public void TestOptimization()
{
// generate x_i, y_i observations on test function
var random = new Random();
int n = 200;
var matX = Vector <double> .Build.Dense(n);
var matY = Vector <double> .Build.Dense(n);
double a = 100;
double b = 102;
for (int i = 0; i < n; i++)
{
double x = (random.NextDouble() / (Math.PI / 4.0)) - (Math.PI / 8.0);
double y = (a * Math.Cos(b * x)) + (b * Math.Sin(a * x)) + (random.NextDouble() * 0.1);
matX[i] = x;
matY[i] = y;
}
LevenbergMarquardt.Function f = (Vector <double> parameters) =>
{
// return y_i - f(x_i, parameters) as column vector
var error = Vector <double> .Build.Dense(n);
double a2 = parameters[0];
double b2 = parameters[1];
for (int i = 0; i < n; i++)
{
double y = (a2 * Math.Cos(b2 * matX[i])) + (b2 * Math.Sin(a2 * matX[i]));
error[i] = matY[i] - y;
}
return(error);
};
var levenbergMarquardt = new LevenbergMarquardt(f);
var parameters0 = Vector <double> .Build.Dense(2);
parameters0[0] = 90;
parameters0[1] = 96;
var rmsError = levenbergMarquardt.Minimize(parameters0);
}
static double CalibrateColorCamera(List <Matrix> worldPoints, List <System.Drawing.PointF> imagePoints, Matrix cameraMatrix, Matrix distCoeffs, Matrix rotation, Matrix translation)
{
int nPoints = worldPoints.Count;
{
Matrix R, t;
CameraMath.DLT(cameraMatrix, distCoeffs, worldPoints, imagePoints, out R, out t);
//var r = Orientation.RotationVector(R);
var r = RoomAliveToolkit.ProjectorCameraEnsemble.RotationVectorFromRotationMatrix(R);
rotation.Copy(r);
translation.Copy(t);
}
// pack parameters into vector
// parameters: fx, fy, cx, cy, k1, k2, + 3 for rotation, 3 translation = 12
int nParameters = 12;
var parameters = new Matrix(nParameters, 1);
{
int pi = 0;
parameters[pi++] = cameraMatrix[0, 0]; // fx
parameters[pi++] = cameraMatrix[1, 1]; // fy
parameters[pi++] = cameraMatrix[0, 2]; // cx
parameters[pi++] = cameraMatrix[1, 2]; // cy
parameters[pi++] = distCoeffs[0]; // k1
parameters[pi++] = distCoeffs[1]; // k2
parameters[pi++] = rotation[0];
parameters[pi++] = rotation[1];
parameters[pi++] = rotation[2];
parameters[pi++] = translation[0];
parameters[pi++] = translation[1];
parameters[pi++] = translation[2];
}
// size of our error vector
int nValues = nPoints * 2; // each component (x,y) is a separate entry
LevenbergMarquardt.Function function = delegate(Matrix p)
{
var fvec = new Matrix(nValues, 1);
// unpack parameters
int pi = 0;
double fx = p[pi++];
double fy = p[pi++];
double cx = p[pi++];
double cy = p[pi++];
double k1 = p[pi++];
double k2 = p[pi++];
var K = Matrix.Identity(3, 3);
K[0, 0] = fx;
K[1, 1] = fy;
K[0, 2] = cx;
K[1, 2] = cy;
var d = Matrix.Zero(5, 1);
d[0] = k1;
d[1] = k2;
var r = new Matrix(3, 1);
r[0] = p[pi++];
r[1] = p[pi++];
r[2] = p[pi++];
var t = new Matrix(3, 1);
t[0] = p[pi++];
t[1] = p[pi++];
t[2] = p[pi++];
//var R = Orientation.Rodrigues(r);
var R = RoomAliveToolkit.ProjectorCameraEnsemble.RotationMatrixFromRotationVector(r);
var x = new Matrix(3, 1);
int fveci = 0;
for (int i = 0; i < worldPoints.Count; i++)
{
// transform world point to local camera coordinates
x.Mult(R, worldPoints[i]);
x.Add(t);
// fvec_i = y_i - f(x_i)
double u, v;
CameraMath.Project(K, d, x[0], x[1], x[2], out u, out v);
var imagePoint = imagePoints[i];
fvec[fveci++] = imagePoint.X - u;
fvec[fveci++] = imagePoint.Y - v;
}
return(fvec);
};
// optimize
var calibrate = new LevenbergMarquardt(function);
while (calibrate.State == LevenbergMarquardt.States.Running)
{
var rmsError = calibrate.MinimizeOneStep(parameters);
Console.WriteLine("rms error = " + rmsError);
}
for (int i = 0; i < nParameters; i++)
{
Console.WriteLine(parameters[i] + "\t");
}
Console.WriteLine();
// unpack parameters
{
int pi = 0;
double fx = parameters[pi++];
double fy = parameters[pi++];
double cx = parameters[pi++];
double cy = parameters[pi++];
double k1 = parameters[pi++];
double k2 = parameters[pi++];
cameraMatrix[0, 0] = fx;
cameraMatrix[1, 1] = fy;
cameraMatrix[0, 2] = cx;
cameraMatrix[1, 2] = cy;
distCoeffs[0] = k1;
distCoeffs[1] = k2;
rotation[0] = parameters[pi++];
rotation[1] = parameters[pi++];
rotation[2] = parameters[pi++];
translation[0] = parameters[pi++];
translation[1] = parameters[pi++];
translation[2] = parameters[pi++];
}
return(calibrate.RMSError);
}
static double CalibrateDepthCamera(List <Matrix> worldPoints, List <System.Drawing.PointF> imagePoints, Matrix cameraMatrix, Matrix distCoeffs)
{
int nPoints = worldPoints.Count;
// pack parameters into vector
// parameters: fx, fy, cx, cy, k1, k2 = 6 parameters
int nParameters = 6;
var parameters = new Matrix(nParameters, 1);
{
int pi = 0;
parameters[pi++] = cameraMatrix[0, 0]; // fx
parameters[pi++] = cameraMatrix[1, 1]; // fy
parameters[pi++] = cameraMatrix[0, 2]; // cx
parameters[pi++] = cameraMatrix[1, 2]; // cy
parameters[pi++] = distCoeffs[0]; // k1
parameters[pi++] = distCoeffs[1]; // k2
}
// size of our error vector
int nValues = nPoints * 2; // each component (x,y) is a separate entry
LevenbergMarquardt.Function function = delegate(Matrix p)
{
var fvec = new Matrix(nValues, 1);
// unpack parameters
int pi = 0;
double fx = p[pi++];
double fy = p[pi++];
double cx = p[pi++];
double cy = p[pi++];
double k1 = p[pi++];
double k2 = p[pi++];
var K = Matrix.Identity(3, 3);
K[0, 0] = fx;
K[1, 1] = fy;
K[0, 2] = cx;
K[1, 2] = cy;
var d = Matrix.Zero(5, 1);
d[0] = k1;
d[1] = k2;
int fveci = 0;
for (int i = 0; i < worldPoints.Count; i++)
{
// fvec_i = y_i - f(x_i)
double u, v;
var x = worldPoints[i];
CameraMath.Project(K, d, x[0], x[1], x[2], out u, out v);
var imagePoint = imagePoints[i];
fvec[fveci++] = imagePoint.X - u;
fvec[fveci++] = imagePoint.Y - v;
}
return(fvec);
};
// optimize
var calibrate = new LevenbergMarquardt(function);
while (calibrate.State == LevenbergMarquardt.States.Running)
{
var rmsError = calibrate.MinimizeOneStep(parameters);
Console.WriteLine("rms error = " + rmsError);
}
for (int i = 0; i < nParameters; i++)
{
Console.WriteLine(parameters[i] + "\t");
}
Console.WriteLine();
// unpack parameters
{
int pi = 0;
double fx = parameters[pi++];
double fy = parameters[pi++];
double cx = parameters[pi++];
double cy = parameters[pi++];
double k1 = parameters[pi++];
double k2 = parameters[pi++];
cameraMatrix[0, 0] = fx;
cameraMatrix[1, 1] = fy;
cameraMatrix[0, 2] = cx;
cameraMatrix[1, 2] = cy;
distCoeffs[0] = k1;
distCoeffs[1] = k2;
}
return(calibrate.RMSError);
}
private static double CalibrateColorCamera(List <Vector <double> > worldPoints, List <System.Drawing.PointF> imagePoints, Matrix <double> cameraMatrix, Vector <double> distCoeffs, Vector <double> rotation, Vector <double> translation, bool silent = true)
{
int nPoints = worldPoints.Count;
{
Matrix <double> R;
Vector <double> t;
DLT(cameraMatrix, distCoeffs, worldPoints, imagePoints, out R, out t);
var r = RotationExtensions.MatrixToAxisAngle(R);
r.CopyTo(rotation);
t.CopyTo(translation);
}
// pack parameters into vector
// parameters: fx, fy, cx, cy, k1, k2, + 3 for rotation, 3 translation = 12
int nParameters = 12;
var parameters = Vector <double> .Build.Dense(nParameters);
{
int pi = 0;
parameters[pi++] = cameraMatrix[0, 0]; // fx
parameters[pi++] = cameraMatrix[1, 1]; // fy
parameters[pi++] = cameraMatrix[0, 2]; // cx
parameters[pi++] = cameraMatrix[1, 2]; // cy
parameters[pi++] = distCoeffs[0]; // k1
parameters[pi++] = distCoeffs[1]; // k2
parameters[pi++] = rotation[0];
parameters[pi++] = rotation[1];
parameters[pi++] = rotation[2];
parameters[pi++] = translation[0];
parameters[pi++] = translation[1];
parameters[pi++] = translation[2];
}
// size of our error vector
int nValues = nPoints * 2; // each component (x,y) is a separate entry
LevenbergMarquardt.Function function = delegate(Vector <double> p)
{
var fvec = Vector <double> .Build.Dense(nValues);
// unpack parameters
int pi = 0;
double fx = p[pi++];
double fy = p[pi++];
double cx = p[pi++];
double cy = p[pi++];
double k1 = p[pi++];
double k2 = p[pi++];
var K = Matrix <double> .Build.DenseIdentity(3, 3);
K[0, 0] = fx;
K[1, 1] = fy;
K[0, 2] = cx;
K[1, 2] = cy;
var d = Vector <double> .Build.Dense(5, 0);
d[0] = k1;
d[1] = k2;
var r = Vector <double> .Build.Dense(3);
r[0] = p[pi++];
r[1] = p[pi++];
r[2] = p[pi++];
var t = Vector <double> .Build.Dense(3);
t[0] = p[pi++];
t[1] = p[pi++];
t[2] = p[pi++];
var R = RotationExtensions.AxisAngleToMatrix(r);
int fveci = 0;
for (int i = 0; i < worldPoints.Count; i++)
{
// transform world point to local camera coordinates
var x = R * worldPoints[i];
x += t;
// fvec_i = y_i - f(x_i)
double u, v;
KinectInternalCalibration.Project(K, d, x[0], x[1], x[2], out u, out v);
var imagePoint = imagePoints[i];
fvec[fveci++] = imagePoint.X - u;
fvec[fveci++] = imagePoint.Y - v;
}
return(fvec);
};
// optimize
var calibrate = new LevenbergMarquardt(function);
while (calibrate.State == LevenbergMarquardt.States.Running)
{
var rmsError = calibrate.MinimizeOneStep(parameters);
if (!silent)
{
Console.WriteLine("rms error = " + rmsError);
}
}
if (!silent)
{
for (int i = 0; i < nParameters; i++)
{
Console.WriteLine(parameters[i] + "\t");
}
Console.WriteLine();
}
// unpack parameters
{
int pi = 0;
double fx = parameters[pi++];
double fy = parameters[pi++];
double cx = parameters[pi++];
double cy = parameters[pi++];
double k1 = parameters[pi++];
double k2 = parameters[pi++];
cameraMatrix[0, 0] = fx;
cameraMatrix[1, 1] = fy;
cameraMatrix[0, 2] = cx;
cameraMatrix[1, 2] = cy;
distCoeffs[0] = k1;
distCoeffs[1] = k2;
rotation[0] = parameters[pi++];
rotation[1] = parameters[pi++];
rotation[2] = parameters[pi++];
translation[0] = parameters[pi++];
translation[1] = parameters[pi++];
translation[2] = parameters[pi++];
}
return(calibrate.RMSError);
}
public static double CalibrateCameraExtrinsicsOnly(List <List <Matrix> > worldPointSets, List <List <System.Drawing.PointF> > imagePointSets,
Matrix cameraMatrix, ref List <Matrix> rotations, ref List <Matrix> translations)
{
int nSets = worldPointSets.Count;
int nPoints = 0;
for (int i = 0; i < nSets; i++)
{
nPoints += worldPointSets[i].Count; // for later
}
var distCoeffs = Matrix.Zero(2, 1);
//// if necessary run DLT on each point set to get initial rotation and translations
//if (rotations == null)
//{
// rotations = new List<Matrix>();
// translations = new List<Matrix>();
// for (int i = 0; i < nSets; i++)
// {
// Matrix R, t;
// CameraMath.DLT(cameraMatrix, distCoeffs, worldPointSets[i], imagePointSets[i], out R, out t);
// var r = CameraMath.RotationVectorFromRotationMatrix(R);
// rotations.Add(r);
// translations.Add(t);
// }
//}
// Levenberg-Marquardt for camera matrix (ignore lens distortion for now)
// pack parameters into vector
// parameters: camera has f, cx, cy; each point set has rotation + translation (6)
//int nParameters = 3 + 6 * nSets;
int nParameters = 6 * nSets;
var parameters = new Matrix(nParameters, 1);
{
int pi = 0;
//parameters[pi++] = cameraMatrix[0, 0]; // f
//parameters[pi++] = cameraMatrix[0, 2]; // cx
//parameters[pi++] = cameraMatrix[1, 2]; // cy
for (int i = 0; i < nSets; i++)
{
parameters[pi++] = rotations[i][0];
parameters[pi++] = rotations[i][1];
parameters[pi++] = rotations[i][2];
parameters[pi++] = translations[i][0];
parameters[pi++] = translations[i][1];
parameters[pi++] = translations[i][2];
}
}
// size of our error vector
int nValues = nPoints * 2; // each component (x,y) is a separate entry
LevenbergMarquardt.Function function = delegate(Matrix p)
{
var fvec = new Matrix(nValues, 1);
// unpack parameters
int pi = 0;
//double f = p[pi++];
//double cx = p[pi++];
//double cy = p[pi++];
var K = Matrix.Identity(3, 3);
//K[0, 0] = f;
//K[1, 1] = f;
//K[0, 2] = cx;
//K[1, 2] = cy;
K[0, 0] = cameraMatrix[0, 0];
K[1, 1] = cameraMatrix[1, 1];
K[0, 2] = cameraMatrix[0, 2];
K[1, 2] = cameraMatrix[1, 2];
var d = Matrix.Zero(2, 1);
int fveci = 0;
for (int i = 0; i < nSets; i++)
{
var rotation = new Matrix(3, 1);
rotation[0] = p[pi++];
rotation[1] = p[pi++];
rotation[2] = p[pi++];
var R = RotationMatrixFromRotationVector(rotation);
var t = new Matrix(3, 1);
t[0] = p[pi++];
t[1] = p[pi++];
t[2] = p[pi++];
var worldPoints = worldPointSets[i];
var imagePoints = imagePointSets[i];
var x = new Matrix(3, 1);
for (int j = 0; j < worldPoints.Count; j++)
{
// transform world point to local camera coordinates
x.Mult(R, worldPoints[j]);
x.Add(t);
// fvec_i = y_i - f(x_i)
double u, v;
CameraMath.Project(K, d, x[0], x[1], x[2], out u, out v);
var imagePoint = imagePoints[j];
fvec[fveci++] = imagePoint.X - u;
fvec[fveci++] = imagePoint.Y - v;
}
}
return(fvec);
};
// optimize
var calibrate = new LevenbergMarquardt(function);
calibrate.minimumReduction = 1.0e-4;
calibrate.Minimize(parameters);
//while (calibrate.State == LevenbergMarquardt.States.Running)
//{
// var rmsError = calibrate.MinimizeOneStep(parameters);
// Console.WriteLine("rms error = " + rmsError);
//}
//for (int i = 0; i < nParameters; i++)
// Console.WriteLine(parameters[i] + "\t");
//Console.WriteLine();
// unpack parameters
{
int pi = 0;
//double f = parameters[pi++];
//double cx = parameters[pi++];
//double cy = parameters[pi++];
//cameraMatrix[0, 0] = f;
//cameraMatrix[1, 1] = f;
//cameraMatrix[0, 2] = cx;
//cameraMatrix[1, 2] = cy;
for (int i = 0; i < nSets; i++)
{
rotations[i][0] = parameters[pi++];
rotations[i][1] = parameters[pi++];
rotations[i][2] = parameters[pi++];
translations[i][0] = parameters[pi++];
translations[i][1] = parameters[pi++];
translations[i][2] = parameters[pi++];
}
}
return(calibrate.RMSError);
}
