/*---------------------------------------------------------------
jacobiansPoseComposition
---------------------------------------------------------------*/
void CPosePDF::jacobiansPoseComposition(
const CPose2D &x,
const CPose2D &u,
CMatrixDouble33 &df_dx,
CMatrixDouble33 &df_du,
const bool compute_df_dx,
const bool compute_df_du )
{
const double spx = sin(x.phi());
const double cpx = cos(x.phi());
if (compute_df_dx)
{
/*
df_dx =
[ 1, 0, -sin(phi_x)*x_u-cos(phi_x)*y_u ]
[ 0, 1, cos(phi_x)*x_u-sin(phi_x)*y_u ]
[ 0, 0, 1 ]
*/
df_dx.unit(3,1.0);
const double xu = u.x();
const double yu = u.y();
df_dx.get_unsafe(0,2) = -spx*xu-cpx*yu;
df_dx.get_unsafe(1,2) = cpx*xu-spx*yu;
}
if (compute_df_du)
{
/*
df_du =
[ cos(phi_x) , -sin(phi_x) , 0 ]
[ sin(phi_x) , cos(phi_x) , 0 ]
[ 0 , 0 , 1 ]
*/
// This is the homogeneous matrix of "x":
df_du.get_unsafe(0,2) =
df_du.get_unsafe(1,2) =
df_du.get_unsafe(2,0) =
df_du.get_unsafe(2,1) = 0;
df_du.get_unsafe(2,2) = 1;
df_du.get_unsafe(0,0) = cpx;
df_du.get_unsafe(0,1) = -spx;
df_du.get_unsafe(1,0) = spx;
df_du.get_unsafe(1,1) = cpx;
}
}
/*---------------------------------------------------------------
HornMethod
---------------------------------------------------------------*/
double scanmatching::HornMethod(
const vector_double &inVector,
vector_double &outVector, // The output vector
bool forceScaleToUnity )
{
MRPT_START
vector_double input;
input.resize( inVector.size() );
input = inVector;
outVector.resize( 7 );
// Compute the centroids
TPoint3D cL(0,0,0), cR(0,0,0);
const size_t nMatches = input.size()/6;
ASSERT_EQUAL_(input.size()%6, 0)
for( unsigned int i = 0; i < nMatches; i++ )
{
cL.x += input[i*6+3];
cL.y += input[i*6+4];
cL.z += input[i*6+5];
cR.x += input[i*6+0];
cR.y += input[i*6+1];
cR.z += input[i*6+2];
}
ASSERT_ABOVE_(nMatches,0)
const double F = 1.0/nMatches;
cL *= F;
cR *= F;
CMatrixDouble33 S; // S.zeros(); // Zeroed by default
// Substract the centroid and compute the S matrix of cross products
for( unsigned int i = 0; i < nMatches; i++ )
{
input[i*6+3] -= cL.x;
input[i*6+4] -= cL.y;
input[i*6+5] -= cL.z;
input[i*6+0] -= cR.x;
input[i*6+1] -= cR.y;
input[i*6+2] -= cR.z;
S.get_unsafe(0,0) += input[i*6+3]*input[i*6+0];
S.get_unsafe(0,1) += input[i*6+3]*input[i*6+1];
S.get_unsafe(0,2) += input[i*6+3]*input[i*6+2];
S.get_unsafe(1,0) += input[i*6+4]*input[i*6+0];
S.get_unsafe(1,1) += input[i*6+4]*input[i*6+1];
S.get_unsafe(1,2) += input[i*6+4]*input[i*6+2];
S.get_unsafe(2,0) += input[i*6+5]*input[i*6+0];
S.get_unsafe(2,1) += input[i*6+5]*input[i*6+1];
S.get_unsafe(2,2) += input[i*6+5]*input[i*6+2];
}
// Construct the N matrix
CMatrixDouble44 N; // N.zeros(); // Zeroed by default
N.set_unsafe( 0,0,S.get_unsafe(0,0) + S.get_unsafe(1,1) + S.get_unsafe(2,2) );
N.set_unsafe( 0,1,S.get_unsafe(1,2) - S.get_unsafe(2,1) );
N.set_unsafe( 0,2,S.get_unsafe(2,0) - S.get_unsafe(0,2) );
N.set_unsafe( 0,3,S.get_unsafe(0,1) - S.get_unsafe(1,0) );
N.set_unsafe( 1,0,N.get_unsafe(0,1) );
N.set_unsafe( 1,1,S.get_unsafe(0,0) - S.get_unsafe(1,1) - S.get_unsafe(2,2) );
N.set_unsafe( 1,2,S.get_unsafe(0,1) + S.get_unsafe(1,0) );
N.set_unsafe( 1,3,S.get_unsafe(2,0) + S.get_unsafe(0,2) );
N.set_unsafe( 2,0,N.get_unsafe(0,2) );
N.set_unsafe( 2,1,N.get_unsafe(1,2) );
N.set_unsafe( 2,2,-S.get_unsafe(0,0) + S.get_unsafe(1,1) - S.get_unsafe(2,2) );
N.set_unsafe( 2,3,S.get_unsafe(1,2) + S.get_unsafe(2,1) );
N.set_unsafe( 3,0,N.get_unsafe(0,3) );
N.set_unsafe( 3,1,N.get_unsafe(1,3) );
N.set_unsafe( 3,2,N.get_unsafe(2,3) );
N.set_unsafe( 3,3,-S.get_unsafe(0,0) - S.get_unsafe(1,1) + S.get_unsafe(2,2) );
// q is the quaternion correspondent to the greatest eigenvector of the N matrix (last column in Z)
CMatrixDouble44 Z, D;
vector_double v;
N.eigenVectors( Z, D );
Z.extractCol( Z.getColCount()-1, v );
ASSERTDEB_( fabs( sqrt( v[0]*v[0] + v[1]*v[1] + v[2]*v[2] + v[3]*v[3] ) - 1.0 ) < 0.1 );
// Make q_r > 0
if( v[0] < 0 ){ v[0] *= -1; v[1] *= -1; v[2] *= -1; v[3] *= -1; }
CPose3DQuat q; // Create a pose rotation with the quaternion
for(unsigned int i = 0; i < 4; i++ ) // insert the quaternion part
outVector[i+3] = q[i+3] = v[i];
// Compute scale
double num = 0.0;
double den = 0.0;
for( unsigned int i = 0; i < nMatches; i++ )
{
num += square( input[i*6+0] ) + square( input[i*6+1] ) + square( input[i*6+2] );
den += square( input[i*6+3] ) + square( input[i*6+4] ) + square( input[i*6+5] );
} // end-for
// The scale:
double s = std::sqrt( num/den );
// Enforce scale to be 1
if( forceScaleToUnity )
s = 1.0;
TPoint3D pp;
q.composePoint( cL.x, cL.y, cL.z, pp.x, pp.y, pp.z );
pp*=s;
outVector[0] = cR.x - pp.x; // X
outVector[1] = cR.y - pp.y; // Y
outVector[2] = cR.z - pp.z; // Z
return s; // return scale
MRPT_END
}
/*---------------------------------------------------------------
se3_l2 (old "HornMethod()")
---------------------------------------------------------------*/
bool se3_l2_internal(
std::vector<mrpt::math::TPoint3D> & points_this, // IN/OUT: It gets modified!
std::vector<mrpt::math::TPoint3D> & points_other, // IN/OUT: It gets modified!
mrpt::poses::CPose3DQuat & out_transform,
double & out_scale,
bool forceScaleToUnity)
{
MRPT_START
ASSERT_EQUAL_(points_this.size(),points_other.size())
// Compute the centroids
TPoint3D ct_others(0,0,0), ct_this(0,0,0);
const size_t nMatches = points_this.size();
if (nMatches<3)
return false; // Nothing we can estimate without 3 points!!
for(size_t i = 0; i < nMatches; i++ )
{
ct_others += points_other[i];
ct_this += points_this [i];
}
const double F = 1.0/nMatches;
ct_others *= F;
ct_this *= F;
CMatrixDouble33 S; // Zeroed by default
// Substract the centroid and compute the S matrix of cross products
for(size_t i = 0; i < nMatches; i++ )
{
points_this[i] -= ct_this;
points_other[i] -= ct_others;
S.get_unsafe(0,0) += points_other[i].x * points_this[i].x;
S.get_unsafe(0,1) += points_other[i].x * points_this[i].y;
S.get_unsafe(0,2) += points_other[i].x * points_this[i].z;
S.get_unsafe(1,0) += points_other[i].y * points_this[i].x;
S.get_unsafe(1,1) += points_other[i].y * points_this[i].y;
S.get_unsafe(1,2) += points_other[i].y * points_this[i].z;
S.get_unsafe(2,0) += points_other[i].z * points_this[i].x;
S.get_unsafe(2,1) += points_other[i].z * points_this[i].y;
S.get_unsafe(2,2) += points_other[i].z * points_this[i].z;
}
// Construct the N matrix
CMatrixDouble44 N; // Zeroed by default
N.set_unsafe( 0,0,S.get_unsafe(0,0) + S.get_unsafe(1,1) + S.get_unsafe(2,2) );
N.set_unsafe( 0,1,S.get_unsafe(1,2) - S.get_unsafe(2,1) );
N.set_unsafe( 0,2,S.get_unsafe(2,0) - S.get_unsafe(0,2) );
N.set_unsafe( 0,3,S.get_unsafe(0,1) - S.get_unsafe(1,0) );
N.set_unsafe( 1,0,N.get_unsafe(0,1) );
N.set_unsafe( 1,1,S.get_unsafe(0,0) - S.get_unsafe(1,1) - S.get_unsafe(2,2) );
N.set_unsafe( 1,2,S.get_unsafe(0,1) + S.get_unsafe(1,0) );
N.set_unsafe( 1,3,S.get_unsafe(2,0) + S.get_unsafe(0,2) );
N.set_unsafe( 2,0,N.get_unsafe(0,2) );
N.set_unsafe( 2,1,N.get_unsafe(1,2) );
N.set_unsafe( 2,2,-S.get_unsafe(0,0) + S.get_unsafe(1,1) - S.get_unsafe(2,2) );
N.set_unsafe( 2,3,S.get_unsafe(1,2) + S.get_unsafe(2,1) );
N.set_unsafe( 3,0,N.get_unsafe(0,3) );
N.set_unsafe( 3,1,N.get_unsafe(1,3) );
N.set_unsafe( 3,2,N.get_unsafe(2,3) );
N.set_unsafe( 3,3,-S.get_unsafe(0,0) - S.get_unsafe(1,1) + S.get_unsafe(2,2) );
// q is the quaternion correspondent to the greatest eigenvector of the N matrix (last column in Z)
CMatrixDouble44 Z, D;
vector<double> v;
N.eigenVectors( Z, D );
Z.extractCol( Z.getColCount()-1, v );
ASSERTDEB_( fabs( sqrt( v[0]*v[0] + v[1]*v[1] + v[2]*v[2] + v[3]*v[3] ) - 1.0 ) < 0.1 );
// Make q_r > 0
if( v[0] < 0 ) {
v[0] *= -1;
v[1] *= -1;
v[2] *= -1;
v[3] *= -1;
}
// out_transform: Create a pose rotation with the quaternion
for(unsigned int i = 0; i < 4; i++ ) // insert the quaternion part
out_transform[i+3] = v[i];
// Compute scale
double s;
if( forceScaleToUnity )
{
s = 1.0; // Enforce scale to be 1
}
else
{
double num = 0.0;
double den = 0.0;
for(size_t i = 0; i < nMatches; i++ )
{
num += square( points_other[i].x ) + square( points_other[i].y ) + square( points_other[i].z );
den += square( points_this[i].x ) + square( points_this[i].y ) + square( points_this[i].z );
} // end-for
// The scale:
s = std::sqrt( num/den );
}
TPoint3D pp;
out_transform.composePoint( ct_others.x, ct_others.y, ct_others.z, pp.x, pp.y, pp.z );
pp*=s;
out_transform[0] = ct_this.x - pp.x; // X
out_transform[1] = ct_this.y - pp.y; // Y
out_transform[2] = ct_this.z - pp.z; // Z
out_scale=s; // return scale
return true;
MRPT_END
} // end se3_l2_internal()
/*---------------------------------------------------------------
leastSquareErrorRigidTransformation
Compute the best transformation (x,y,phi) given a set of
correspondences between 2D points in two different maps.
This method is intensively used within ICP.
---------------------------------------------------------------*/
bool tfest::se2_l2(
const TMatchingPairList& in_correspondences, TPose2D& out_transformation,
CMatrixDouble33* out_estimateCovariance)
{
MRPT_START
const size_t N = in_correspondences.size();
if (N < 2) return false;
const float N_inv = 1.0f / N; // For efficiency, keep this value.
// ----------------------------------------------------------------------
// Compute the estimated pose. Notation from the paper:
// "Mobile robot motion estimation by 2d scan matching with genetic and
// iterative
// closest point algorithms", J.L. Martinez Rodriguez, A.J. Gonzalez, J. Morales
// Rodriguez, A. Mandow Andaluz, A. J. Garcia Cerezo,
// Journal of Field Robotics, 2006.
// ----------------------------------------------------------------------
// ----------------------------------------------------------------------
// For the formulas of the covariance, see:
// http://www.mrpt.org/Paper:Occupancy_Grid_Matching
// and Jose Luis Blanco's PhD thesis.
// ----------------------------------------------------------------------
#if MRPT_HAS_SSE2
// SSE vectorized version:
//{
// TMatchingPair dumm;
// MRPT_COMPILE_TIME_ASSERT(sizeof(dumm.this_x)==sizeof(float))
// MRPT_COMPILE_TIME_ASSERT(sizeof(dumm.other_x)==sizeof(float))
//}
__m128 sum_a_xyz = _mm_setzero_ps(); // All 4 zeros (0.0f)
__m128 sum_b_xyz = _mm_setzero_ps(); // All 4 zeros (0.0f)
// [ f0 f1 f2 f3 ]
// xa*xb ya*yb xa*yb xb*ya
__m128 sum_ab_xyz = _mm_setzero_ps(); // All 4 zeros (0.0f)
for (TMatchingPairList::const_iterator corrIt = in_correspondences.begin();
corrIt != in_correspondences.end(); corrIt++)
{
// Get the pair of points in the correspondence:
// a_xyyx = [ xa ay | xa ya ]
// b_xyyx = [ xb yb | yb xb ]
// (product)
// [ xa*xb ya*yb xa*yb xb*ya
// LO0 LO1 HI2 HI3
// Note: _MM_SHUFFLE(hi3,hi2,lo1,lo0)
const __m128 a_xyz = _mm_loadu_ps(&corrIt->this_x); // *Unaligned* load
const __m128 b_xyz =
_mm_loadu_ps(&corrIt->other_x); // *Unaligned* load
const __m128 a_xyxy =
_mm_shuffle_ps(a_xyz, a_xyz, _MM_SHUFFLE(1, 0, 1, 0));
const __m128 b_xyyx =
_mm_shuffle_ps(b_xyz, b_xyz, _MM_SHUFFLE(0, 1, 1, 0));
// Compute the terms:
sum_a_xyz = _mm_add_ps(sum_a_xyz, a_xyz);
sum_b_xyz = _mm_add_ps(sum_b_xyz, b_xyz);
// [ f0 f1 f2 f3 ]
// xa*xb ya*yb xa*yb xb*ya
sum_ab_xyz = _mm_add_ps(sum_ab_xyz, _mm_mul_ps(a_xyxy, b_xyyx));
}
alignas(MRPT_MAX_ALIGN_BYTES) float sums_a[4], sums_b[4];
_mm_store_ps(sums_a, sum_a_xyz);
_mm_store_ps(sums_b, sum_b_xyz);
const float& SumXa = sums_a[0];
const float& SumYa = sums_a[1];
const float& SumXb = sums_b[0];
const float& SumYb = sums_b[1];
// Compute all four means:
const __m128 Ninv_4val =
_mm_set1_ps(N_inv); // load 4 copies of the same value
sum_a_xyz = _mm_mul_ps(sum_a_xyz, Ninv_4val);
sum_b_xyz = _mm_mul_ps(sum_b_xyz, Ninv_4val);
// means_a[0]: mean_x_a
// means_a[1]: mean_y_a
// means_b[0]: mean_x_b
// means_b[1]: mean_y_b
alignas(MRPT_MAX_ALIGN_BYTES) float means_a[4], means_b[4];
_mm_store_ps(means_a, sum_a_xyz);
_mm_store_ps(means_b, sum_b_xyz);
const float& mean_x_a = means_a[0];
const float& mean_y_a = means_a[1];
const float& mean_x_b = means_b[0];
const float& mean_y_b = means_b[1];
// Sxx Syy Sxy Syx
// xa*xb ya*yb xa*yb xb*ya
alignas(MRPT_MAX_ALIGN_BYTES) float cross_sums[4];
_mm_store_ps(cross_sums, sum_ab_xyz);
const float& Sxx = cross_sums[0];
const float& Syy = cross_sums[1];
const float& Sxy = cross_sums[2];
const float& Syx = cross_sums[3];
// Auxiliary variables Ax,Ay:
const float Ax = N * (Sxx + Syy) - SumXa * SumXb - SumYa * SumYb;
const float Ay = SumXa * SumYb + N * (Syx - Sxy) - SumXb * SumYa;
#else
// Non vectorized version:
float SumXa = 0, SumXb = 0, SumYa = 0, SumYb = 0;
float Sxx = 0, Sxy = 0, Syx = 0, Syy = 0;
for (TMatchingPairList::const_iterator corrIt = in_correspondences.begin();
corrIt != in_correspondences.end(); corrIt++)
{
// Get the pair of points in the correspondence:
const float xa = corrIt->this_x;
const float ya = corrIt->this_y;
const float xb = corrIt->other_x;
const float yb = corrIt->other_y;
// Compute the terms:
SumXa += xa;
SumYa += ya;
SumXb += xb;
SumYb += yb;
Sxx += xa * xb;
Sxy += xa * yb;
Syx += ya * xb;
Syy += ya * yb;
} // End of "for all correspondences"...
const float mean_x_a = SumXa * N_inv;
const float mean_y_a = SumYa * N_inv;
const float mean_x_b = SumXb * N_inv;
const float mean_y_b = SumYb * N_inv;
// Auxiliary variables Ax,Ay:
const float Ax = N * (Sxx + Syy) - SumXa * SumXb - SumYa * SumYb;
const float Ay = SumXa * SumYb + N * (Syx - Sxy) - SumXb * SumYa;
#endif
out_transformation.phi =
(Ax != 0 || Ay != 0)
? atan2(static_cast<double>(Ay), static_cast<double>(Ax))
: 0.0;
const double ccos = cos(out_transformation.phi);
const double csin = sin(out_transformation.phi);
out_transformation.x = mean_x_a - mean_x_b * ccos + mean_y_b * csin;
out_transformation.y = mean_y_a - mean_x_b * csin - mean_y_b * ccos;
if (out_estimateCovariance)
{
CMatrixDouble33* C = out_estimateCovariance; // less typing!
// Compute the normalized covariance matrix:
// -------------------------------------------
double var_x_a = 0, var_y_a = 0, var_x_b = 0, var_y_b = 0;
const double N_1_inv = 1.0 / (N - 1);
// 0) Precompute the unbiased variances estimations:
// ----------------------------------------------------
for (TMatchingPairList::const_iterator corrIt =
in_correspondences.begin();
corrIt != in_correspondences.end(); corrIt++)
{
var_x_a += square(corrIt->this_x - mean_x_a);
var_y_a += square(corrIt->this_y - mean_y_a);
var_x_b += square(corrIt->other_x - mean_x_b);
var_y_b += square(corrIt->other_y - mean_y_b);
}
var_x_a *= N_1_inv; // /= (N-1)
var_y_a *= N_1_inv;
var_x_b *= N_1_inv;
var_y_b *= N_1_inv;
// 1) Compute BETA = s_Delta^2 / s_p^2
// --------------------------------
const double BETA = (var_x_a + var_y_a + var_x_b + var_y_b) *
pow(static_cast<double>(N), 2.0) *
static_cast<double>(N - 1);
// 2) And the final covariance matrix:
// (remember: this matrix has yet to be
// multiplied by var_p to be the actual covariance!)
// -------------------------------------------------------
const double D = square(Ax) + square(Ay);
C->get_unsafe(0, 0) =
2.0 * N_inv + BETA * square((mean_x_b * Ay + mean_y_b * Ax) / D);
C->get_unsafe(1, 1) =
2.0 * N_inv + BETA * square((mean_x_b * Ax - mean_y_b * Ay) / D);
C->get_unsafe(2, 2) = BETA / D;
C->get_unsafe(0, 1) = C->get_unsafe(1, 0) =
-BETA * (mean_x_b * Ay + mean_y_b * Ax) *
(mean_x_b * Ax - mean_y_b * Ay) / square(D);
C->get_unsafe(0, 2) = C->get_unsafe(2, 0) =
BETA * (mean_x_b * Ay + mean_y_b * Ax) / pow(D, 1.5);
C->get_unsafe(1, 2) = C->get_unsafe(2, 1) =
BETA * (mean_y_b * Ay - mean_x_b * Ax) / pow(D, 1.5);
}
return true;
MRPT_END
}
