public CvMat Solve()
{
// 重心の計算
CvPoint3D64f fromCenter = new CvPoint3D64f();
CvPoint3D64f toCenter = new CvPoint3D64f();
double weightSum = 0;
foreach (var tuple in _correspondings)
{
fromCenter += tuple.Item1 * tuple.Item3;
toCenter += tuple.Item2 * tuple.Item3;
weightSum += tuple.Item3;
}
if (weightSum != 0)
{
fromCenter *= 1.0 / weightSum;
toCenter *= 1.0 / weightSum;
}
// q: quaternion; 4x1
// fn, tn: from[n], to[n]; 3x1
// Xn: (tn - fn, (tn+fn)×[1,0,0], (tn+fn)×[0,1,0], (tn+fn)×[0,0,1]); 3x4
// M: Σi(Xi^t Wi Xi); 4x4
// Wi: I; 3x3
// J = q^t Mq -> min
// 最小二乗法
using (CvMat M = new CvMat(4, 4, MatrixType.F64C1))
{
M.Zero();
foreach (var tuple in _correspondings)
{
// 重心からの距離
CvPoint3D64f fromVector = tuple.Item1 - fromCenter;
CvPoint3D64f toVector = tuple.Item2 - toCenter;
using (CvMat Xi = new CvMat(3, 4, MatrixType.F64C1))
{
CvPoint3D64f diff = toVector - fromVector;
CvPoint3D64f sum = toVector + fromVector;
CvPoint3D64f second = CvEx.Cross(sum, new CvPoint3D64f(1, 0, 0));
CvPoint3D64f third = CvEx.Cross(sum, new CvPoint3D64f(0, 1, 0));
CvPoint3D64f fourth = CvEx.Cross(sum, new CvPoint3D64f(0, 0, 1));
CvEx.FillCvMat(Xi, new double[] { diff.X, second.X, third.X, fourth.X, diff.Y, second.Y, third.Y, fourth.Y, diff.Z, second.Z, third.Z, fourth.Z });
using (CvMat XiTranspose = Xi.Transpose())
using (CvMat addend = XiTranspose * Xi * tuple.Item3)
{
M.Add(addend, M);
}
}
}
using (CvMat MTemp = CvEx.CloneCvMat(M))
using (CvMat eVals = new CvMat(4, 1, MatrixType.F64C1))
using (CvMat eVects = new CvMat(4, 4, MatrixType.F64C1))
{
//Cv.EigenVV(MTemp, eVects, eVals, 0.000001);
Cv.SVD(MTemp, eVals, eVects, null, SVDFlag.U_T | SVDFlag.ModifyA);
int minEIndex = 3;
/*
* if (false)
* {
* double minE = double.MaxValue;
* for (int i = 0; i < 4; i++)
* {
* double eVal = Math.Abs(eVals[i, 0]);
* if (eVal < minE)
* {
* minE = eVal;
* minEIndex = i;
* }
* }
* }
*/
CvMat ret = new CvMat(4, 4, MatrixType.F64C1);
ret.Zero();
ret[3, 3] = 1.0;
CvMat rotateConversion;
/*
* if (false)
* {
* // こっちの変換はほとんど恒等のときに誤差が大きい
* CvMat q = eVects.GetRow(minEIndex);
*
* // クォータニオンから回転ベクトルを計算
* double theta = Math.Acos(q[0, 0]) * 2;
* double sin = Math.Sin(theta / 2);
* CvPoint3D64f rot = new CvPoint3D64f(q[0, 1] / sin * theta, q[0, 2] / sin * theta, q[0, 3] / sin * theta);
* // 回転ベクトルから回転行列を計算
* ret.GetSubRect(out rotateConversion, new CvRect(0, 0, 3, 3));
* using (CvMat rotVector = new CvMat(1, 3, MatrixType.F64C1))
* {
* rotVector[0, 0] = rot.X;
* rotVector[0, 1] = rot.Y;
* rotVector[0, 2] = rot.Z;
* Cv.Rodrigues2(rotVector, rotateConversion);
* }
* }
* else
* {*/
CvMat rotationMat = CvEx.QuaternionToMat3D(eVects[minEIndex, 0], eVects[minEIndex, 1], eVects[minEIndex, 2], eVects[minEIndex, 3]);
ret.GetSubRect(out rotateConversion, new CvRect(0, 0, 3, 3));
rotationMat.Copy(rotateConversion);
//}
// 回転後の重心の並進成分の計算
using (CvMat fromCenterMat = new CvMat(3, 1, MatrixType.F64C1))
{
CvEx.FillCvMat(fromCenterMat, new double[] { fromCenter.X, fromCenter.Y, fromCenter.Z });
using (CvMat rotFromCenterMat = rotateConversion * fromCenterMat)
{
CvPoint3D64f rotFromCenter = new CvPoint3D64f(rotFromCenterMat[0, 0], rotFromCenterMat[1, 0], rotFromCenterMat[2, 0]);
CvPoint3D64f offset = toCenter - rotFromCenter;
ret[0, 3] = offset.X;
ret[1, 3] = offset.Y;
ret[2, 3] = offset.Z;
return(ret);
}
}
}
}
}
