Visual Servoing Platform  version 3.2.0 under development (2018-10-16)

#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)
 
vpMatrix convert () const
 
void computeDisplacement (vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)
 
void computeDisplacement (const vpColVector &nd, vpRotationMatrix &aRb, vpTranslationVector &atb, vpColVector &n)
 
void eye ()
 
vpHomography inverse () 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
 
vpHomographyoperator/= (double v)
 
vpHomographyoperator= (const vpHomography &H)
 
vpHomographyoperator= (const vpMatrix &H)
 
vpImagePoint projection (const vpImagePoint &p)
 
void resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true)
 
void save (std::ofstream &f) const
 
void setIdentity ()
 
Inherited functionalities from vpArray2D
unsigned int getCols () const
 
double getMaxValue () const
 
double getMinValue () const
 
unsigned int getRows () const
 
unsigned int size () const
 
void resize (const unsigned int nrows, const unsigned int ncols, const bool flagNullify=true, const bool recopy_=true)
 
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, const 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, const 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
 

Detailed Description

Implementation of an homography and operations on homographies.

This class aims to compute the homography wrt. two images [29].

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 [24]. 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
// 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
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;
}
Examples:
homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.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::vpHomography ( )

initialize an homography as Identity

Definition at line 60 of file vpHomography.cpp.

References eye().

vpHomography::vpHomography ( const vpHomography H)

initialize an homography from another homography

Definition at line 66 of file vpHomography.cpp.

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::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::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::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().

virtual vpHomography::~vpHomography ( )
inlinevirtual

Member Function Documentation

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().

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.

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(), and vpHomogeneousMatrix::insert().

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

Construction from homogeneous matrix and a plane.

Definition at line 93 of file vpHomography.cpp.

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:
homographyHartleyDLT2DObject.cpp, homographyHLM2DObject.cpp, homographyHLM3DObject.cpp, testDisplacement.cpp, and tutorial-homography-from-points.cpp.

Definition at line 61 of file vpHomographyExtract.cpp.

Referenced by computeDisplacement().

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(), convert(), vpMatrix::det(), vpRotationMatrix::eye(), vpRotationMatrix::isARotationMatrix(), vpColVector::resize(), vpMath::sqr(), vpMatrix::svd(), vpRotationMatrix::t(), vpTranslationVector::t(), and vpColVector::t().

vpMatrix vpHomography::convert ( ) const

Converts an homography to a matrix.

Returns
The 3x3 matrix corresponding to the homography.

Definition at line 741 of file vpHomography.cpp.

Referenced by computeDisplacement(), vpMbtDistanceKltPoints::computeHomography(), project(), and robust().

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().

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 468 of file vpHomography.cpp.

Referenced by setIdentity(), and vpHomography().

double vpArray2D< double >::getMaxValue ( ) const
inherited

Return the array max value.

Examples:
servoMomentImage.cpp, testArray2D.cpp, and testMatrix.cpp.
double vpArray2D< double >::getMinValue ( ) const
inherited

Return the array min value.

Examples:
servoMomentImage.cpp, testArray2D.cpp, and testMatrix.cpp.
vpArray2D<double > vpArray2D< double >::hadamard ( const vpArray2D< double > &  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} $
Examples:
testArray2D.cpp.
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) [23].

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 [24].

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().

vpHomography vpHomography::inverse ( ) const

invert the homography

Invert the homography.

Returns
$\bf H^{-1}$

Definition at line 165 of file vpHomography.cpp.

References vpHomogeneousMatrix::convert(), and vpMatrix::pseudoInverse().

Referenced by vpTemplateTrackerWarpHomography::getParamInverse(), and inverse().

void vpHomography::inverse ( vpHomography bHa) const

invert the homography

Invert the homography.

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

Definition at line 185 of file vpHomography.cpp.

References inverse().

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 391 of file vpHomography.cpp.

References vpPlane::getD(), vpPlane::getNormal(), vpException::ioError, and vpColVector::t().

static bool vpArray2D< double >::load ( const std::string &  filename,
vpArray2D< double > &  A,
const 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 316 of file vpArray2D.h.

References vpException::badValue, and vpArray2D< Type >::resize().

static bool vpArray2D< double >::loadYAML ( const std::string &  filename,
vpArray2D< double > &  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:
servoFrankaPBVS.cpp.

Definition at line 424 of file vpArray2D.h.

References vpArray2D< Type >::resize().

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 216 of file vpHomography.cpp.

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

Multiply an homography by a scalar.

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

Definition at line 266 of file vpHomography.cpp.

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

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

Operation a = aHb * b.

Parameters
b: 3 dimension vector.

Definition at line 236 of file vpHomography.cpp.

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

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 286 of file vpHomography.cpp.

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

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

Divide an homography by a scalar.

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

Definition at line 319 of file vpHomography.cpp.

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

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

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

Definition at line 335 of file vpHomography.cpp.

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

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

Copy operator. Allow operation such as aHb = H

Parameters
H: Homography matrix to be copied.

Definition at line 355 of file vpHomography.cpp.

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

Copy operator. Allow operation such as aHb = H

Parameters
H: Matrix to be copied.

Definition at line 371 of file vpHomography.cpp.

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

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

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

Definition at line 262 of file vpArray2D.h.

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

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

Definition at line 264 of file vpArray2D.h.

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

Given iPa a point with coordinates $(u_a,v_a)$ expressed in pixel in image a, and the homography bHa that links image a and b, computes the coordinates of the point $(u_b,v_b)$ 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 500 of file vpHomography.cpp.

References convert(), vpCameraParameters::get_K(), vpCameraParameters::get_K_inverse(), vpImagePoint::get_u(), and vpImagePoint::get_v().

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 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 526 of file vpHomography.cpp.

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

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 719 of file vpHomography.cpp.

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

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.

void vpArray2D< double >::resize ( const unsigned int  nrows,
const unsigned int  ncols,
const bool  flagNullify = true,
const 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 if needed and if flagNullify is set to false.
Examples:
testArray2D.cpp, testMatrix.cpp, testMatrixDeterminant.cpp, testMatrixInverse.cpp, testMatrixPseudoInverse.cpp, and testSvd.cpp.

Definition at line 171 of file vpArray2D.h.

References vpArray2D< Type >::colNum, vpArray2D< Type >::dsize, vpException::memoryAllocationError, vpArray2D< Type >::rowNum, and vpArray2D< Type >::rowPtrs.

Referenced by vpMatrix::diag(), vpMatrix::eye(), vpMatrix::init(), vpMatrix::operator=(), and vpMatrix::stack().

void vpHomography::resize ( const unsigned int  nrows,
const unsigned int  ncols,
const 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 260 of file vpHomography.h.

References vpException::fatalError, and vpArray2D< Type >::save().

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 571 of file vpHomography.cpp.

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

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 194 of file vpHomography.cpp.

References vpException::ioError.

static bool vpArray2D< double >::save ( const std::string &  filename,
const vpArray2D< double > &  A,
const 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 506 of file vpArray2D.h.

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

static bool vpArray2D< double >::saveYAML ( const std::string &  filename,
const vpArray2D< double > &  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::saveYAML("matrix.yml", M, "example: a YAML-formatted header");
vpArray2D::saveYAML("matrixIndent.yml", M, "example:\n - a YAML-formatted
header\n - with inner indentation");

Content of matrix.yml:

example: a YAML-formatted header
rows: 3
cols: 4
- [0, 0, 0, 0]
- [0, 0, 0, 0]
- [0, 0, 0, 0]

Content of matrixIndent.yml:

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

Definition at line 595 of file vpArray2D.h.

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

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 485 of file vpHomography.cpp.

References eye().

Friends And Related Function Documentation

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

unsigned int vpArray2D< double >::colNum
protectedinherited

Number of columns in the array.

Definition at line 76 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpMatrix::eye(), vpMatrix::getRow(), vpColVector::hadamard(), vpMatrix::hadamard(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpRowVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpRowVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpRowVector::operator*=(), vpMatrix::operator*=(), vpRowVector::operator+(), vpRowVector::operator+=(), vpMatrix::operator+=(), vpRowVector::operator-(), vpRowVector::operator-=(), vpMatrix::operator-=(), vpRowVector::operator/(), vpMatrix::operator/(), vpRowVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpMatrix::setIdentity(), vpMatrix::solveByQR(), vpMatrix::solveBySVD(), vpMatrix::stack(), vpRowVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpRowVector::sum(), vpMatrix::sum(), vpRowVector::sumSquare(), vpMatrix::sumSquare(), vpRowVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().

double * vpArray2D< double >::data
inherited

Address of the first element of the data array.

Examples:
testArray2D.cpp, testDisplacement.cpp, testImageFilter.cpp, testMatrix.cpp, testPoseVector.cpp, testTranslationVector.cpp, and tutorial-matlab.cpp.

Definition at line 84 of file vpArray2D.h.

Referenced by vpMatrix::AtA(), vpQuaternionVector::buildFrom(), vpHomogeneousMatrix::buildFrom(), vpRzyzVector::buildFrom(), vpThetaUVector::buildFrom(), vpRxyzVector::buildFrom(), vpRzyxVector::buildFrom(), vpSubColVector::checkParentStatus(), vpSubRowVector::checkParentStatus(), vpSubMatrix::checkParentStatus(), vpColVector::clear(), vpHomogeneousMatrix::convert(), vpMatrix::detByLU(), vpTranslationVector::euclideanNorm(), vpRowVector::euclideanNorm(), vpMatrix::euclideanNorm(), vpMatrix::expm(), vpThetaUVector::extract(), vpMatrix::getRow(), vpThetaUVector::getTheta(), vpThetaUVector::getU(), vpColVector::hadamard(), vpMatrix::hadamard(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpColVector::insert(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpTranslationVector::operator*(), vpRowVector::operator*(), vpColVector::operator*(), operator*(), vpMatrix::operator*(), vpTranslationVector::operator-(), vpRowVector::operator-(), vpColVector::operator-(), vpTranslationVector::operator/(), vpRowVector::operator/(), vpColVector::operator/(), operator/(), operator/=(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpQuaternionVector::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpRzyzVector::operator=(), vpRxyzVector::operator=(), vpRzyxVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpThetaUVector::operator=(), vpColVector::operator==(), vpColVector::operator[](), vpMatrix::qr(), vpMatrix::qrPivot(), vpRowVector::reshape(), vpColVector::reshape(), vpQuaternionVector::set(), vpMatrix::stack(), vpMatrix::stackRows(), vpColVector::sum(), vpColVector::sumSquare(), vpRotationVector::t(), vpTranslationVector::t(), vpPoseVector::t(), vpRowVector::t(), vpColVector::t(), vpRotationVector::toStdVector(), vpRowVector::toStdVector(), vpColVector::toStdVector(), vpColVector::vpColVector(), vpMatrix::vpMatrix(), vpQuaternionVector::w(), vpQuaternionVector::x(), vpQuaternionVector::y(), vpQuaternionVector::z(), vpSubColVector::~vpSubColVector(), vpSubMatrix::~vpSubMatrix(), and vpSubRowVector::~vpSubRowVector().

unsigned int vpArray2D< double >::rowNum
protectedinherited

Number of rows in the array.

Definition at line 74 of file vpArray2D.h.

Referenced by vpMatrix::AAt(), vpMatrix::AtA(), vpColVector::clear(), vpMatrix::detByLU(), vpMatrix::diag(), vpMatrix::eigenValues(), vpMatrix::expm(), vpColVector::extract(), vpMatrix::eye(), vpColVector::hadamard(), vpMatrix::hadamard(), vpColVector::infinityNorm(), vpMatrix::infinityNorm(), vpSubColVector::init(), vpSubRowVector::init(), vpSubMatrix::init(), vpMatrix::insert(), vpMatrix::inverseByCholesky(), vpMatrix::inverseTriangular(), vpRotationMatrix::operator*(), vpTranslationVector::operator*(), vpHomogeneousMatrix::operator*(), vpColVector::operator*(), vpMatrix::operator*(), vpRotationMatrix::operator*=(), vpTranslationVector::operator*=(), vpColVector::operator*=(), vpMatrix::operator*=(), vpColVector::operator+(), vpColVector::operator+=(), vpMatrix::operator+=(), vpColVector::operator-(), vpColVector::operator-=(), vpMatrix::operator-=(), vpColVector::operator/(), vpMatrix::operator/(), vpTranslationVector::operator/=(), vpColVector::operator/=(), vpMatrix::operator/=(), vpMatrix::operator<<(), vpColVector::operator<<(), vpSubColVector::operator=(), vpSubRowVector::operator=(), vpSubMatrix::operator=(), vpTranslationVector::operator=(), vpRowVector::operator=(), vpColVector::operator=(), vpMatrix::operator=(), vpColVector::operator==(), vpMatrix::qr(), vpMatrix::qrPivot(), vpColVector::reshape(), vpMatrix::setIdentity(), vpMatrix::stack(), vpColVector::stack(), vpMatrix::stackColumns(), vpMatrix::stackRows(), vpColVector::sum(), vpMatrix::sum(), vpRotationVector::sumSquare(), vpTranslationVector::sumSquare(), vpColVector::sumSquare(), vpMatrix::sumSquare(), vpTranslationVector::t(), vpPoseVector::t(), vpColVector::t(), vpMatrix::t(), vpMatrix::transpose(), vpColVector::vpColVector(), and vpMatrix::vpMatrix().