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Decomposing Projection Using OpenCV and C++

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#include <opencv/cv.hpp>
#include <opencv2/core.hpp>
#include <opencv2/calib3d.hpp>
#include "transformation.hpp"

//https://www.cnblogs.com/shengguang/p/5932522.html
void HouseHolderQR(const cv::Mat &A, cv::Mat &Q, cv::Mat &R)
{
    assert ( A.channels() == 1 );
    assert ( A.rows >= A.cols );
    auto sign = [](double value) { return value >= 0 ? 1: -1; };
    const auto totalRows = A.rows;
    const auto totalCols = A.cols;
    R = A.clone();
    Q = cv::Mat::eye ( totalRows, totalRows, A.type() );
    for ( int col = 0; col < A.cols; ++ col )
    {
        cv::Mat matAROI = cv::Mat ( R, cv::Range ( col, totalRows ), cv::Range ( col, totalCols ) );
        cv::Mat y = matAROI.col ( 0 );
        auto yNorm = norm ( y );
        cv::Mat e1 = cv::Mat::eye ( y.rows, 1, A.type() );
        cv::Mat w = y + sign(y.at<double>(0,0)) *  yNorm * e1;
        cv::Mat v = w / norm( w );
        cv::Mat vT; cv::transpose(v, vT );
        cv::Mat I = cv::Mat::eye( matAROI.rows, matAROI.rows, A.type() );
        cv::Mat I_2VVT = I - 2 * v * vT;
        cv::Mat matH = cv::Mat::eye ( totalRows, totalRows, A.type() );
        cv::Mat matHROI = cv::Mat(matH, cv::Range ( col, totalRows ), cv::Range ( col, totalRows ) );
        I_2VVT.copyTo ( matHROI );
        R = matH * R;
        Q = Q * matH;
    }
}

int main()
{


/*
Thera are two notations for Projection Matrix

1)P=K[R|t]
                                                              ┌X┐
                                                      ┌R,t┐   |Y|
    X_Cam=R*X+t  ==> Homogeneous Coordinate ==> X_Cam=|0,1|   |Z|
                                                      └   ┘4x4└1┘4x1

                                         ┌X┐
                                ┌   ┐    |Y|
    image plane  <--x=K[I|0]3x4 |R,t|    |Z|
                                └0,1┘4x4 └1┘4x1

    P=K[R|t]

2)P=KR[I|-X0]
                                                              ┌X┐
                                                       ┌R -Rc┐|Y|
    X_Cam=R*[X_w-C]  ==> Homogeneous Coordinate ==>    |     ||Z|
                                                       └0  1 ┘└1┘
                                       ┌X┐
                                ┌R -Rc┐|Y|
    image plane  <--x=K[I|0]3x4 |0  1 ||Z|
                                └     ┘└1┘
    P=K[R|-RC]= KR[I|-C]


(1) and (2) ==> t=-RC

*/
    int numberOfPixelInHeight,numberOfPixelInWidth;
    double heightOfSensor, widthOfSensor;
    double focalLength=1.50;
    double mx, my, U0, V0;
    numberOfPixelInHeight=600;
    numberOfPixelInWidth=800;

    heightOfSensor=10;
    widthOfSensor=10;


    my=(numberOfPixelInHeight)/heightOfSensor ;
    U0=(numberOfPixelInHeight)/2 ;

    mx=(numberOfPixelInWidth)/widthOfSensor;
    V0=(numberOfPixelInWidth)/2;

    cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) <<
    focalLength*mx, 0, V0,
    0,focalLength*my,U0,
    0,0,1);

    double tx,ty,tz,roll,pitch,yaw;

    tx=1.0;
    ty=2.1;
    tz=-1.4;

    cv::Mat translation = (cv::Mat_<double>(3,1) <<tx,ty,tz);

    cv::Vec3d theta;

    roll=+M_PI/4 ;
    pitch=+M_PI/10;
    yaw=-+M_PI/6;

    theta[0]=roll;
    theta[1]=pitch;
    theta[2]=yaw;
    cv::Mat rotation=eulerAnglesToRotationMatrix(theta);
    //1)P=K[R|t]
    cv::Mat R_T;
    cv::hconcat(rotation, translation, R_T);
    cv::Mat projectionMatrix=cameraMatrix*R_T;



    cv::Mat calculatedCameraMatrix,calculatedRotation,calculatedTranslation;

    cv::decomposeProjectionMatrix(projectionMatrix,calculatedCameraMatrix,calculatedRotation,calculatedTranslation);


    std::cout<<"==============================Ground Truth==============================" <<std::endl;

    std::cout<<"Rotation Matrix (Ground Truth)" <<std::endl;
    std::cout<<rotation <<std::endl;

    std::cout<<"Translation Matrix (Ground Truth)" <<std::endl;
    std::cout<<translation <<std::endl;

    std::cout<<"Camera Matrix (Ground Truth)" <<std::endl;
    std::cout<<cameraMatrix <<std::endl;

    std::cout<<"==============================Decomposing Using OpenCV==============================" <<std::endl;


    std::cout<<"Computed Rotation Matrix (OpenCV)" <<std::endl;
    std::cout<<calculatedRotation <<std::endl;

    std::cout<<"Computed Translation Matrix (OpenCV)" <<std::endl;
    //std::cout<<calculatedTranslation/calculatedTranslation.at<double>(3,0) <<std::endl;
    cv::Mat tempT=(cv::Mat_<double>(3,1)<<
                   calculatedTranslation.at<double>(0,0)/calculatedTranslation.at<double>(3,0),
                   calculatedTranslation.at<double>(1,0)/calculatedTranslation.at<double>(3,0),
                   calculatedTranslation.at<double>(2,0)/calculatedTranslation.at<double>(3,0));
    std::cout<<-rotation*tempT<<std::endl;

    std::cout<<"Computed Camera Matrix (OpenCV)" <<std::endl;
    std::cout<<calculatedCameraMatrix <<std::endl;

///////////////////////////////////////decomposing the projection matrix///////////////////////////////////////////

/*

    P=KR[I|-X0]=[H_inf3x3|h3x1]
    KR=H_inf3x3
    1)X0
    -KRX0=h3x1 => X0=-(KR)^-1*h3x1 ==>X0=-(H_inf3x3)^-1*h3x1
    2)K,R

    KR=H_inf3x3 =>(KR)^-1= H_inf3x3^-1 =>R^-1*K^-1=H_inf3x3^-1 | R^-1*K^-1=Q*R => R=Q^-1, K=R^-1
                                         H_inf3x3^-1=Q*R       |

*/


    cv::Mat H_inf3x3=(cv::Mat_<double>(3,3)<< projectionMatrix.at<double>(0,0),projectionMatrix.at<double>(0,1),projectionMatrix.at<double>(0,2)
                      ,projectionMatrix.at<double>(1,0),projectionMatrix.at<double>(1,1),projectionMatrix.at<double>(1,2)
                      ,projectionMatrix.at<double>(2,0),projectionMatrix.at<double>(2,1),projectionMatrix.at<double>(2,2));

    cv::Mat h3x1=(cv::Mat_<double>(3,1)<<projectionMatrix.at<double>(0,3),projectionMatrix.at<double>(1,3),projectionMatrix.at<double>(2,3) );



    cv::Mat Q,R;
    cv::Mat H_inf3x3_inv=H_inf3x3.inv();
    //R=Q^-1, K=R^-1


    HouseHolderQR(H_inf3x3_inv, Q, R);
    cv::Mat K=R.inv();

    std::cout<<"==============================Decomposing Using My Code==============================" <<std::endl;
    //due to homogeneity we divide it by last element
    std::cout<<"Estimated Camera Matrix\n"<<K/K.at<double>(2,2) <<std::endl;

    cv::Mat rotationMatrix=Q.inv();
    std::cout<<"Estimated Camera Rotation\n"<<rotationMatrix*-1 <<std::endl;

    std::cout<<"Estimated Camera Translation" <<std::endl;

    //t=-R*C, Q.inv()=R
    std::cout<<-1*(-Q.inv()*(-H_inf3x3.inv()*h3x1 ))<<std::endl;

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#include <opencv/cv.hpp>

#include <opencv2/core.hpp>

#include <opencv2/calib3d.hpp>

#include "transformation.hpp"

//https://www.cnblogs.com/shengguang/p/5932522.html

void HouseHolderQR(const cv::Mat &A, cv::Mat &Q, cv::Mat &R)

{

assert ( A.channels() == 1 );

assert ( A.rows >= A.cols );

auto sign = [](double value) { return value >= 0 ? 1: -1; };

const auto totalRows = A.rows;

const auto totalCols = A.cols;

R = A.clone();

Q = cv::Mat::eye ( totalRows, totalRows, A.type() );

for ( int col = 0; col < A.cols; ++ col )

{

cv::Mat matAROI = cv::Mat ( R, cv::Range ( col, totalRows ), cv::Range ( col, totalCols ) );

cv::Mat y = matAROI.col ( 0 );

auto yNorm = norm ( y );

cv::Mat e1 = cv::Mat::eye ( y.rows, 1, A.type() );

cv::Mat w = y + sign(y.at<double>(0,0)) * yNorm * e1;

cv::Mat v = w / norm( w );

cv::Mat vT; cv::transpose(v, vT );

cv::Mat I = cv::Mat::eye( matAROI.rows, matAROI.rows, A.type() );

cv::Mat I_2VVT = I - 2 * v * vT;

cv::Mat matH = cv::Mat::eye ( totalRows, totalRows, A.type() );

cv::Mat matHROI = cv::Mat(matH, cv::Range ( col, totalRows ), cv::Range ( col, totalRows ) );

I_2VVT.copyTo ( matHROI );

R = matH * R;

Q = Q * matH;

}

int main()

{

Thera are two notations for Projection Matrix

1)P=K[R|t]

┌X┐

┌R,t┐ |Y|

X_Cam=R*X+t ==> Homogeneous Coordinate ==> X_Cam=|0,1| |Z|

└ ┘4x4└1┘4x1

┌X┐

┌ ┐ |Y|

image plane <--x=K[I|0]3x4 |R,t| |Z|

└0,1┘4x4 └1┘4x1

P=K[R|t]

2)P=KR[I|-X0]

┌X┐

┌R -Rc┐|Y|

X_Cam=R*[X_w-C] ==> Homogeneous Coordinate ==> | ||Z|

└0 1 ┘└1┘

┌X┐

┌R -Rc┐|Y|

image plane <--x=K[I|0]3x4 |0 1 ||Z|

└ ┘└1┘

P=K[R|-RC]= KR[I|-C]

(1) and (2) ==> t=-RC

int numberOfPixelInHeight,numberOfPixelInWidth;

double heightOfSensor, widthOfSensor;

double focalLength=1.50;

double mx, my, U0, V0;

numberOfPixelInHeight=600;

numberOfPixelInWidth=800;

heightOfSensor=10;

widthOfSensor=10;

my=(numberOfPixelInHeight)/heightOfSensor ;

U0=(numberOfPixelInHeight)/2 ;

mx=(numberOfPixelInWidth)/widthOfSensor;

V0=(numberOfPixelInWidth)/2;

cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) <<

focalLength*mx, 0, V0,

0,focalLength*my,U0,

0,0,1);

double tx,ty,tz,roll,pitch,yaw;

tx=1.0;

ty=2.1;

tz=-1.4;

cv::Mat translation = (cv::Mat_<double>(3,1) <<tx,ty,tz);

cv::Vec3d theta;

roll=+M_PI/4 ;

pitch=+M_PI/10;

yaw=-+M_PI/6;

theta[0]=roll;

theta[1]=pitch;

theta[2]=yaw;

cv::Mat rotation=eulerAnglesToRotationMatrix(theta);

//1)P=K[R|t]

cv::Mat R_T;

cv::hconcat(rotation, translation, R_T);

cv::Mat projectionMatrix=cameraMatrix*R_T;

cv::Mat calculatedCameraMatrix,calculatedRotation,calculatedTranslation;

cv::decomposeProjectionMatrix(projectionMatrix,calculatedCameraMatrix,calculatedRotation,calculatedTranslation);

std::cout<<"==============================Ground Truth==============================" <<std::endl;

std::cout<<"Rotation Matrix (Ground Truth)" <<std::endl;

std::cout<<rotation <<std::endl;

std::cout<<"Translation Matrix (Ground Truth)" <<std::endl;

std::cout<<translation <<std::endl;

std::cout<<"Camera Matrix (Ground Truth)" <<std::endl;

std::cout<<cameraMatrix <<std::endl;

std::cout<<"==============================Decomposing Using OpenCV==============================" <<std::endl;

std::cout<<"Computed Rotation Matrix (OpenCV)" <<std::endl;

std::cout<<calculatedRotation <<std::endl;

std::cout<<"Computed Translation Matrix (OpenCV)" <<std::endl;

//std::cout<<calculatedTranslation/calculatedTranslation.at<double>(3,0) <<std::endl;

cv::Mat tempT=(cv::Mat_<double>(3,1)<<

calculatedTranslation.at<double>(0,0)/calculatedTranslation.at<double>(3,0),

calculatedTranslation.at<double>(1,0)/calculatedTranslation.at<double>(3,0),

calculatedTranslation.at<double>(2,0)/calculatedTranslation.at<double>(3,0));

std::cout<<-rotation*tempT<<std::endl;

std::cout<<"Computed Camera Matrix (OpenCV)" <<std::endl;

std::cout<<calculatedCameraMatrix <<std::endl;

///////////////////////////////////////decomposing the projection matrix///////////////////////////////////////////

P=KR[I|-X0]=[H_inf3x3|h3x1]

KR=H_inf3x3

1)X0

-KRX0=h3x1 => X0=-(KR)^-1*h3x1 ==>X0=-(H_inf3x3)^-1*h3x1

2)K,R

KR=H_inf3x3 =>(KR)^-1= H_inf3x3^-1 =>R^-1*K^-1=H_inf3x3^-1 | R^-1*K^-1=Q*R => R=Q^-1, K=R^-1

H_inf3x3^-1=Q*R |

cv::Mat H_inf3x3=(cv::Mat_<double>(3,3)<< projectionMatrix.at<double>(0,0),projectionMatrix.at<double>(0,1),projectionMatrix.at<double>(0,2)

,projectionMatrix.at<double>(1,0),projectionMatrix.at<double>(1,1),projectionMatrix.at<double>(1,2)

,projectionMatrix.at<double>(2,0),projectionMatrix.at<double>(2,1),projectionMatrix.at<double>(2,2));

cv::Mat h3x1=(cv::Mat_<double>(3,1)<<projectionMatrix.at<double>(0,3),projectionMatrix.at<double>(1,3),projectionMatrix.at<double>(2,3) );

cv::Mat Q,R;

cv::Mat H_inf3x3_inv=H_inf3x3.inv();

//R=Q^-1, K=R^-1

HouseHolderQR(H_inf3x3_inv, Q, R);

cv::Mat K=R.inv();

std::cout<<"==============================Decomposing Using My Code==============================" <<std::endl;

//due to homogeneity we divide it by last element

std::cout<<"Estimated Camera Matrix\n"<<K/K.at<double>(2,2) <<std::endl;

cv::Mat rotationMatrix=Q.inv();

std::cout<<"Estimated Camera Rotation\n"<<rotationMatrix*-1 <<std::endl;

std::cout<<"Estimated Camera Translation" <<std::endl;

//t=-R*C, Q.inv()=R

std::cout<<-1*(-Q.inv()*(-H_inf3x3.inv()*h3x1 ))<<std::endl;

And the output is:

==============================Ground Truth==============================
Rotation Matrix (Ground Truth)
[0.823639103546332, 0.5427868801100539, -0.1643199010764935;
 -0.4755282581475767, 0.5031184295835893, -0.7216264418079997;
 -0.3090169943749474, 0.6724985119639573, 0.6724985119639574]
Translation Matrix (Ground Truth)
[1;
 2.1;
 -1.4]
Camera Matrix (Ground Truth)
[120, 0, 400;
 0, 90, 300;
 0, 0, 1]
==============================Decomposing Using OpenCV==============================
Computed Rotation Matrix (OpenCV)
[0.823639103546332, 0.5427868801100539, -0.1643199010764936;
 -0.4755282581475769, 0.5031184295835893, -0.7216264418079997;
 -0.3090169943749474, 0.6724985119639573, 0.6724985119639574]
Computed Translation Matrix (OpenCV)
[0.9999999999999988;
 2.1;
 -1.4]
Computed Camera Matrix (OpenCV)
[120, -1.4210854715202e-14, 400;
 0, 90.00000000000001, 300;
 0, 0, 1]
==============================Decomposing Using My Code==============================
Estimated Camera Matrix
[120, -5.776629175002766e-14, 399.9999999999999;
 -5.608036291626306e-15, 89.99999999999994, 299.9999999999999;
 -1.49192016182457e-17, -1.561251128379126e-16, 1]
Estimated Camera Rotation
[0.8236391035463322, 0.5427868801100542, -0.1643199010764936;
 -0.4755282581475767, 0.5031184295835892, -0.7216264418079998;
 -0.3090169943749475, 0.6724985119639573, 0.6724985119639575]
Estimated Camera Translation
[1;
 2.099999999999999;
 -1.4]

==============================Ground Truth==============================

Rotation Matrix (Ground Truth)

[0.823639103546332, 0.5427868801100539, -0.1643199010764935;

-0.4755282581475767, 0.5031184295835893, -0.7216264418079997;

-0.3090169943749474, 0.6724985119639573, 0.6724985119639574]

Translation Matrix (Ground Truth)

[1;

2.1;

-1.4]

Camera Matrix (Ground Truth)

[120, 0, 400;

0, 90, 300;

0, 0, 1]

==============================Decomposing Using OpenCV==============================

Computed Rotation Matrix (OpenCV)

[0.823639103546332, 0.5427868801100539, -0.1643199010764936;

-0.4755282581475769, 0.5031184295835893, -0.7216264418079997;

-0.3090169943749474, 0.6724985119639573, 0.6724985119639574]

Computed Translation Matrix (OpenCV)

[0.9999999999999988;

2.1;

-1.4]

Computed Camera Matrix (OpenCV)

[120, -1.4210854715202e-14, 400;

0, 90.00000000000001, 300;

0, 0, 1]

==============================Decomposing Using My Code==============================

Estimated Camera Matrix

[120, -5.776629175002766e-14, 399.9999999999999;

-5.608036291626306e-15, 89.99999999999994, 299.9999999999999;

-1.49192016182457e-17, -1.561251128379126e-16, 1]

Estimated Camera Rotation

[0.8236391035463322, 0.5427868801100542, -0.1643199010764936;

-0.4755282581475767, 0.5031184295835892, -0.7216264418079998;

-0.3090169943749475, 0.6724985119639573, 0.6724985119639575]

Estimated Camera Translation

[1;

2.099999999999999;

-1.4]

Decomposing Projection Using OpenCV and C++ Read More »

Camera Projection Matrix with Eigen

Leave a Comment / C++, Computer Vision, Tutorials / admin

void projectFromCameraCoordinateToCameraPlane( Eigen::Matrix3Xd &pointsInCameraCoordinate, Eigen::Matrix3d &cameraIntrinsicMatrix,Eigen::Matrix2Xd &pointsInCameraPlane)
{
/*
Intrinsic camera Matrix is something like this:

focalLength  ===> unit is mm
mx=  ==>unit is Pixel/mm
U0=  ===> unit is Pixel

my=-(numberOfPixelInHeight)/heightOfSensor ;
U0=(numberOfPixelInHeight)/2 ;

mx=(numberOfPixelInWidth)/heightOfSensor; 
V0=(numberOfPixelInWidth)/2;

Gamma=0

X,Y,Z,W are homogeneous position of point in camera coordinate

┌ ┐	 ┌                         	 ┐┌ ┐
v`	 |f*mx		Gamma		V0	0||X|	
u`	=|0			f*my		U0	0||Y|
w`	 |0			0			 1	0||Z|
└ ┘	 └                         	 ┘└W┘

									 ▲y
									 |	
			----►V					 |	
			|	 ____________________|_____________________
			|	|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
		U	▼	|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|____________► x
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
				|__|__|__|__|__|__|__|__|__|__|__|__|__|__|



To project points from camera coordinate to camera plane:

V`=X*f*mx + V0*Z 
U`=Y*f*my + U0*Z
W`=Z

U=U`/W` ,V=V`/W`


V=f*mx*X/Z + V0 
U=f*my*Y/Z + U0

(U,V) is the index of corresponding point in the image
*/
	
	Eigen::Matrix3Xd pointsInCameraPlaneHomogeneous(pointsInCameraCoordinate.rows(),pointsInCameraCoordinate.cols());	

	pointsInCameraPlaneHomogeneous=cameraIntrinsicMatrix*pointsInCameraCoordinate;
	std::cout<<"pointsInCameraPlaneHomogeneous"<<std::endl;	
 	std::cout<<pointsInCameraPlaneHomogeneous<<std::endl;	
	for(int i=0;i<pointsInCameraPlaneHomogeneous.cols();i++  )
	{
		pointsInCameraPlaneHomogeneous(0,i)=pointsInCameraPlaneHomogeneous(0,i)/pointsInCameraPlaneHomogeneous(2,i);
		pointsInCameraPlaneHomogeneous(1,i)=pointsInCameraPlaneHomogeneous(1,i)/pointsInCameraPlaneHomogeneous(2,i);
	}
	pointsInCameraPlane=pointsInCameraPlaneHomogeneous.block(0,0,pointsInCameraPlaneHomogeneous.rows()-1,pointsInCameraPlaneHomogeneous.cols());
}

void transformPoints(Eigen::Matrix3Xd &points, Eigen::Matrix3d &rotationMatrix, Eigen::Vector3d &translationVector,Eigen::Matrix3Xd &transformedPoints)
{
	transformedPoints=(rotationMatrix*points).colwise() + translationVector ;
}

void projectFromCameraCoordinateToCameraPlane_Example()
{
	
/*
 OpenCV coordinate system
                  ▲
                 /
                /
              Z/
              /
             /
------------------------------► X
            |
            |
            |
            |
          Y |
            ▼
*/	
	
	int numberOfPixelInHeight,numberOfPixelInWidth;
	double heightOfSensor, widthOfSensor;
	double focalLength=1.5;
	double mx, my, U0, V0;
	numberOfPixelInHeight=600;
    numberOfPixelInWidth=600;
	
	heightOfSensor=10;
	widthOfSensor=10;
	
	my=(numberOfPixelInHeight)/heightOfSensor ;
	U0=(numberOfPixelInHeight)/2 ;

	mx=(numberOfPixelInWidth)/widthOfSensor; 
	V0=(numberOfPixelInWidth)/2;
	
	double L = 0.2;
	Eigen::Matrix3Xd controlPointsInWorldCoordinate(3,6);
	Eigen::Matrix3Xd controlPointsInCameraCoordinate(3,6);

	
	Eigen::Matrix3d cameraIntrinsicMatrix;
	cameraIntrinsicMatrix<<focalLength*mx, 0, V0,
						   0,focalLength*my,U0,
						   0,0,1;

	controlPointsInWorldCoordinate.col(0)= Eigen::Vector3d(-L, -L, 0);
	controlPointsInWorldCoordinate.col(1)= Eigen::Vector3d(2 * L, -L, 0.2);
	controlPointsInWorldCoordinate.col(2)= Eigen::Vector3d(L, L, 0.2);
	controlPointsInWorldCoordinate.col(3)= Eigen::Vector3d(-L, L, 0);
	controlPointsInWorldCoordinate.col(4)= Eigen::Vector3d(-2 * L, L, 0);
	controlPointsInWorldCoordinate.col(5)= Eigen::Vector3d(0, 0, 0.5);
	
	
	Eigen::Matrix3d rotationMatrix;
	rotationMatrix<< 1,0,0
					,0,1,0
					,0,0,1;

	Eigen::Vector3d translationVector(3,1);
	translationVector<<-0.1, 0.1, 1.2;
	
	transformPoints(controlPointsInWorldCoordinate, rotationMatrix, translationVector, controlPointsInCameraCoordinate );

	Eigen::Matrix2Xd pointsInCameraPlane(2,controlPointsInCameraCoordinate.cols());
	projectFromCameraCoordinateToCameraPlane(controlPointsInCameraCoordinate,cameraIntrinsicMatrix,pointsInCameraPlane);
    
    
    std::vector<cv::Point3d> cvPointsInCameraCoordinate;
    std::vector<cv::Point2d> cvpointsInCameraPlane;
    cvPointsInCameraCoordinate.push_back(cv::Point3d(-L, -L, 0));
    cvPointsInCameraCoordinate.push_back(cv::Point3d(2 * L, -L, 0.2));
    cvPointsInCameraCoordinate.push_back(cv::Point3d(L, L, 0.2));
    cvPointsInCameraCoordinate.push_back(cv::Point3d(-L, L, 0));
    cvPointsInCameraCoordinate.push_back(cv::Point3d(-2 * L, L, 0));
    cvPointsInCameraCoordinate.push_back(cv::Point3d(0, 0, 0.5));


    cv::Mat cameraMatrix= (cv::Mat_<double>(3,3) <<
    focalLength*mx, 0, V0,
    0,focalLength*my,U0,
    0,0,1);


    cv::Mat rvec= cv::Mat::eye(3,3, CV_64F);
    cv::Mat tvec=(cv::Mat_<double>(3,1)<<-0.1, 0.1, 1.2);
    cv::projectPoints(cvPointsInCameraCoordinate,rvec,tvec,cameraMatrix,cv::noArray(),cvpointsInCameraPlane);
	
    std::cout<<"cameraIntrinsicMatrix" <<std::endl;
    std::cout<<cameraIntrinsicMatrix <<std::endl;

    std::cout<<cameraMatrix <<std::endl;

	
	
    Eigen::MatrixXd image(numberOfPixelInHeight,numberOfPixelInWidth);
    image=MatrixXd::Zero(numberOfPixelInHeight,numberOfPixelInWidth);
    int U,V;
    for(int i=0;i<pointsInCameraPlane.cols();i++)
    {
        U=int(pointsInCameraPlane(0,i));
        V=int(pointsInCameraPlane(1,i));
        std::cout<<U<<","<<V <<std::endl;
        image(U,V)=255;
        std::cout<<cvpointsInCameraPlane.at(i)<<std::endl;

    }
    Mat dst;
    eigen2cv(image, dst);
    std::string fileName=std::string("eigen_camera_projection_result_focal_")+std::to_string(focalLength)+ std::string("_.jpg");
    cv::imwrite(fileName,dst);
}

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void projectFromCameraCoordinateToCameraPlane( Eigen::Matrix3Xd &pointsInCameraCoordinate, Eigen::Matrix3d &cameraIntrinsicMatrix,Eigen::Matrix2Xd &pointsInCameraPlane)

{

Intrinsic camera Matrix is something like this:

focalLength ===> unit is mm

mx= ==>unit is Pixel/mm

U0= ===> unit is Pixel

my=-(numberOfPixelInHeight)/heightOfSensor ;

U0=(numberOfPixelInHeight)/2 ;

mx=(numberOfPixelInWidth)/heightOfSensor;

V0=(numberOfPixelInWidth)/2;

Gamma=0

X,Y,Z,W are homogeneous position of point in camera coordinate

┌ ┐ ┌ ┐┌ ┐

v` |f*mx Gamma V0 0||X|

u` =|0 f*my U0 0||Y|

w` |0 0 1 0||Z|

└ ┘ └ ┘└W┘

▲y

----►V |

| ____________________|_____________________

| |__|__|__|__|__|__|__|__|__|__|__|__|__|__|

U ▼ |__|__|__|__|__|__|__|__|__|__|__|__|__|__|

|__|__|__|__|__|__|__|__|__|__|__|__|__|__|

|__|__|__|__|__|__|__|__|__|__|__|__|__|__|____________► x

|__|__|__|__|__|__|__|__|__|__|__|__|__|__|

To project points from camera coordinate to camera plane:

V`=X*f*mx + V0*Z

U`=Y*f*my + U0*Z

W`=Z

U=U`/W` ,V=V`/W`

V=f*mx*X/Z + V0

U=f*my*Y/Z + U0

(U,V) is the index of corresponding point in the image

Eigen::Matrix3Xd pointsInCameraPlaneHomogeneous(pointsInCameraCoordinate.rows(),pointsInCameraCoordinate.cols());

pointsInCameraPlaneHomogeneous=cameraIntrinsicMatrix*pointsInCameraCoordinate;

std::cout<<"pointsInCameraPlaneHomogeneous"<<std::endl;

std::cout<<pointsInCameraPlaneHomogeneous<<std::endl;

for(int i=0;i<pointsInCameraPlaneHomogeneous.cols();i++ )

{

pointsInCameraPlaneHomogeneous(0,i)=pointsInCameraPlaneHomogeneous(0,i)/pointsInCameraPlaneHomogeneous(2,i);

pointsInCameraPlaneHomogeneous(1,i)=pointsInCameraPlaneHomogeneous(1,i)/pointsInCameraPlaneHomogeneous(2,i);

}

pointsInCameraPlane=pointsInCameraPlaneHomogeneous.block(0,0,pointsInCameraPlaneHomogeneous.rows()-1,pointsInCameraPlaneHomogeneous.cols());

}

void transformPoints(Eigen::Matrix3Xd &points, Eigen::Matrix3d &rotationMatrix, Eigen::Vector3d &translationVector,Eigen::Matrix3Xd &transformedPoints)

{

transformedPoints=(rotationMatrix*points).colwise() + translationVector ;

}

void projectFromCameraCoordinateToCameraPlane_Example()

{

OpenCV coordinate system

▲

------------------------------► X

Y |

▼

int numberOfPixelInHeight,numberOfPixelInWidth;

double heightOfSensor, widthOfSensor;

double focalLength=1.5;

double mx, my, U0, V0;

numberOfPixelInHeight=600;

numberOfPixelInWidth=600;

heightOfSensor=10;

widthOfSensor=10;

my=(numberOfPixelInHeight)/heightOfSensor ;

U0=(numberOfPixelInHeight)/2 ;

mx=(numberOfPixelInWidth)/widthOfSensor;

V0=(numberOfPixelInWidth)/2;

double L = 0.2;

Eigen::Matrix3Xd controlPointsInWorldCoordinate(3,6);

Eigen::Matrix3Xd controlPointsInCameraCoordinate(3,6);

Eigen::Matrix3d cameraIntrinsicMatrix;

cameraIntrinsicMatrix<<focalLength*mx, 0, V0,

0,focalLength*my,U0,

0,0,1;

controlPointsInWorldCoordinate.col(0)= Eigen::Vector3d(-L, -L, 0);

controlPointsInWorldCoordinate.col(1)= Eigen::Vector3d(2 * L, -L, 0.2);

controlPointsInWorldCoordinate.col(2)= Eigen::Vector3d(L, L, 0.2);

controlPointsInWorldCoordinate.col(3)= Eigen::Vector3d(-L, L, 0);

controlPointsInWorldCoordinate.col(4)= Eigen::Vector3d(-2 * L, L, 0);

controlPointsInWorldCoordinate.col(5)= Eigen::Vector3d(0, 0, 0.5);

Eigen::Matrix3d rotationMatrix;

rotationMatrix<< 1,0,0

,0,1,0

,0,0,1;

Eigen::Vector3d translationVector(3,1);

translationVector<<-0.1, 0.1, 1.2;

transformPoints(controlPointsInWorldCoordinate, rotationMatrix, translationVector, controlPointsInCameraCoordinate );

Eigen::Matrix2Xd pointsInCameraPlane(2,controlPointsInCameraCoordinate.cols());

projectFromCameraCoordinateToCameraPlane(controlPointsInCameraCoordinate,cameraIntrinsicMatrix,pointsInCameraPlane);

std::vector<cv::Point3d> cvPointsInCameraCoordinate;

std::vector<cv::Point2d> cvpointsInCameraPlane;

cvPointsInCameraCoordinate.push_back(cv::Point3d(-L, -L, 0));

cvPointsInCameraCoordinate.push_back(cv::Point3d(2 * L, -L, 0.2));

cvPointsInCameraCoordinate.push_back(cv::Point3d(L, L, 0.2));

cvPointsInCameraCoordinate.push_back(cv::Point3d(-L, L, 0));

cvPointsInCameraCoordinate.push_back(cv::Point3d(-2 * L, L, 0));

cvPointsInCameraCoordinate.push_back(cv::Point3d(0, 0, 0.5));

cv::Mat cameraMatrix= (cv::Mat_<double>(3,3) <<

focalLength*mx, 0, V0,

0,focalLength*my,U0,

0,0,1);

cv::Mat rvec= cv::Mat::eye(3,3, CV_64F);

cv::Mat tvec=(cv::Mat_<double>(3,1)<<-0.1, 0.1, 1.2);

cv::projectPoints(cvPointsInCameraCoordinate,rvec,tvec,cameraMatrix,cv::noArray(),cvpointsInCameraPlane);

std::cout<<"cameraIntrinsicMatrix" <<std::endl;

std::cout<<cameraIntrinsicMatrix <<std::endl;

std::cout<<cameraMatrix <<std::endl;

Eigen::MatrixXd image(numberOfPixelInHeight,numberOfPixelInWidth);

image=MatrixXd::Zero(numberOfPixelInHeight,numberOfPixelInWidth);

int U,V;

for(int i=0;i<pointsInCameraPlane.cols();i++)

{

U=int(pointsInCameraPlane(0,i));

V=int(pointsInCameraPlane(1,i));

std::cout<<U<<","<<V <<std::endl;

image(U,V)=255;

std::cout<<cvpointsInCameraPlane.at(i)<<std::endl;

}

Mat dst;

eigen2cv(image, dst);

std::string fileName=std::string("eigen_camera_projection_result_focal_")+std::to_string(focalLength)+ std::string("_.jpg");

cv::imwrite(fileName,dst);

}

Camera Projection Matrix with Eigen Read More »

Create OpenCV Matrix (cv::Mat, cv::Mat_ ) From Various Data Types

Leave a Comment / C++, Tutorials / admin

1) cv:: Mat_ You can create a matrix with cv:: Mat_

cv::Mat cameraMatrix(3, 3, cv::DataType::type);
cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) <<focalLength*mx, 0, V0,0,focalLength*my,U0,0,0,1);

1 2	cv::Mat cameraMatrix(3, 3, cv::DataType::type); cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) <<focalLengthmx, 0, V0,0,focalLengthmy,U0,0,0,1);

2) cv::Mat or like this with cv::Mat

/*
              C1   C2    C3    C4
    CV_8U     0    8     16    24
    CV_8S     1    9     17    25
    CV_16U    2    10    18    26
    CV_16S    3    11    19    27
    CV_32S    4    12    20    28
    CV_32F    5    13    21    29
    CV_64F    6    14    22    30
*/

cv::Mat mat_CV_64FC1(number_of_rows, number_of_columns,CV_64FC1);

C1 C2 C3 C4

CV_8U 0 8 16 24

CV_8S 1 9 17 25

CV_16U 2 10 18 26

CV_16S 3 11 19 27

CV_32S 4 12 20 28

CV_32F 5 13 21 29

CV_64F 6 14 22 30

cv::Mat mat_CV_64FC1(number_of_rows, number_of_columns,CV_64FC1);

if you forgot the list of data types you use

cv::Mat A(number_of_rows, number_of_columns, cv::DataType<float>::type);

1	cv::Mat A(number_of_rows, number_of_columns, cv::DataType<float>::type);

more data types here

Create OpenCV Matrix (cv::Mat, cv::Mat_ ) From Various Data Types Read More »

Computing Fundamental Matrix and Drawing Epipolar Lines for Stereo Vision Cameras in OpenCV

Leave a Comment / C++, Computer Vision, Tutorials / admin

Following my other post, you can extract the equation for epipolar lines. Basically choosing one point in one image and using fundamental matrix, we will get a line in the other image:

    /*
    FM_7POINT   7-point algorithm
    FM_8POINT   8-point algorithm
    FM_LMEDS    least-median algorithm. 7-point algorithm is used.
    FM_RANSAC   ANSAC algorithm. It needs at least 15 points. 7-point algorithm is used
    */	

    cv::Mat fundamentalMatrix= cv::findFundamentalMat(imagePointsLeftCamera, imagePointsRightCamera, cv::FM_8POINT);
    std::vector<cv::Vec3d> leftLines, rightLines;
    cv::computeCorrespondEpilines(imagePointsLeftCamera, 1, fundamentalMatrix, rightLines);
    cv::computeCorrespondEpilines(imagePointsRightCamera, 2, fundamentalMatrix, leftLines);
	
    cv::Mat leftImageRGB(leftImage.size(), CV_8UC3);
    cv::cvtColor(leftImage, leftImageRGB, CV_GRAY2RGB);
	
    cv::Mat rightImageRGB(rightImage.size(), CV_8UC3);
    cv::cvtColor(rightImage, rightImageRGB, CV_GRAY2RGB);

    cv::Mat imagePointLeftCameraMatrix=cv::Mat_<double>(3,1);

    for(std::size_t i=0;i<rightLines.size();i=i+1)
    {
        cv::Vec3d l=rightLines.at(i);
	double a=l.val[0];
        double b=l.val[1];
        double c=l.val[2];
        std::cout<<"------------------------a,b,c Using OpenCV (ax+by+c=0)------------------------------"<<std::endl;
        std::cout<< a <<", "<<b <<", "<<c <<std::endl;
        std::cout<<"------------------------calculating a,b,c (ax+by+c=0) ------------------------------"<<std::endl;
        
        imagePointLeftCameraMatrix.at<double>(0,0)=imagePointsLeftCamera[i].x;
        imagePointLeftCameraMatrix.at<double>(1,0)=imagePointsLeftCamera[i].y;
        imagePointLeftCameraMatrix.at<double>(2,0)=1;
        cv::Mat rightLineMatrix=fundamentalMatrix*imagePointLeftCameraMatrix;
        
        std::cout<< rightLineMatrix.at<double>(0,0) <<", "<<rightLineMatrix.at<double>(0,1) <<", "<<rightLineMatrix.at<double>(0,2) <<std::endl;

        /////////////////////////////////drawing the line on the image/////////////////////////////////
        /*ax+by+c=0*/
        double x0,y0,x1,y1;
        x0=0;
        y0=(-c-a*x0)/b;
	x1=rightImageRGB.cols;
        y1=(-c-a*x1)/b;

	std::cout<<"error: "<< a*imagePointsRightCamera.at(i).x+ b*imagePointsRightCamera.at(i).y +c<<std::endl;
	cv::line(rightImageRGB, cvPoint(x0,y0), cvPoint(x1,y1), cvScalar(0,255,0), 1);
    }

    cv::imwrite("leftImageEpipolarLine.jpg",leftImageRGB);

FM_7POINT 7-point algorithm

FM_8POINT 8-point algorithm

FM_LMEDS least-median algorithm. 7-point algorithm is used.

FM_RANSAC ANSAC algorithm. It needs at least 15 points. 7-point algorithm is used

cv::Mat fundamentalMatrix= cv::findFundamentalMat(imagePointsLeftCamera, imagePointsRightCamera, cv::FM_8POINT);

std::vector<cv::Vec3d> leftLines, rightLines;

cv::computeCorrespondEpilines(imagePointsLeftCamera, 1, fundamentalMatrix, rightLines);

cv::computeCorrespondEpilines(imagePointsRightCamera, 2, fundamentalMatrix, leftLines);

cv::Mat leftImageRGB(leftImage.size(), CV_8UC3);

cv::cvtColor(leftImage, leftImageRGB, CV_GRAY2RGB);

cv::Mat rightImageRGB(rightImage.size(), CV_8UC3);

cv::cvtColor(rightImage, rightImageRGB, CV_GRAY2RGB);

cv::Mat imagePointLeftCameraMatrix=cv::Mat_<double>(3,1);

for(std::size_t i=0;i<rightLines.size();i=i+1)

{

cv::Vec3d l=rightLines.at(i);

double a=l.val[0];

double b=l.val[1];

double c=l.val[2];

std::cout<<"------------------------a,b,c Using OpenCV (ax+by+c=0)------------------------------"<<std::endl;

std::cout<< a <<", "<<b <<", "<<c <<std::endl;

std::cout<<"------------------------calculating a,b,c (ax+by+c=0) ------------------------------"<<std::endl;

imagePointLeftCameraMatrix.at<double>(0,0)=imagePointsLeftCamera[i].x;

imagePointLeftCameraMatrix.at<double>(1,0)=imagePointsLeftCamera[i].y;

imagePointLeftCameraMatrix.at<double>(2,0)=1;

cv::Mat rightLineMatrix=fundamentalMatrix*imagePointLeftCameraMatrix;

std::cout<< rightLineMatrix.at<double>(0,0) <<", "<<rightLineMatrix.at<double>(0,1) <<", "<<rightLineMatrix.at<double>(0,2) <<std::endl;

/////////////////////////////////drawing the line on the image/////////////////////////////////

/*ax+by+c=0*/

double x0,y0,x1,y1;

x0=0;

y0=(-c-a*x0)/b;

x1=rightImageRGB.cols;

y1=(-c-a*x1)/b;

std::cout<<"error: "<< a*imagePointsRightCamera.at(i).x+ b*imagePointsRightCamera.at(i).y +c<<std::endl;

cv::line(rightImageRGB, cvPoint(x0,y0), cvPoint(x1,y1), cvScalar(0,255,0), 1);

}

cv::imwrite("leftImageEpipolarLine.jpg",leftImageRGB);

Computing Fundamental Matrix and Drawing Epipolar Lines for Stereo Vision Cameras in OpenCV Read More »

Creating a Simulated Stereo Vision Cameras With OpenCV and C++

Leave a Comment / C++, Computer Vision, Linear Algebra, Tutorials / admin

n this tutorial, I created an ellipsoid in 3D space and create two cameras in right and left and captured the image:

cv::Mat leftCameraRotation,rightCameraRotation;
	double rollLeft, pitchLeft,  yawLeft,rollRight, pitchRight,  yawRight ,txLeft,tyLeft,tzLeft,txRight,tyRight,tzRight;

	cv::Vec3d thetaLeft,thetaRight;

	rollLeft=0 ;
	pitchLeft=+M_PI/10;
	yawLeft=0;
	
	thetaLeft[0]=rollLeft;
	thetaLeft[1]=pitchLeft;
	thetaLeft[2]=yawLeft;
	
	rollRight=0;
	pitchRight= -M_PI/10;
	yawRight= 0;
		
	thetaRight[0]=rollRight;
	thetaRight[1]=pitchRight;
	thetaRight[2]=yawRight;
	
	txLeft=-1;
	tyLeft=0.0;
	tzLeft=-4.0;
		
	txRight=1.0;
	tyRight=0.0;
	tzRight=-4.0;
	
	leftCameraRotation =eulerAnglesToRotationMatrix(thetaLeft);
	rightCameraRotation =eulerAnglesToRotationMatrix(thetaRight);
		
	cv::Mat leftCameraTranslation = (cv::Mat_<double>(3,1) <<txLeft,tyLeft,tzLeft);
	cv::Mat rightCameraTranslation = (cv::Mat_<double>(3,1) <<txRight,tyRight,tzRight);
	
	std::vector<cv::Point3d> objectPointsInWorldCoordinate;
	double X,Y,Z,radius;
	

////////////////////////////////////////creating ellipsoid in the world coordinate///////////////////////	
	double phiStepSize,thetaStepSize;
	phiStepSize=0.7;
	thetaStepSize=0.6;
	double a,b,c;
	a=2;
	b=3;
	c=1.6;
	for(double phi=-M_PI;phi<M_PI;phi=phi+phiStepSize)
	{
		for(double theta=-M_PI/2;theta<M_PI/2;theta=theta+thetaStepSize)
		{
			X=a*cos(theta)*cos(phi);
			Y=b*cos(theta)*sin(phi);
			Z=c*sin(theta);
			objectPointsInWorldCoordinate.push_back(cv::Point3d(X, Y, Z));
		}
	}

	int numberOfPixelInHeight,numberOfPixelInWidth;
	double heightOfSensor, widthOfSensor;
	double focalLength=2.0;
	double mx, my, U0, V0;
	numberOfPixelInHeight=600;
	numberOfPixelInWidth=600;
	
	heightOfSensor=10;
	widthOfSensor=10;
	
	my=(numberOfPixelInHeight)/heightOfSensor ;
	U0=(numberOfPixelInHeight)/2 ;

	mx=(numberOfPixelInWidth)/widthOfSensor; 
	V0=(numberOfPixelInWidth)/2;

	cv::Mat K = (cv::Mat_<double>(3,3) <<
	focalLength*mx, 0, V0,
	0,focalLength*my,U0,
	0,0,1);
	
	std::vector<cv::Point2d> imagePointsLeftCamera,imagePointsRightCamera;
	cv::projectPoints(objectPointsInWorldCoordinate, leftCameraRotation, leftCameraTranslation, K, cv::noArray(), imagePointsLeftCamera);
	cv::projectPoints(objectPointsInWorldCoordinate, rightCameraRotation, rightCameraTranslation, K, cv::noArray(), imagePointsRightCamera);

////////////////////////////////////////////////storing images from right and left camera//////////////////////////////////////////////

	std::string fileName;
	cv::Mat rightImage,leftImage;
	int U,V;
	leftImage=cv::Mat::zeros(numberOfPixelInHeight,numberOfPixelInWidth,CV_8UC1);

	for(std::size_t i=0;i<imagePointsLeftCamera.size();i++)
	{
		V=int(imagePointsLeftCamera.at(i).x);
		U=int(imagePointsLeftCamera.at(i).y);
		leftImage.at<char>(U,V)=255;
	}

	fileName=std::string("imagePointsLeftCamera")+std::to_string(focalLength)+ std::string("_.jpg");
	cv::imwrite(fileName,leftImage);

	rightImage=cv::Mat::zeros(numberOfPixelInHeight,numberOfPixelInWidth,CV_8UC1);
	for(std::size_t i=0;i<imagePointsRightCamera.size();i++)
	{
		V=int(imagePointsRightCamera.at(i).x);
		U=int(imagePointsRightCamera.at(i).y);
		rightImage.at<char>(U,V)=255;
	}

	fileName=std::string("imagePointsRightCamera")+std::to_string(focalLength)+ std::string("_.jpg");
	cv::imwrite(fileName,rightImage);

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cv::Mat leftCameraRotation,rightCameraRotation;

double rollLeft, pitchLeft, yawLeft,rollRight, pitchRight, yawRight ,txLeft,tyLeft,tzLeft,txRight,tyRight,tzRight;

cv::Vec3d thetaLeft,thetaRight;

rollLeft=0 ;

pitchLeft=+M_PI/10;

yawLeft=0;

thetaLeft[0]=rollLeft;

thetaLeft[1]=pitchLeft;

thetaLeft[2]=yawLeft;

rollRight=0;

pitchRight= -M_PI/10;

yawRight= 0;

thetaRight[0]=rollRight;

thetaRight[1]=pitchRight;

thetaRight[2]=yawRight;

txLeft=-1;

tyLeft=0.0;

tzLeft=-4.0;

txRight=1.0;

tyRight=0.0;

tzRight=-4.0;

leftCameraRotation =eulerAnglesToRotationMatrix(thetaLeft);

rightCameraRotation =eulerAnglesToRotationMatrix(thetaRight);

cv::Mat leftCameraTranslation = (cv::Mat_<double>(3,1) <<txLeft,tyLeft,tzLeft);

cv::Mat rightCameraTranslation = (cv::Mat_<double>(3,1) <<txRight,tyRight,tzRight);

std::vector<cv::Point3d> objectPointsInWorldCoordinate;

double X,Y,Z,radius;

////////////////////////////////////////creating ellipsoid in the world coordinate///////////////////////

double phiStepSize,thetaStepSize;

phiStepSize=0.7;

thetaStepSize=0.6;

double a,b,c;

a=2;

b=3;

c=1.6;

for(double phi=-M_PI;phi<M_PI;phi=phi+phiStepSize)

{

for(double theta=-M_PI/2;theta<M_PI/2;theta=theta+thetaStepSize)

{

X=a*cos(theta)*cos(phi);

Y=b*cos(theta)*sin(phi);

Z=c*sin(theta);

objectPointsInWorldCoordinate.push_back(cv::Point3d(X, Y, Z));

}

int numberOfPixelInHeight,numberOfPixelInWidth;

double heightOfSensor, widthOfSensor;

double focalLength=2.0;

double mx, my, U0, V0;

numberOfPixelInHeight=600;

numberOfPixelInWidth=600;

heightOfSensor=10;

widthOfSensor=10;

my=(numberOfPixelInHeight)/heightOfSensor ;

U0=(numberOfPixelInHeight)/2 ;

mx=(numberOfPixelInWidth)/widthOfSensor;

V0=(numberOfPixelInWidth)/2;

cv::Mat K = (cv::Mat_<double>(3,3) <<

focalLength*mx, 0, V0,

0,focalLength*my,U0,

0,0,1);

std::vector<cv::Point2d> imagePointsLeftCamera,imagePointsRightCamera;

cv::projectPoints(objectPointsInWorldCoordinate, leftCameraRotation, leftCameraTranslation, K, cv::noArray(), imagePointsLeftCamera);

cv::projectPoints(objectPointsInWorldCoordinate, rightCameraRotation, rightCameraTranslation, K, cv::noArray(), imagePointsRightCamera);

////////////////////////////////////////////////storing images from right and left camera//////////////////////////////////////////////

std::string fileName;

cv::Mat rightImage,leftImage;

int U,V;

leftImage=cv::Mat::zeros(numberOfPixelInHeight,numberOfPixelInWidth,CV_8UC1);

for(std::size_t i=0;i<imagePointsLeftCamera.size();i++)

{

V=int(imagePointsLeftCamera.at(i).x);

U=int(imagePointsLeftCamera.at(i).y);

leftImage.at<char>(U,V)=255;

}

fileName=std::string("imagePointsLeftCamera")+std::to_string(focalLength)+ std::string("_.jpg");

cv::imwrite(fileName,leftImage);

rightImage=cv::Mat::zeros(numberOfPixelInHeight,numberOfPixelInWidth,CV_8UC1);

for(std::size_t i=0;i<imagePointsRightCamera.size();i++)

{

V=int(imagePointsRightCamera.at(i).x);

U=int(imagePointsRightCamera.at(i).y);

rightImage.at<char>(U,V)=255;

}

fileName=std::string("imagePointsRightCamera")+std::to_string(focalLength)+ std::string("_.jpg");

cv::imwrite(fileName,rightImage);

Creating a Simulated Stereo Vision Cameras With OpenCV and C++ Read More »

How to use image_geometry and camera_info_manager in ROS

Leave a Comment / C++, Computer Vision, ROS, Tutorials / admin

camera_info_publisher.cpp:

#include <camera_info_manager/camera_info_manager.h>
int main(int argc, char** argv)
{
    ros::init(argc, argv, "camera_info_publisher");
    ros::NodeHandle nh;

    const std::string cname="prosilica";
    const std::string url="file://${ROS_HOME}/camera_info/prosilica.yaml";
    ros::Publisher pubCameraInfo = nh.advertise<sensor_msgs::CameraInfo>("camera/camera_info", 1);
    camera_info_manager::CameraInfoManager cinfo(nh,cname,url);
    sensor_msgs::CameraInfo msgCameraInfo;
    ros::Rate loop_rate(5);
    while (nh.ok())
    {
        msgCameraInfo=cinfo.getCameraInfo();
        pubCameraInfo.publish(msgCameraInfo);
        ros::spinOnce();
        loop_rate.sleep();
    }
}

#include <camera_info_manager/camera_info_manager.h>

int main(int argc, char** argv)

{

ros::init(argc, argv, "camera_info_publisher");

ros::NodeHandle nh;

const std::string cname="prosilica";

const std::string url="file://${ROS_HOME}/camera_info/prosilica.yaml";

ros::Publisher pubCameraInfo = nh.advertise<sensor_msgs::CameraInfo>("camera/camera_info", 1);

camera_info_manager::CameraInfoManager cinfo(nh,cname,url);

sensor_msgs::CameraInfo msgCameraInfo;

ros::Rate loop_rate(5);

while (nh.ok())

{

msgCameraInfo=cinfo.getCameraInfo();

pubCameraInfo.publish(msgCameraInfo);

ros::spinOnce();

loop_rate.sleep();

}

image_geometry_demo.cpp:

#include <ros/ros.h>
#include <image_geometry/pinhole_camera_model.h>

void cameraInfoCallback(const sensor_msgs::CameraInfoConstPtr& info_msg)
{
    std::cout<<"===============================cameraInfoCallback===============================" <<std::endl;
    image_geometry::PinholeCameraModel cam_model_;
    cam_model_.fromCameraInfo(info_msg);
    // projection_matrix is the matrix you should use if you don't want to use project3dToPixel() and want to use opencv API
    cv::Matx34d projection_matrix=cam_model_.fullProjectionMatrix();
    std::cout<<cam_model_.project3dToPixel(cv::Point3d(-0.1392072,-0.02571392, 2.50376511) )<<std::endl;
}

int main(int argc,char ** argv)
{
    ros::init(argc,argv,"image_geometry_demo",1);
    ros::NodeHandle nh;
    ros::Subscriber sub = nh.subscribe("camera/camera_info", 1000, cameraInfoCallback);
    ros::spin();
}

#include <ros/ros.h>

#include <image_geometry/pinhole_camera_model.h>

void cameraInfoCallback(const sensor_msgs::CameraInfoConstPtr& info_msg)

{

std::cout<<"===============================cameraInfoCallback===============================" <<std::endl;

image_geometry::PinholeCameraModel cam_model_;

cam_model_.fromCameraInfo(info_msg);

// projection_matrix is the matrix you should use if you don't want to use project3dToPixel() and want to use opencv API

cv::Matx34d projection_matrix=cam_model_.fullProjectionMatrix();

std::cout<<cam_model_.project3dToPixel(cv::Point3d(-0.1392072,-0.02571392, 2.50376511) )<<std::endl;

}

int main(int argc,char ** argv)

{

ros::init(argc,argv,"image_geometry_demo",1);

ros::NodeHandle nh;

ros::Subscriber sub = nh.subscribe("camera/camera_info", 1000, cameraInfoCallback);

ros::spin();

}

CMakeLists.txt

find_package(catkin REQUIRED COMPONENTS image_geometry camera_info_manager roscpp)

1	find_package(catkin REQUIRED COMPONENTS image_geometry camera_info_manager roscpp)

How to use image_geometry and camera_info_manager in ROS Read More »

Simulating A Virtual Camera With OpenCV and Reverse Projection From 2D to 3D

Leave a Comment / C++, Tutorials / admin

Projection of Points from 3D in the camera plane: Computed rays from the camera origin in the direction of points:

void virtualCameraSimulator(int argc, char ** argv)
{
    int numberOfPixelInHeight,numberOfPixelInWidth;
    double heightOfSensor, widthOfSensor;
    double focalLength=0.5;
    double mx, my, U0, V0;
    numberOfPixelInHeight=600;
    numberOfPixelInWidth=600;

    heightOfSensor=10;
    widthOfSensor=10;

    my=(numberOfPixelInHeight)/heightOfSensor ;
    U0=(numberOfPixelInHeight)/2 ;

    mx=(numberOfPixelInWidth)/widthOfSensor;
    V0=(numberOfPixelInWidth)/2;



    cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) <<
    focalLength*mx, 0, V0,
    0,focalLength*my,U0,
    0,0,1);


    cv::Mat distortionCoefficient= (cv::Mat_<double>(5,1) <<0, 0, 0, 0, 0);

////////////////////////////////////////////setting up virtual camera extrinsic ///////////////////////////////////////////////////////
    cv::Mat cameraRotation=cv::Mat::eye(3,3, CV_64F);
    double roll,pitch,yaw;
    cv::Vec3d theta;
    roll=0 ;
    pitch=0;
    yaw=0;

    theta[0]=roll;
    theta[1]=pitch;
    theta[2]=yaw;

    cameraRotation =eulerAnglesToRotationMatrix(theta);

    double tx,ty,tz;
    tx=0;
    ty=0;
    tz=0;
    cv::Mat cameraTranslation = (cv::Mat_<double>(3,1) <<tx,ty,tz);

//////////////////////////////////////////projecting 3D points from world into virtual camera //////////////////////////////

    std::vector<cv::Point3d> objectpoints;
    std::vector<cv::Point2d> projectedPoints;

/*
Points are in the following form (OpenCV coordinate):

                  Z
                ▲
               /
              /
             /      1   2    X
            |------------ ⯈
           1|           .
           2|       .   .   .
           3|           .
           4|           .
            | Y
            ⯆
*/


    std::string pathToPointFile(argv[1]);

    io::CSVReader<3> in(pathToPointFile);
    in.read_header(io::ignore_extra_column, "x", "y", "z");
    double x,y,z;

    pcl::PointXYZ point;
    boost::shared_ptr<pcl::PointCloud<pcl::PointXYZ> > pointsInCameraCloud(new pcl::PointCloud<pcl::PointXYZ>);

    while(in.read_row(x,y,z))
    {
        objectpoints.push_back(cv::Point3d(x,y,z));
        pointsInCameraCloud->push_back(pcl::PointXYZ(x,y,z));
    }
    cv::projectPoints(objectpoints, cameraRotation, cameraTranslation, cameraMatrix, distortionCoefficient, projectedPoints);

///////////////////////////////////////////////saving the image //////////////////////////////////////////

    double U,V;

    cv::Mat cameraImage=cv::Mat::zeros(numberOfPixelInHeight,numberOfPixelInWidth,CV_8UC1);
    cv::line(cameraImage,cv::Point2d(numberOfPixelInWidth/2,0),cv::Point2d(numberOfPixelInWidth/2,numberOfPixelInHeight),cv::Scalar(255,255,255));
    cv::line(cameraImage,cv::Point2d(0,numberOfPixelInHeight/2),cv::Point2d(numberOfPixelInWidth,numberOfPixelInHeight/2),cv::Scalar(255,255,255));
    for(std::size_t i=0;i<projectedPoints.size();i++)
    {
        V=int(projectedPoints.at(i).x);
        U=int(projectedPoints.at(i).y);
        //std::cout<<U <<"," <<V  <<std::endl;
        cameraImage.at<char>(int(U),int(V))=char(255);
    }


    std::string fileName=std::string("image_")+std::to_string(focalLength)+ std::string("_.jpg");
    cv::imwrite(fileName,cameraImage);


/////////////////////////////////////////// ray tracing////////////////////////////////////////////
    std::vector<cv::Point3d> directionRays;
    reverseProjection(distortionCoefficient , cameraMatrix, projectedPoints, directionRays);

/////////////////////////////////////////// 3D visualization////////////////////////////////////////////

    boost::shared_ptr<pcl::visualization::PCLVisualizer> viewer (new pcl::visualization::PCLVisualizer ("3D Viewer"));
    viewer->setBackgroundColor (0, 0, 0);
    int pointSize=5;
    double 	coordinateFrameScaleSize=1;
    std::string coordinateName;
    coordinateName="World";
    int viewport = 0;


    viewer->addCoordinateSystem(coordinateFrameScaleSize,Eigen::Affine3f::Identity(),coordinateName,viewport);
    double rayScale=5;
    double r,g,b;
    r=0.0;
    g=1.0;
    b=1.0;

    for(std::size_t i=0;i<directionRays.size();i++)
    {
        std::cout<< directionRays[i].x<<","<<directionRays[i].y<<","<<directionRays[i].z <<std::endl;
        viewer->addLine(pcl::PointXYZ(0 ,0 , 0), pcl::PointXYZ(rayScale*directionRays[i].x,rayScale*directionRays[i].y,rayScale*directionRays[i].z), r, g, b, std::to_string(i+100),viewport);
    }



    int Red,Blue,Green;

    Red=255;
    Green=0;
    Blue=0;
    pcl::visualization::PointCloudColorHandlerCustom<pcl::PointXYZ >  tgt_h ( pointsInCameraCloud,Red,Green,Blue   );
    viewer->addPointCloud<pcl::PointXYZ> (pointsInCameraCloud ,tgt_h ,  std::to_string(1), 0);
    viewer->setPointCloudRenderingProperties(pcl::visualization::PCL_VISUALIZER_POINT_SIZE, pointSize, std::to_string(1));


    while (!viewer->wasStopped ())
    {
        viewer->spinOnce (100);
        boost::this_thread::sleep (boost::posix_time::microseconds (100000));
    }
}

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void virtualCameraSimulator(int argc, char ** argv)

{

int numberOfPixelInHeight,numberOfPixelInWidth;

double heightOfSensor, widthOfSensor;

double focalLength=0.5;

double mx, my, U0, V0;

numberOfPixelInHeight=600;

numberOfPixelInWidth=600;

heightOfSensor=10;

widthOfSensor=10;

my=(numberOfPixelInHeight)/heightOfSensor ;

U0=(numberOfPixelInHeight)/2 ;

mx=(numberOfPixelInWidth)/widthOfSensor;

V0=(numberOfPixelInWidth)/2;

cv::Mat cameraMatrix = (cv::Mat_<double>(3,3) <<

focalLength*mx, 0, V0,

0,focalLength*my,U0,

0,0,1);

cv::Mat distortionCoefficient= (cv::Mat_<double>(5,1) <<0, 0, 0, 0, 0);

////////////////////////////////////////////setting up virtual camera extrinsic ///////////////////////////////////////////////////////

cv::Mat cameraRotation=cv::Mat::eye(3,3, CV_64F);

double roll,pitch,yaw;

cv::Vec3d theta;

roll=0 ;

pitch=0;

yaw=0;

theta[0]=roll;

theta[1]=pitch;

theta[2]=yaw;

cameraRotation =eulerAnglesToRotationMatrix(theta);

double tx,ty,tz;

tx=0;

ty=0;

tz=0;

cv::Mat cameraTranslation = (cv::Mat_<double>(3,1) <<tx,ty,tz);

//////////////////////////////////////////projecting 3D points from world into virtual camera //////////////////////////////

std::vector<cv::Point3d> objectpoints;

std::vector<cv::Point2d> projectedPoints;

Points are in the following form (OpenCV coordinate):

▲

/ 1 2 X

|------------ ⯈

1| .

2| . . .

3| .

4| .

| Y

⯆

std::string pathToPointFile(argv[1]);

io::CSVReader<3> in(pathToPointFile);

in.read_header(io::ignore_extra_column, "x", "y", "z");

double x,y,z;

pcl::PointXYZ point;

boost::shared_ptr<pcl::PointCloud<pcl::PointXYZ> > pointsInCameraCloud(new pcl::PointCloud<pcl::PointXYZ>);

while(in.read_row(x,y,z))

{

objectpoints.push_back(cv::Point3d(x,y,z));

pointsInCameraCloud->push_back(pcl::PointXYZ(x,y,z));

}

cv::projectPoints(objectpoints, cameraRotation, cameraTranslation, cameraMatrix, distortionCoefficient, projectedPoints);

///////////////////////////////////////////////saving the image //////////////////////////////////////////

double U,V;

cv::Mat cameraImage=cv::Mat::zeros(numberOfPixelInHeight,numberOfPixelInWidth,CV_8UC1);

cv::line(cameraImage,cv::Point2d(numberOfPixelInWidth/2,0),cv::Point2d(numberOfPixelInWidth/2,numberOfPixelInHeight),cv::Scalar(255,255,255));

cv::line(cameraImage,cv::Point2d(0,numberOfPixelInHeight/2),cv::Point2d(numberOfPixelInWidth,numberOfPixelInHeight/2),cv::Scalar(255,255,255));

for(std::size_t i=0;i<projectedPoints.size();i++)

{

V=int(projectedPoints.at(i).x);

U=int(projectedPoints.at(i).y);

//std::cout<<U <<"," <<V <<std::endl;

cameraImage.at<char>(int(U),int(V))=char(255);

}

std::string fileName=std::string("image_")+std::to_string(focalLength)+ std::string("_.jpg");

cv::imwrite(fileName,cameraImage);

/////////////////////////////////////////// ray tracing////////////////////////////////////////////

std::vector<cv::Point3d> directionRays;

reverseProjection(distortionCoefficient , cameraMatrix, projectedPoints, directionRays);

/////////////////////////////////////////// 3D visualization////////////////////////////////////////////

boost::shared_ptr<pcl::visualization::PCLVisualizer> viewer (new pcl::visualization::PCLVisualizer ("3D Viewer"));

viewer->setBackgroundColor (0, 0, 0);

int pointSize=5;

double coordinateFrameScaleSize=1;

std::string coordinateName;

coordinateName="World";

int viewport = 0;

viewer->addCoordinateSystem(coordinateFrameScaleSize,Eigen::Affine3f::Identity(),coordinateName,viewport);

double rayScale=5;

double r,g,b;

r=0.0;

g=1.0;

b=1.0;

for(std::size_t i=0;i<directionRays.size();i++)

{

std::cout<< directionRays[i].x<<","<<directionRays[i].y<<","<<directionRays[i].z <<std::endl;

viewer->addLine(pcl::PointXYZ(0 ,0 , 0), pcl::PointXYZ(rayScale*directionRays[i].x,rayScale*directionRays[i].y,rayScale*directionRays[i].z), r, g, b, std::to_string(i+100),viewport);

}

int Red,Blue,Green;

Red=255;

Green=0;

Blue=0;

pcl::visualization::PointCloudColorHandlerCustom<pcl::PointXYZ > tgt_h ( pointsInCameraCloud,Red,Green,Blue );

viewer->addPointCloud<pcl::PointXYZ> (pointsInCameraCloud ,tgt_h , std::to_string(1), 0);

viewer->setPointCloudRenderingProperties(pcl::visualization::PCL_VISUALIZER_POINT_SIZE, pointSize, std::to_string(1));

while (!viewer->wasStopped ())

{

viewer->spinOnce (100);

boost::this_thread::sleep (boost::posix_time::microseconds (100000));

}

points are stored in CSV file like this:

x,y,z   
2,1, 1
1,2, 1
2,2, 1 
3,2, 1 
2,3, 1
2,4, 1

x,y,z

2,1, 1

1,2, 1

2,2, 1

3,2, 1

2,3, 1

2,4, 1

The content of “reverse_projection.hpp”

/////////////////////////////////////////implementing OpenCV undistortPoints///////////////////////////////////////

    cv::Mat imagePointMatrix=cv::Mat_<double>(3,1);
    cv::Mat imageRayMatrix=cv::Mat_<double>(3,1);

    std::cout<<"===============Inverse of Camera Matrix(OpenCV)==========================="<<std::endl;
    std::cout<<cameraMatrix.inv()<<std::endl;

    std::cout<<"=====================Inverse of Camera Matrix====================="<<std::endl;

    cv::Mat inv=(cv::Mat_<double>(3,3)<< cameraMatrix.at<double>(1,1)  ,0,-cameraMatrix.at<double>(1,1)*cameraMatrix.at<double>(0,2)
                 ,0,cameraMatrix.at<double>(0,0),-cameraMatrix.at<double>(1,2)*cameraMatrix.at<double>(0,0)
                 ,0,0,cameraMatrix.at<double>(0,0)*cameraMatrix.at<double>(1,1));
    std::cout<<inv/(cameraMatrix.at<double>(1,1)*cameraMatrix.at<double>(0,0))<<std::endl;

    std::cout<<"=====================Computed Rays===================== "<<std::endl;


    for(std::size_t i=0;i<imagePointsInCamera.size();i++)
    {
        imagePointMatrix.at<double>(0,0)=imagePointsInCamera[i].x;
        imagePointMatrix.at<double>(1,0)=imagePointsInCamera[i].y;
        imagePointMatrix.at<double>(2,0)=1.0;
        imageRayMatrix=cameraMatrix.inv()*imagePointMatrix;



        std::cout<<imageRayMatrix <<std::endl;


    }
/*
    (u,v) is the input point, (u', v') is the output point
    camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1]
    P=[fx' 0 cx' tx; 0 fy' cy' ty; 0 0 1 tz]
    x" = (u - cx)/fx
    y" = (v - cy)/fy
    (x',y') = undistort(x",y",dist_coeffs)
    [X,Y,W]T = R*[x' y' 1]T
    x = X/W, y = Y/W
    only performed if P=[fx' 0 cx' [tx]; 0 fy' cy' [ty]; 0 0 1 [tz]] is specified
    u' = x*fx' + cx'
    v' = y*fy' + cy',
*/

    std::vector<cv::Point2d> imagePointsInCameraNormalizedCoordinate;
    cv::undistortPoints(imagePointsInCamera,imagePointsInCameraNormalizedCoordinate,cameraMatrix,distortionCoefficient);
    std::vector<cv::Point3d> imagePointsInCameraNormalizedCoordinateHomogeneous;
    cv::convertPointsToHomogeneous(imagePointsInCameraNormalizedCoordinate,imagePointsInCameraNormalizedCoordinateHomogeneous);
    cv::Mat imagePointsInCameraNormalizedCoordinateHomogeneousMatrix=cv::Mat(imagePointsInCameraNormalizedCoordinateHomogeneous);
    imagePointsInCameraNormalizedCoordinateHomogeneousMatrix=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.reshape(1).t();
    double a,b,c;
    std::cout<<"=====================OpenCV Rays=====================" <<std::endl;

    for(int i=0;i<imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.cols;i++)
    {
        a=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.at<double>(0,i);
        b=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.at<double>(1,i);
        c=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.at<double>(2,i);
        std::cout<<a <<std::endl;
        std::cout<<b <<std::endl;
        std::cout<<c <<std::endl;
        directionRays.push_back(cv::Point3d(a,b,c));

    }
/*
The inverse of a 3x3 matrix:
| a11 a12 a13 |-1
| a21 a22 a23 |    =  1/DET * A^-1
| a31 a32 a33 |

with A^-1  =

|  a33a22-a32a23  -(a33a12-a32a13)   a23a12-a22a13 |
|-(a33a21-a31a23)   a33a11-a31a13  -(a23a11-a21a13)|
|  a32a21-a31a22  -(a32a11-a31a12)   a22a11-a21a12 |

and DET  =  a11(a33a22-a32a23) - a21(a33a12-a32a13) + a31(a23a12-a22a13)

Camera Matrix:

|fx 0 cx|
|0 fy cy|
|0 0  1 |

Rays are  A^-1*p:

 1    |fy 0   -fycx|  |u|
----- |0  fx -cy*fx| *|v| = [ (u- cx)/fx, (v-cx)/fy, 1]
fx*fy |0  0   fy*fx|  |1|

*/

/////////////////////////////////////////implementing OpenCV undistortPoints///////////////////////////////////////

cv::Mat imagePointMatrix=cv::Mat_<double>(3,1);

cv::Mat imageRayMatrix=cv::Mat_<double>(3,1);

std::cout<<"===============Inverse of Camera Matrix(OpenCV)==========================="<<std::endl;

std::cout<<cameraMatrix.inv()<<std::endl;

std::cout<<"=====================Inverse of Camera Matrix====================="<<std::endl;

cv::Mat inv=(cv::Mat_<double>(3,3)<< cameraMatrix.at<double>(1,1) ,0,-cameraMatrix.at<double>(1,1)*cameraMatrix.at<double>(0,2)

,0,cameraMatrix.at<double>(0,0),-cameraMatrix.at<double>(1,2)*cameraMatrix.at<double>(0,0)

,0,0,cameraMatrix.at<double>(0,0)*cameraMatrix.at<double>(1,1));

std::cout<<inv/(cameraMatrix.at<double>(1,1)*cameraMatrix.at<double>(0,0))<<std::endl;

std::cout<<"=====================Computed Rays===================== "<<std::endl;

for(std::size_t i=0;i<imagePointsInCamera.size();i++)

{

imagePointMatrix.at<double>(0,0)=imagePointsInCamera[i].x;

imagePointMatrix.at<double>(1,0)=imagePointsInCamera[i].y;

imagePointMatrix.at<double>(2,0)=1.0;

imageRayMatrix=cameraMatrix.inv()*imagePointMatrix;

std::cout<<imageRayMatrix <<std::endl;

}

(u,v) is the input point, (u', v') is the output point

camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1]

P=[fx' 0 cx' tx; 0 fy' cy' ty; 0 0 1 tz]

x" = (u - cx)/fx

y" = (v - cy)/fy

(x',y') = undistort(x",y",dist_coeffs)

[X,Y,W]T = R*[x' y' 1]T

x = X/W, y = Y/W

only performed if P=[fx' 0 cx' [tx]; 0 fy' cy' [ty]; 0 0 1 [tz]] is specified

u' = x*fx' + cx'

v' = y*fy' + cy',

std::vector<cv::Point2d> imagePointsInCameraNormalizedCoordinate;

cv::undistortPoints(imagePointsInCamera,imagePointsInCameraNormalizedCoordinate,cameraMatrix,distortionCoefficient);

std::vector<cv::Point3d> imagePointsInCameraNormalizedCoordinateHomogeneous;

cv::convertPointsToHomogeneous(imagePointsInCameraNormalizedCoordinate,imagePointsInCameraNormalizedCoordinateHomogeneous);

cv::Mat imagePointsInCameraNormalizedCoordinateHomogeneousMatrix=cv::Mat(imagePointsInCameraNormalizedCoordinateHomogeneous);

imagePointsInCameraNormalizedCoordinateHomogeneousMatrix=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.reshape(1).t();

double a,b,c;

std::cout<<"=====================OpenCV Rays=====================" <<std::endl;

for(int i=0;i<imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.cols;i++)

{

a=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.at<double>(0,i);

b=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.at<double>(1,i);

c=imagePointsInCameraNormalizedCoordinateHomogeneousMatrix.at<double>(2,i);

std::cout<<a <<std::endl;

std::cout<<b <<std::endl;

std::cout<<c <<std::endl;

directionRays.push_back(cv::Point3d(a,b,c));

}

The inverse of a 3x3 matrix:

| a11 a12 a13 |-1

| a21 a22 a23 | = 1/DET * A^-1

| a31 a32 a33 |

with A^-1 =

| a33a22-a32a23 -(a33a12-a32a13) a23a12-a22a13 |

|-(a33a21-a31a23) a33a11-a31a13 -(a23a11-a21a13)|

| a32a21-a31a22 -(a32a11-a31a12) a22a11-a21a12 |

and DET = a11(a33a22-a32a23) - a21(a33a12-a32a13) + a31(a23a12-a22a13)

Camera Matrix:

|fx 0 cx|

|0 fy cy|

|0 0 1 |

Rays are A^-1*p:

1 |fy 0 -fycx| |u|

----- |0 fx -cy*fx| *|v| = [ (u- cx)/fx, (v-cx)/fy, 1]

fx*fy |0 0 fy*fx| |1|

The content of “transformation.hpp“

#include <opencv2/opencv.hpp>
#include <Eigen/Eigen>

cv::Mat eulerAnglesToRotationMatrix(cv::Vec3d &theta)
{
    // Calculate rotation about x axis
    cv::Mat R_x = (cv::Mat_<double>(3,3) <<
               1,       0,              0,
               0,       cos(theta[0]),   -sin(theta[0]),
               0,       sin(theta[0]),   cos(theta[0])
               );

    // Calculate rotation about y axis
    cv::Mat R_y = (cv::Mat_<double>(3,3) <<
               cos(theta[1]),    0,      sin(theta[1]),
               0,               1,      0,
               -sin(theta[1]),   0,      cos(theta[1])
               );

    // Calculate rotation about z axis
    cv::Mat R_z = (cv::Mat_<double>(3,3) <<
               cos(theta[2]),    -sin(theta[2]),      0,
               sin(theta[2]),    cos(theta[2]),       0,
               0,               0,                  1);


    // Combined rotation matrix
    cv::Mat R = R_z * R_y * R_x;

    return R;

}

bool isRotationMatrix(cv::Mat &R)
{
    cv::Mat Rt;
    cv::transpose(R, Rt);
    cv::Mat shouldBeIdentity = Rt * R;
    cv::Mat I = cv::Mat::eye(3,3, shouldBeIdentity.type());

    return  cv::norm(I, shouldBeIdentity) < 1e-6;

}

cv::Vec3d rotationMatrixToEulerAngles(cv::Mat &R)
{

    assert(isRotationMatrix(R));

    float sy = sqrt(R.at<double>(0,0) * R.at<double>(0,0) +  R.at<double>(1,0) * R.at<double>(1,0) );

    bool singular = sy < 1e-6; // If

    float x, y, z;
    if (!singular)
    {
        x = atan2(R.at<double>(2,1) , R.at<double>(2,2));
        y = atan2(-R.at<double>(2,0), sy);
        z = atan2(R.at<double>(1,0), R.at<double>(0,0));
    }
    else
    {
        x = atan2(-R.at<double>(1,2), R.at<double>(1,1));
        y = atan2(-R.at<double>(2,0), sy);
        z = 0;
    }
    return cv::Vec3f(x, y, z);
}

void transformPoints(cv::Mat rotation,cv::Mat translation, std::vector<cv::Point3d> &inputPoints,std::vector<cv::Point3d> &outputPoints)
{

    std::vector<cv::Point3d> pointsInLeftCamera;
    for(std::size_t i=0;i<inputPoints.size();i++)
    {
        cv::Point3d X=cv::Point3d(inputPoints[i].x ,inputPoints[i].y, inputPoints[i].z );
        cv::Mat X_mat=cv::Mat(X);
        cv::Mat pointInCameraMatrix=rotation*X_mat+translation;
        cv::Point3d pointInCameraCoordinate= cv::Point3d( pointInCameraMatrix.at<double>(0,0),pointInCameraMatrix.at<double>(1,0), pointInCameraMatrix.at<double>(2,0) );
        outputPoints.push_back(pointInCameraCoordinate);
    }
}

Eigen::Matrix3d eulerAnglesToRotationMatrix(double roll, double pitch,double yaw)
{
    Eigen::AngleAxisd rollAngle(roll, Eigen::Vector3d::UnitX());
    Eigen::AngleAxisd pitchAngle(pitch, Eigen::Vector3d::UnitY());
    Eigen::AngleAxisd yawAngle(yaw, Eigen::Vector3d::UnitZ());
    Eigen::Quaternion<double> q = yawAngle * pitchAngle * rollAngle;
    Eigen::Matrix3d rotationMatrix = q.matrix();
    return rotationMatrix;
}

#include <opencv2/opencv.hpp>

#include <Eigen/Eigen>

cv::Mat eulerAnglesToRotationMatrix(cv::Vec3d &theta)

{

// Calculate rotation about x axis

cv::Mat R_x = (cv::Mat_<double>(3,3) <<

1, 0, 0,

0, cos(theta[0]), -sin(theta[0]),

0, sin(theta[0]), cos(theta[0])

);

// Calculate rotation about y axis

cv::Mat R_y = (cv::Mat_<double>(3,3) <<

cos(theta[1]), 0, sin(theta[1]),

0, 1, 0,

-sin(theta[1]), 0, cos(theta[1])

);

// Calculate rotation about z axis

cv::Mat R_z = (cv::Mat_<double>(3,3) <<

cos(theta[2]), -sin(theta[2]), 0,

sin(theta[2]), cos(theta[2]), 0,

0, 0, 1);

// Combined rotation matrix

cv::Mat R = R_z * R_y * R_x;

return R;

}

bool isRotationMatrix(cv::Mat &R)

{

cv::Mat Rt;

cv::transpose(R, Rt);

cv::Mat shouldBeIdentity = Rt * R;

cv::Mat I = cv::Mat::eye(3,3, shouldBeIdentity.type());

return cv::norm(I, shouldBeIdentity) < 1e-6;

}

cv::Vec3d rotationMatrixToEulerAngles(cv::Mat &R)

{

assert(isRotationMatrix(R));

float sy = sqrt(R.at<double>(0,0) * R.at<double>(0,0) + R.at<double>(1,0) * R.at<double>(1,0) );

bool singular = sy < 1e-6; // If

float x, y, z;

if (!singular)

{

x = atan2(R.at<double>(2,1) , R.at<double>(2,2));

y = atan2(-R.at<double>(2,0), sy);

z = atan2(R.at<double>(1,0), R.at<double>(0,0));

}

else

{

x = atan2(-R.at<double>(1,2), R.at<double>(1,1));

y = atan2(-R.at<double>(2,0), sy);

z = 0;

}

return cv::Vec3f(x, y, z);

}

void transformPoints(cv::Mat rotation,cv::Mat translation, std::vector<cv::Point3d> &inputPoints,std::vector<cv::Point3d> &outputPoints)

{

std::vector<cv::Point3d> pointsInLeftCamera;

for(std::size_t i=0;i<inputPoints.size();i++)

{

cv::Point3d X=cv::Point3d(inputPoints[i].x ,inputPoints[i].y, inputPoints[i].z );

cv::Mat X_mat=cv::Mat(X);

cv::Mat pointInCameraMatrix=rotation*X_mat+translation;

cv::Point3d pointInCameraCoordinate= cv::Point3d( pointInCameraMatrix.at<double>(0,0),pointInCameraMatrix.at<double>(1,0), pointInCameraMatrix.at<double>(2,0) );

outputPoints.push_back(pointInCameraCoordinate);

}

Eigen::Matrix3d eulerAnglesToRotationMatrix(double roll, double pitch,double yaw)

{

Eigen::AngleAxisd rollAngle(roll, Eigen::Vector3d::UnitX());

Eigen::AngleAxisd pitchAngle(pitch, Eigen::Vector3d::UnitY());

Eigen::AngleAxisd yawAngle(yaw, Eigen::Vector3d::UnitZ());

Eigen::Quaternion<double> q = yawAngle * pitchAngle * rollAngle;

Eigen::Matrix3d rotationMatrix = q.matrix();

return rotationMatrix;

}

Simulating A Virtual Camera With OpenCV and Reverse Projection From 2D to 3D Read More »

Camera Calibration Based on Direct Linear Transform Explained

2 Comments / C++, Computer Vision, Tutorials / admin

Camera Calibration Based on Direct Linear Transform Explained Read More »

How to develop GUI Application with PyQt (python Qt)

Leave a Comment / C++, Python, Tutorials / admin

There are two main methods for developing GUI application with qt: 1) Adding all widgets in your code (your cpp or python code) 2) Creating qt UI files, adding widgets there and load everything into your application. 1)Adding all widgets in your code Here is the snippet for adding all widgets and their slots in code:

import sys
print(sys.version)
import warnings
warnings.filterwarnings('ignore')


from PyQt5 import QtCore, QtWidgets
from PyQt5.QtWidgets import QMainWindow, QLabel, QSlider
from PyQt5.QtCore import QSize, Qt, pyqtSlot,pyqtSignal 



class HelloWindow(QMainWindow):
    
    pushButtonClicked = pyqtSignal()
    valueUpdating = pyqtSignal(int)
    
    
    def pushButtonClicked(self):
        self.title.setText("PyQt updated!")
            
    def valueUpdating(self, value):
        self.title.setText(str(value))
    
    def __init__(self):
        QMainWindow.__init__(self)

        self.setMinimumSize(QSize(640, 480))    
        self.setWindowTitle("Hello world") 

        self.title = QLabel("PyQt!", self)
        self.title.setAlignment(QtCore.Qt.AlignCenter) 


        self.pushButton = QtWidgets.QPushButton(self)
        self.pushButton.setGeometry(QtCore.QRect(140, 200, 99, 27))#x,y, width, height
        self.pushButton.setObjectName("pushButton")
        self.pushButton.setText("Click Me!")
        self.pushButton.clicked.connect(self.pushButtonClicked)
        
        self.slider = QtWidgets.QSlider(self)
        self.slider.setGeometry(QtCore.QRect(100, 20, 100, 30))
        self.slider.setFocusPolicy(Qt.StrongFocus)
        self.slider.setTickPosition(QSlider.TicksBothSides)
        self.slider.setSingleStep(1)
        self.slider.setPageStep(1)
        self.slider.setMaximum(100)
        self.slider.setMinimum(0)
        self.slider.setOrientation(Qt.Horizontal)
        
        self.slider.valueChanged.connect(self.valueUpdating)
        


if __name__ == "__main__":
    app = QtWidgets.QApplication(sys.argv)
    mainWin = HelloWindow()
    mainWin.show()
    sys.exit( app.exec_() )

import sys

print(sys.version)

import warnings

warnings.filterwarnings('ignore')

from PyQt5 import QtCore, QtWidgets

from PyQt5.QtWidgets import QMainWindow, QLabel, QSlider

from PyQt5.QtCore import QSize, Qt, pyqtSlot,pyqtSignal

class HelloWindow(QMainWindow):

pushButtonClicked = pyqtSignal()

valueUpdating = pyqtSignal(int)

def pushButtonClicked(self):

self.title.setText("PyQt updated!")

def valueUpdating(self, value):

self.title.setText(str(value))

def __init__(self):

QMainWindow.__init__(self)

self.setMinimumSize(QSize(640, 480))

self.setWindowTitle("Hello world")

self.title = QLabel("PyQt!", self)

self.title.setAlignment(QtCore.Qt.AlignCenter)

self.pushButton = QtWidgets.QPushButton(self)

self.pushButton.setGeometry(QtCore.QRect(140, 200, 99, 27))#x,y, width, height

self.pushButton.setObjectName("pushButton")

self.pushButton.setText("Click Me!")

self.pushButton.clicked.connect(self.pushButtonClicked)

self.slider = QtWidgets.QSlider(self)

self.slider.setGeometry(QtCore.QRect(100, 20, 100, 30))

self.slider.setFocusPolicy(Qt.StrongFocus)

self.slider.setTickPosition(QSlider.TicksBothSides)

self.slider.setSingleStep(1)

self.slider.setPageStep(1)

self.slider.setMaximum(100)

self.slider.setMinimum(0)

self.slider.setOrientation(Qt.Horizontal)

self.slider.valueChanged.connect(self.valueUpdating)

if __name__ == "__main__":

app = QtWidgets.QApplication(sys.argv)

mainWin = HelloWindow()

mainWin.show()

sys.exit( app.exec_() )

How to develop GUI Application with PyQt (python Qt) Read More »

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