/**
* Extracts the epipoles from the trifocal tensor. Extracted epipoles will have a norm of 1 as an
* artifact of using SVD.
*
* @param tensor Input: Trifocal tensor. Not Modified
* @param e2 Output: Epipole in image 2. Homogeneous coordinates. Modified
* @param e3 Output: Epipole in image 3. Homogeneous coordinates. Modified
*/
public void process(TrifocalTensor tensor, Point3D_F64 e2, Point3D_F64 e3) {
svd.decompose(tensor.T1);
SingularOps.nullVector(svd, true, v1);
SingularOps.nullVector(svd, false, u1);
svd.decompose(tensor.T2);
SingularOps.nullVector(svd, true, v2);
SingularOps.nullVector(svd, false, u2);
svd.decompose(tensor.T3);
SingularOps.nullVector(svd, true, v3);
SingularOps.nullVector(svd, false, u3);
for (int i = 0; i < 3; i++) {
U.set(i, 0, u1.get(i));
U.set(i, 1, u2.get(i));
U.set(i, 2, u3.get(i));
V.set(i, 0, v1.get(i));
V.set(i, 1, v2.get(i));
V.set(i, 2, v3.get(i));
}
svd.decompose(U);
SingularOps.nullVector(svd, false, tempE);
e2.set(tempE.get(0), tempE.get(1), tempE.get(2));
svd.decompose(V);
SingularOps.nullVector(svd, false, tempE);
e3.set(tempE.get(0), tempE.get(1), tempE.get(2));
}
@Override
public void encode(CalibratedPoseAndPoint model, double[] param) {
int paramIndex = 0;
// first decode the transformation
for (int i = 0; i < numViews; i++) {
// don't encode if it is already known
if (knownView[i]) continue;
Se3_F64 se = model.getWorldToCamera(i);
// force the "rotation matrix" to be an exact rotation matrix
// otherwise Rodrigues will have issues with the noise
if (!svd.decompose(se.getR())) throw new RuntimeException("SVD failed");
DenseMatrix64F U = svd.getU(null, false);
DenseMatrix64F V = svd.getV(null, false);
CommonOps.multTransB(U, V, R);
// extract Rodrigues coordinates
RotationMatrixGenerator.matrixToRodrigues(R, rotation);
param[paramIndex++] = rotation.unitAxisRotation.x * rotation.theta;
param[paramIndex++] = rotation.unitAxisRotation.y * rotation.theta;
param[paramIndex++] = rotation.unitAxisRotation.z * rotation.theta;
Vector3D_F64 T = se.getT();
param[paramIndex++] = T.x;
param[paramIndex++] = T.y;
param[paramIndex++] = T.z;
}
for (int i = 0; i < numPoints; i++) {
Point3D_F64 p = model.getPoint(i);
param[paramIndex++] = p.x;
param[paramIndex++] = p.y;
param[paramIndex++] = p.z;
}
}
/**
* Computes a basis (the principle components) from the most dominant eigenvectors.
*
* @param numComponents Number of vectors it will use to describe the data. Typically much smaller
* than the number of elements in the input vector.
*/
public void computeBasis(int numComponents) {
if (numComponents > A.getNumCols())
throw new IllegalArgumentException("More components requested that the data's length.");
if (sampleIndex != A.getNumRows())
throw new IllegalArgumentException("Not all the data has been added");
if (numComponents > sampleIndex)
throw new IllegalArgumentException(
"More data needed to compute the desired number of components");
this.numComponents = numComponents;
// compute the mean of all the samples
for (int i = 0; i < A.getNumRows(); i++) {
for (int j = 0; j < mean.length; j++) {
mean[j] += A.get(i, j);
}
}
for (int j = 0; j < mean.length; j++) {
mean[j] /= A.getNumRows();
}
// subtract the mean from the original data
for (int i = 0; i < A.getNumRows(); i++) {
for (int j = 0; j < mean.length; j++) {
A.set(i, j, A.get(i, j) - mean[j]);
}
}
// Compute SVD and save time by not computing U
SingularValueDecomposition<DenseMatrix64F> svd =
DecompositionFactory.svd(A.numRows, A.numCols, false, true, false);
if (!svd.decompose(A)) throw new RuntimeException("SVD failed");
V_t = svd.getV(null, true);
DenseMatrix64F W = svd.getW(null);
// Singular values are in an arbitrary order initially
SingularOps.descendingOrder(null, false, W, V_t, true);
// strip off unneeded components and find the basis
V_t.reshape(numComponents, mean.length, true);
}