static bool testScreenHessian()
{
Eigen::Matrix<double, 6, 1> delta = Eigen::Matrix<double, 6, 1>::Zero();
Eigen::Matrix<double, 6, 6> shNumericX, shNumericY, shX, shY;
SE3<double> pose;
pose.set( Math::deg2Rad( 10.0 ), Math::deg2Rad( 40.0 ), Math::deg2Rad( -120.0 ), -100.0, 200.0, 300.0 );
Eigen::Matrix<double, 3, 3> K( Eigen::Matrix<double, 3, 3>::Zero() );
K( 0, 0 ) = 650.0; K( 0, 2 ) = 320.0;
K( 1, 1 ) = 650.0; K( 1, 2 ) = 240.0;
K( 2, 2 ) = 1.0;
Eigen::Matrix<double, 3, 1> point, ptrans;
Eigen::Matrix<double, 2, 1> sp, ff, fb, bf, bb, xxf, xxb, hess;
point[ 0 ] = 100; point[ 1 ] = 200; point[ 2 ] = 300;
// project the point with current parameters
pose.transform( ptrans, point );
projectWithCam( sp, ptrans, K );
double h = 0.001;
for( size_t i = 0; i < 6; i++ ){
for( size_t j = 0; j < 6; j++ ){
if( i == j ){
// +
delta[ j ] = h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( xxf, ptrans, K );
delta[ j ] = -2 * h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( xxb, ptrans, K );
hess = ( xxb - 2 * sp + xxf ) / ( h*h );
// back to start
delta[ j ] = h;
pose.apply( delta );
delta[ j ] = 0;
} else {
delta[ i ] = h;
delta[ j ] = h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( ff, ptrans, K );
pose.apply( -delta );
delta[ i ] = h;
delta[ j ] = -h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( fb, ptrans, K );
pose.apply( -delta );
delta[ i ] = -h;
delta[ j ] = h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( bf, ptrans, K );
pose.apply( -delta );
delta[ i ] = -h;
delta[ j ] = -h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( bb, ptrans, K );
pose.apply( -delta );
hess = ( ff - bf - fb + bb ) / ( 4 * h * h );
delta.setZero();
}
shNumericX( i, j ) = hess[ 0 ];
shNumericY( i, j ) = hess[ 1 ];
}
}
pose.transform( ptrans, point );
pose.screenHessian( shX, shY, ptrans, K );
bool b, ret = true;
Eigen::Matrix<double, 6, 6> jDiff;
jDiff = shNumericX - shX;
b = ( jDiff.array().abs().sum() / ( double )( jDiff.rows() * jDiff.cols() ) ) < 0.0001;
CVTTEST_PRINT( "Pose ScreenHessian X", b );
if( !b ){
std::cout << "Analytic:\n" << shX << std::endl;
std::cout << "Numeric:\n" << shNumericX << std::endl;
std::cout << "Difference:\n" << jDiff << std::endl;
}
ret &= b;
jDiff = shNumericY - shY;
b = ( jDiff.array().abs().sum() / ( double )( jDiff.rows() * jDiff.cols() ) ) < 0.0001;
CVTTEST_PRINT( "Pose ScreenHessian Y", b );
if( !b ){
std::cout << "Analytic:\n" << shY << std::endl;
std::cout << "Numeric:\n" << shNumericY << std::endl;
std::cout << "Difference:\n" << jDiff << std::endl;
}
ret &= b;
return ret;
}
static bool testHessian()
{
Eigen::Matrix<double, 6, 1> delta = Eigen::Matrix<double, 6, 1>::Zero();
Eigen::Matrix<double, 24, 6> hN, hA;
SE3<double> pose;
pose.set( Math::deg2Rad( 10.0 ), Math::deg2Rad( 40.0 ), Math::deg2Rad( -120.0 ), -100.0, 200.0, 300.0 );
Eigen::Matrix<double, 3, 3> K( Eigen::Matrix<double, 3, 3>::Zero() );
K( 0, 0 ) = 650.0; K( 0, 2 ) = 320.0;
K( 1, 1 ) = 650.0; K( 1, 2 ) = 240.0;
K( 2, 2 ) = 1.0;
Eigen::Matrix<double, 3, 1> point;
Eigen::Matrix<double, 3, 1> p, ff, fb, bf, bb, xxf, xxb, hess;
point[ 0 ] = 16;
point[ 1 ] = 80;
point[ 2 ] = 13;
pose.transform( p, point );
double h = 0.0001;
for( size_t i = 0; i < 6; i++ ){
for( size_t j = 0; j < 6; j++ ){
delta.setZero();
if( i == j ){
// +
delta[ j ] = h;
pose.apply( delta );
pose.transform( xxf, point );
pose.apply( -delta );
delta[ j ] = -h;
pose.apply( delta );
pose.transform( xxb, point );
pose.apply( -delta );
hess = ( xxb - 2 * p + xxf ) / ( h*h );
} else {
delta[ i ] = h;
delta[ j ] = h;
pose.apply( delta );
pose.transform( ff, point );
pose.apply( -delta );
delta[ i ] = h;
delta[ j ] = -h;
pose.apply( delta );
pose.transform( fb, point );
pose.apply( -delta );
delta[ i ] = -h;
delta[ j ] = h;
pose.apply( delta );
pose.transform( bf, point );
pose.apply( -delta );
delta[ i ] = -h;
delta[ j ] = -h;
pose.apply( delta );
pose.transform( bb, point );
pose.apply( -delta );
hess = ( ff - bf - fb + bb ) / ( 4 * h * h );
}
hN( 4 * i , j ) = hess[ 0 ];
hN( 4 * i + 1 , j ) = hess[ 1 ];
hN( 4 * i + 2 , j ) = hess[ 2 ];
hN( 4 * i + 3 , j ) = 0.0;
}
}
pose.hessian( hA, p );
bool b, ret = true;
Eigen::Matrix<double, 24, 6> jDiff;
jDiff = hN - hA;
b = ( jDiff.array().abs().sum() / ( double )( jDiff.rows() * jDiff.cols() ) ) < 0.00001;
CVTTEST_PRINT( "Pose Hessian", b );
if( !b ){
std::cout << "Analytic:\n" << hA << std::endl;
std::cout << "Numeric:\n" << hN << std::endl;
std::cout << "Difference:\n" << jDiff << std::endl;
}
ret &= b;
return ret;
}
static bool testScreenJacobian()
{
Eigen::Matrix<double, 6, 1> delta = Eigen::Matrix<double, 6, 1>::Zero();
Eigen::Matrix<double, 2, 6> shNumeric, sh;
SE3<double> pose;
pose.set( Math::deg2Rad( 10.0 ), Math::deg2Rad( 40.0 ), Math::deg2Rad( -120.0 ), -100.0, 200.0, 300.0 );
Eigen::Matrix<double, 3, 3> K( Eigen::Matrix<double, 3, 3>::Zero() );
K( 0, 0 ) = 650.0; K( 0, 2 ) = 320.0;
K( 1, 1 ) = 650.0; K( 1, 2 ) = 240.0;
K( 2, 2 ) = 1.0;
Eigen::Matrix<double, 3, 1> point, ptrans;
Eigen::Matrix<double, 2, 1> sp, ff, bb, jac;
point[ 0 ] = 100; point[ 1 ] = 200; point[ 2 ] = 300;
// project the point with current parameters
pose.transform( ptrans, point );
projectWithCam( sp, ptrans, K );
double h = 0.001;
for( size_t i = 0; i < 6; i++ ){
delta[ i ] = h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( ff, ptrans, K );
pose.apply( -delta );
delta[ i ] = -h;
pose.apply( delta );
pose.transform( ptrans, point );
projectWithCam( bb, ptrans, K );
pose.apply( -delta );
jac = ( ff - bb ) / ( 2 * h );
delta.setZero();
shNumeric( 0, i ) = jac[ 0 ];
shNumeric( 1, i ) = jac[ 1 ];
}
pose.transform( ptrans, point );
pose.screenJacobian( sh, ptrans, K );
bool b, ret = true;
Eigen::Matrix<double, 2, 6> jDiff;
jDiff = shNumeric - sh;
b = ( jDiff.array().abs().sum() / ( double )( jDiff.rows() * jDiff.cols() ) ) < 0.0001;
CVTTEST_PRINT( "Pose ScreenJacobian", b );
if( !b ){
std::cout << "Analytic:\n" << sh << std::endl;
std::cout << "Numeric:\n" << shNumeric << std::endl;
std::cout << "Difference:\n" << jDiff << std::endl;
}
ret &= b;
return ret;
}
