Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

ENH: Added jacobian computation to ComposeScaleSkewVersorTransform #1755

Merged
merged 2 commits into from
Apr 7, 2020
Merged

ENH: Added jacobian computation to ComposeScaleSkewVersorTransform #1755

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
fabb2bd
ENH: Added jacobian computation to ComposeScaleSkewVersorTransform
aylward Apr 7, 2020
26453f5
STYLE: Improved clarity and completeness of documentation.
aylward Apr 7, 2020
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
132 changes: 86 additions & 46 deletions Modules/Core/Transform/include/itkComposeScaleSkewVersor3DTransform.hxx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -306,71 +306,111 @@ ComposeScaleSkewVersor3DTransform<TParametersValueType>::PrintSelf(std::ostream
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComputeJacobianWithRespectToParameters(
const InputPointType & itkNotUsed(p),
JacobianType & itkNotUsed(jacobian)) const
const InputPointType & p,
JacobianType & jacobian) const
{
// This document how the jacobian can be computed for certain parameters;
// however, the proper computation of the scale and skew parameters is
// now given or computed, so ultimately an exception is thrown.
// Jacobian computed via
// pip install sympy
//
// from sympy import Derivative, simplify
// from sympy import symbols
// from sympy.matrices import Matrix
// x0, x1, x2, v0, v1, v2, w, o0, o1, o2, s0, s1, s2, k0, k1, k2 =
// symbols('x0 x1 x2 v0 v1 v2 w o0 o1 o2 s0 s1 s2 k0 k1 k2')
// M = Matrix([[1-2*(v1*v1+v2*v2), 2*(v0*v1-v2*w), 2*(v0*v2+v1*w), o0],
// [2*(v0*v1+v2*w), 1-2*(v0*v0+v2*v2), 2*(v1*v2-v0*w), o1],
// [2*(v0*v2-v1*w), 2*(v1*v2+v0*w), 1-2*(v0*v0+v1*v1), o2],
// [0, 0, 0, 1]])
// # Quaterion to Matrix from:
// # https://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/index.htm
// S = Matrix([[s0, 0, 0, 0], [0, s1, 0, 0], [0, 0, s2, 0], [0, 0, 0, 1]])
// K = Matrix([[1, k0, k1, 0], [0, 1, k2, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
// x = Matrix(4,1,[x0,x1,x2,1])
// f = M*S*K*x
// fx = Derivative(f,v1) # substitute v0, v2, s0 etc for v1 to list all equs.
// simplify(fx)
//

/*
using ValueType = typename VersorType::ValueType;

// compute derivatives with respect to rotation
const ValueType vx = this->GetVersor().GetX();
const ValueType vy = this->GetVersor().GetY();
const ValueType vz = this->GetVersor().GetZ();
const ValueType vw = this->GetVersor().GetW();
const ValueType v0 = this->GetVersor().GetX();
const ValueType v1 = this->GetVersor().GetY();
const ValueType v2 = this->GetVersor().GetZ();
const ValueType w = this->GetVersor().GetW();

jacobian.SetSize(3, this->GetNumberOfLocalParameters());
jacobian.Fill(0.0);

const double px = p[0] - this->GetCenter()[0];
const double py = p[1] - this->GetCenter()[1];
const double pz = p[2] - this->GetCenter()[2];
const ValueType s0 = this->GetScale()[0];
const ValueType s1 = this->GetScale()[1];
const ValueType s2 = this->GetScale()[2];

const double vxx = vx * vx;
const double vyy = vy * vy;
const double vzz = vz * vz;
const double vww = vw * vw;
const ValueType k0 = this->GetSkew()[0];
const ValueType k1 = this->GetSkew()[1];
const ValueType k2 = this->GetSkew()[2];

const double vxy = vx * vy;
const double vxz = vx * vz;
const double vxw = vx * vw;
const double x0 = p[0] - this->GetCenter()[0];
const double x1 = p[1] - this->GetCenter()[1];
const double x2 = p[2] - this->GetCenter()[2];

const double vyz = vy * vz;
const double vyw = vy * vw;
jacobian.SetSize(3, this->GetNumberOfLocalParameters());
jacobian.Fill(0.0);

const double vzw = vz * vw;
double v0v0 = v0 * v0;
double v0v1 = v0 * v1;
double v0v2 = v0 * v2;
double v0w = v0 * w;
double v1v1 = v1 * v1;
double v1v2 = v1 * v2;
double v1w = v1 * w;
double v2v2 = v2 * v2;
double v2w = v2 * w;

// compute Jacobian with respect to quaternion parameters
jacobian[0][0] = 2.0 * ((vyw + vxz) * py + (vzw - vxy) * pz) / vw;
jacobian[1][0] = 2.0 * ((vyw - vxz) * px - 2 * vxw * py + (vxx - vww) * pz) / vw;
jacobian[2][0] = 2.0 * ((vzw + vxy) * px + (vww - vxx) * py - 2 * vxw * pz) / vw;

jacobian[0][1] = 2.0 * (-2 * vyw * px + (vxw + vyz) * py + (vww - vyy) * pz) / vw;
jacobian[1][1] = 2.0 * ((vxw - vyz) * px + (vzw + vxy) * pz) / vw;
jacobian[2][1] = 2.0 * ((vyy - vww) * px + (vzw - vxy) * py - 2 * vyw * pz) / vw;

jacobian[0][2] = 2.0 * (-2 * vzw * px + (vzz - vww) * py + (vxw - vyz) * pz) / vw;
jacobian[1][2] = 2.0 * ((vww - vzz) * px - 2 * vzw * py + (vyw + vxz) * pz) / vw;
jacobian[2][2] = 2.0 * ((vxw + vyz) * px + (vyw - vxz) * py) / vw;
jacobian[0][0] = 2 * s1 * v1 * x1 + x2 * (2 * k2 * s1 * v1 + 2 * s2 * v2);
jacobian[1][0] =
2 * s0 * v1 * x0 + x1 * (2 * k0 * s0 * v1 - 4 * s1 * v0) - x2 * (-2 * k1 * s0 * v1 + 4 * k2 * s1 * v0 + 2 * s2 * w);
jacobian[2][0] =
2 * s0 * v2 * x0 + 2 * x1 * (k0 * s0 * v2 + s1 * w) + x2 * (2 * k1 * s0 * v2 + 2 * k2 * s1 * w - 4 * s2 * v0);

jacobian[0][1] = -4 * s0 * v1 * x0 - x1 * (4 * k0 * s0 * v1 - 2 * s1 * v0) +
x2 * (-4 * k1 * s0 * v1 + 2 * k2 * s1 * v0 + 2 * s2 * w);
jacobian[1][1] = 2 * k0 * s0 * v0 * x1 + 2 * s0 * v0 * x0 - x2 * (-2 * k1 * s0 * v0 - 2 * s2 * v2);
jacobian[2][1] =
-2 * s0 * w * x0 + 2 * x1 * (-k0 * s0 * w + s1 * v2) + x2 * (-2 * k1 * s0 * w + 2 * k2 * s1 * v2 - 4 * s2 * v1);

jacobian[0][2] =
-4 * s0 * v2 * x0 - x1 * (4 * k0 * s0 * v2 + 2 * s1 * w) + x2 * (-4 * k1 * s0 * v2 - 2 * k2 * s1 * w + 2 * s2 * v0);
jacobian[1][2] =
2 * s0 * w * x0 + x1 * (2 * k0 * s0 * w - 4 * s1 * v2) - x2 * (-2 * k1 * s0 * w + 4 * k2 * s1 * v2 - 2 * s2 * v1);
jacobian[2][2] = 2 * s0 * v0 * x0 + 2 * x1 * (k0 * s0 * v0 + s1 * v1) + x2 * (2 * k1 * s0 * v0 + 2 * k2 * s1 * v1);

jacobian[0][3] = 1.0;
jacobian[1][4] = 1.0;
jacobian[2][5] = 1.0;

jacobian[0][6] = px; // These are incorrect!
jacobian[1][7] = py;
jacobian[2][8] = pz;
jacobian[0][6] =
-k0 * x1 * (2 * v1v1 + 2 * v2v2 - 1) - k1 * x2 * (2 * v1v1 + 2 * v2v2 - 1) - x0 * (2 * v1v1 + 2 * v2v2 - 1);
jacobian[1][6] = 2 * k0 * x1 * (v0v1 + v2w) + 2 * k1 * x2 * (v0v1 + v2w) + 2 * x0 * (v0v1 + v2w);
jacobian[2][6] = 2 * k0 * x1 * (v0v2 - v1w) + 2 * k1 * x2 * (v0v2 - v1w) + 2 * x0 * (v0v2 - v1w);

jacobian[0][7] = 2 * k2 * x2 * (v0v1 - v2w) - x1 * (-2 * v0v1 + 2 * v2w);
jacobian[1][7] = -k2 * x2 * (2 * v0v0 + 2 * v2v2 - 1) + x1 * (-2 * v0v0 - 2 * v2v2 + 1);
jacobian[2][7] = 2 * k2 * x2 * (v0w + v1v2) + 2 * x1 * (v0w + v1v2);

jacobian[0][8] = x2 * (2 * v0v2 + 2 * v1w);
jacobian[1][8] = -x2 * (2 * v0w - 2 * v1v2);
jacobian[2][8] = x2 * (-2 * v0v0 - 2 * v1v1 + 1);

jacobian[0][9] = -s0 * x1 * (2 * v1v1 + 2 * v2v2 - 1);
jacobian[1][9] = 2 * s0 * x1 * (v0v1 + v2w);
jacobian[2][9] = 2 * s0 * x1 * (v0v2 - v1w);

jacobian[0][9] = px; // These are incorrect!
jacobian[1][10] = py;
jacobian[2][11] = pz;
*/
jacobian[0][10] = -s0 * x2 * (2 * v1v1 + 2 * v2v2 - 1);
jacobian[1][10] = 2 * s0 * x2 * (v0v1 + v2w);
jacobian[2][10] = 2 * s0 * x2 * (v0v2 - v1w);

itkExceptionMacro(<< "Computing the Jacobian of a ComposeScaleSkewVersor3D"
<< " transform is not supported at this time.");
jacobian[0][11] = 2 * s1 * x2 * (v0v1 - v2w);
jacobian[1][11] = -s1 * x2 * (2 * v0v0 + 2 * v2v2 - 1);
jacobian[2][11] = 2 * s1 * x2 * (v0w + v1v2);
}

} // namespace itk
Expand Down
51 changes: 43 additions & 8 deletions Modules/Core/Transform/test/itkComposeScaleSkewVersor3DTransformTest.cxx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -535,18 +535,53 @@ itkComposeScaleSkewVersor3DTransformTest(int, char *[])
}
std::cout << "SetMatrix() points check Passed !" << std::endl;

#if 0 // TODO: Need to instrument inverse of ScaleVersor3DTransform
TransformType::Pointer tInverse = TransformType::New();
if (!transform->GetInverse(tInverse))
{
std::cout << "Cannot create inverse transform" << std::endl;
return EXIT_FAILURE;
}
std::cout << "translation: " << transform;
std::cout << "translationInverse: " << tInverse;

std::cout << "Testing jacobian" << std::endl;
TransformType::InputPointType pnt;
pnt[0] = 10;
pnt[1] = 20;
pnt[2] = -10;
TransformType::Pointer idT = TransformType::New();
for (unsigned int mc = 0; mc < np; ++mc)
{
std::cout << "Testing parameter #" << mc << std::endl;
idT->SetIdentity();
ParametersType params = idT->GetParameters();
params[mc] = 0.1;
idT->SetParameters(params);
TransformType::InputPointType pntT = idT->TransformPoint(pnt);
TransformType::JacobianType jacob;
idT->ComputeJacobianWithRespectToParameters(pnt, jacob);
for (unsigned int i = 0; i < np; ++i)
{
TransformType::Pointer tInverse = TransformType::New();
if(!transform->GetInverse(tInverse))
ParametersType params1 = params;
params1[i] += epsilon;
idT->SetParameters(params1);
TransformType::InputPointType pnt1 = idT->TransformPoint(pnt);
ParametersType params2 = params;
params2[i] -= epsilon;
idT->SetParameters(params2);
TransformType::InputPointType pnt2 = idT->TransformPoint(pnt);
for (unsigned int d = 0; d < 3; ++d)
{
std::cout << "Cannot create inverse transform" << std::endl;
return EXIT_FAILURE;
double pntDiff = (pnt1[d] - pnt2[d]) / (2 * epsilon);
if (fabs(pntDiff - jacob[d][i]) > fabs(0.1 * pntDiff))
{
std::cout << "Ideal = " << pntDiff << " Jacob = " << jacob[d][i] << std::endl;
std::cout << "Jacobian not matching finite difference." << std::endl;
return EXIT_FAILURE;
}
}
std::cout << "translation: " << transform;
std::cout << "translationInverse: " << tInverse;
}
#endif
}
}
std::cout << std::endl << "Test PASSED ! " << std::endl;

Expand Down