudoInverse(), resize(), and vpRobust::TUKEY.

◆ save() [1/2]

static bool vpArray2D< double >::save ( const std::string &  filename,
const vpArray2D< Type > &  A,
bool  binary = false,
const char *  header = "" 
)
inlinestaticinherited

Save a matrix to a file.

Parameters
filename: Absolute file name.
A: Array to be saved.
binary: If true the matrix is saved in a binary file, else a text file.
header: Optional line that will be saved at the beginning of the file.
Returns
Returns true if success.

Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.

See also
load()

Definition at line 733 of file vpArray2D.h.

◆ save() [2/2]

void vpHomography::save ( std::ofstream &  f) const

Save an homography in a file. The laod() function allows then to read and set the homography from this file.

See also
load()

Definition at line 203 of file vpHomography.cpp.

References vpException::ioError.

◆ saveYAML()

static bool vpArray2D< double >::saveYAML ( const std::string &  filename,
const vpArray2D< Type > &  A,
const char *  header = "" 
)
inlinestaticinherited

Save an array in a YAML-formatted file.

Parameters
filename: absolute file name.
A: array to be saved in the file.
header: optional lines that will be saved at the beginning of the file. Should be YAML-formatted and will adapt to the indentation if any.
Returns
Returns true if success.

Here is an example of outputs.

vpArray2D<double> M(3,4);
vpArray2D::saveYAML("matrix.yml", M, "example: a YAML-formatted header");
vpArray2D::saveYAML("matrixIndent.yml", M, "example:\n - a YAML-formatted
header\n - with inner indentation");
vpArray2D::saveYAML
static bool saveYAML(const std::string &filename, const vpArray2D< Type > &A, const char *header="")
Definition: vpArray2D.h:824

Content of matrix.yml:

example: a YAML-formatted header
rows: 3
cols: 4
data:
- [0, 0, 0, 0]
- [0, 0, 0, 0]
- [0, 0, 0, 0]
vpArray2D< double >::data
double * data
Address of the first element of the data array.
Definition: vpArray2D.h:142

Content of matrixIndent.yml:

example:
- a YAML-formatted header
- with inner indentation
rows: 3
cols: 4
data:
- [0, 0, 0, 0]
- [0, 0, 0, 0]
- [0, 0, 0, 0]
See also
loadYAML()
Examples
tutorial-franka-acquire-calib-data.cpp, and tutorial-universal-robots-acquire-calib-data.cpp.

Definition at line 824 of file vpArray2D.h.

◆ setIdentity()

void vpHomography::setIdentity ( )
Deprecated:
You should rather use eye().
Deprecated:
You should rather use eye().

Set the homography as identity transformation.

See also
eye()

Definition at line 504 of file vpHomography.cpp.

References eye().

◆ size()

unsigned int vpArray2D< double >::size ( ) const
inlineinherited

Return the number of elements of the 2D array.

Examples
testColVector.cpp, testDisplacement.cpp, testMatrix.cpp, testMatrixInitialization.cpp, testPoseVector.cpp, testRobotViper650-frames.cpp, testRobotViper850-frames.cpp, testRowVector.cpp, testThread2.cpp, testTranslationVector.cpp, testTukeyEstimator.cpp, testUniversalRobotsGetData.cpp, tutorial-ibvs-4pts-wireframe-robot-afma6.cpp, tutorial-ibvs-4pts-wireframe-robot-viper.cpp, tutorial-matching-surf-homography-deprecated.cpp, tutorial-mb-generic-tracker-rgbd-realsense.cpp, and tutorial-mb-generic-tracker-rgbd-structure-core.cpp.

Definition at line 290 of file vpArray2D.h.

Friends And Related Function Documentation

◆ operator==()

bool operator== ( const vpArray2D< double > &  A) const
related

Definition at line 958 of file vpArray2D.h.

◆ vpGEMM()

void vpGEMM ( const vpArray2D< double > &  A,
const vpArray2D< double > &  B,
const double &  alpha,
const vpArray2D< double > &  C,
const double &  beta,
vpArray2D< double > &  D,
const unsigned int &  ops = 0 
)
related

This function performs generalized matrix multiplication: D = alpha*op(A)*op(B) + beta*op(C), where op(X) is X or X^T. Operation on A, B and C matrices is described by enumeration vpGEMMmethod().

For example, to compute D = alpha*A^T*B^T+beta*C we need to call :

vpGEMM(A, B, alpha, C, beta, D, VP_GEMM_A_T + VP_GEMM_B_T);
vpArray2D< double >::vpGEMM
void vpGEMM(const vpArray2D< double > &A, const vpArray2D< double > &B, const double &alpha, const vpArray2D< double > &C, const double &beta, vpArray2D< double > &D, const unsigned int &ops=0)
Definition: vpGEMM.h:393

If C is not used, vpGEMM must be called using an empty array null. Thus to compute D = alpha*A^T*B, we have to call:

vpGEMM(A, B, alpha, null, 0, D, VP_GEMM_B_T);
Exceptions
vpException::incorrectMatrixSizeErrorif the sizes of the matrices do not allow the operations.
Parameters
A: An array that could be a vpMatrix.
B: An array that could be a vpMatrix.
alpha: A scalar.
C: An array that could be a vpMatrix.
beta: A scalar.
D: The resulting array that could be a vpMatrix.
ops: A scalar describing operation applied on the matrices. Possible values are the one defined in vpGEMMmethod(): VP_GEMM_A_T, VP_GEMM_B_T, VP_GEMM_C_T.

Definition at line 393 of file vpGEMM.h.

◆ vpGEMMmethod

enum vpGEMMmethod
related

Enumeration of the operations applied on matrices in vpGEMM() function.

Operations are :

  • VP_GEMM_A_T to use the transpose matrix of A instead of the matrix A
  • VP_GEMM_B_T to use the transpose matrix of B instead of the matrix B
  • VP_GEMM_C_T to use the transpose matrix of C instead of the matrix C

Definition at line 57 of file vpGEMM.h.

Member Data Documentation

◆ colNum

unsigned int vpArray2D< double >::colNum
protectedinherited

Number of columns in the array.

Definition at line 134 of file vpArray2D.h.

◆ data

double * vpArray2D< double >::data
inherited

Address of the first element of the data array.

Examples
testDisplacement.cpp, testMatrix.cpp, testTranslationVector.cpp, testUniversalRobotsGetData.cpp, tutorial-bridge-opencv-matrix.cpp, and tutorial-matlab.cpp.

Definition at line 142 of file vpArray2D.h.

◆ dsize

unsigned int vpArray2D< double >::dsize
protectedinherited

Current array size (rowNum * colNum)

Definition at line 138 of file vpArray2D.h.

◆ rowNum

unsigned int vpArray2D< double >::rowNum
protectedinherited

Number of rows in the array.

Definition at line 132 of file vpArray2D.h.

◆ rowPtrs

double ** vpArray2D< double >::rowPtrs
protectedinherited

Address of the first element of each rows.

Definition at line 136 of file vpArray2D.h.