/**
* constructor to create a view
*
* @param projection: projection image as Grid2D
* @param radon: radon transformed and derived image as Grid2D
* @param projMatrix: projection matrix as Projection
*/
public View(Grid2D projection, Grid2D radon, Projection projMatrix) {
// Initialize center matrix //
CENTER = new SimpleMatrix(3, 4);
CENTER.setDiagValue(new SimpleVector(1.0, 1.0, 1.0));
// get data out of projection //
this.projectionWidth = projection.getWidth();
this.projectionHeight = projection.getHeight();
// get data out of radon transformed image //
this.radonWidth = radon.getWidth();
this.radonHeight = radon.getHeight();
this.projectionDiag =
Math.sqrt(projectionWidth * projectionWidth + projectionHeight * projectionHeight);
this.lineIncrement = radonWidth / projectionDiag;
this.angleIncrement = radonHeight / Math.PI;
// store radon transformed image //
this.radon = radon;
// get projection matrix P (3x4) //
this.P = SimpleOperators.multiplyMatrixProd(projMatrix.getK(), CENTER);
this.P = SimpleOperators.multiplyMatrixProd(this.P, projMatrix.getRt());
// get source position C (nullspace of the projection) //
DecompositionSVD decoP = new DecompositionSVD(this.P);
this.C = decoP.getV().getCol(3);
// normalize source vectors by last component //
// it is important that the last component is positive to have a positive center
// as it is defined in oriented projective geometry
this.C = this.C.dividedBy(this.C.getElement(3));
}
/**
* method to calculate a mapping K from two source positions C0, C1 to a plane C0 (C1) is the
* source position from the first (second) view
*/
public void createMappingToEpipolarPlane() {
// set up source matrices //
SimpleVector C0 = this.view1.C;
SimpleVector C1 = this.view2.C;
// compute Pluecker coordinates //
double L01 = C0.getElement(0) * C1.getElement(1) - C0.getElement(1) * C1.getElement(0);
double L02 = C0.getElement(0) * C1.getElement(2) - C0.getElement(2) * C1.getElement(0);
double L03 = C0.getElement(0) * C1.getElement(3) - C0.getElement(3) * C1.getElement(0);
double L12 = C0.getElement(1) * C1.getElement(2) - C0.getElement(2) * C1.getElement(1);
double L13 = C0.getElement(1) * C1.getElement(3) - C0.getElement(3) * C1.getElement(1);
double L23 = C0.getElement(2) * C1.getElement(3) - C0.getElement(3) * C1.getElement(2);
// construct B (6x1) //
SimpleVector B = new SimpleVector(L01, L02, L03, L12, L13, L23);
// compute infinity point in direction of B //
SimpleVector N = new SimpleVector(-L03, -L13, -L23, 0);
// compute plane E0 containing B and X0=(0,0,0,1) //
SimpleVector E0 = SimpleOperators.getPlueckerJoin(B, new SimpleVector(0, 0, 0, 1));
// find othonormal basis from plane normals //
// (vectors are of 3x1)
SimpleVector a2 = new SimpleVector(E0.getElement(0), E0.getElement(1), E0.getElement(2));
SimpleVector a3 = new SimpleVector(N.getElement(0), N.getElement(1), N.getElement(2));
// set vectors to unit length
a2.normalizeL2();
a3.normalizeL2();
// calculate cross product to get the last basis vector //
SimpleVector a1 = General.crossProduct(a2, a3).negated();
// (a1 is already of unit length -> no normalization needed)
// set up assembly matrix A (4x3) //
SimpleMatrix A = new SimpleMatrix(4, 3);
A.setSubColValue(0, 0, a1);
A.setSubColValue(0, 1, a2);
A.setSubColValue(0, 2, C0);
// store mapping matrix K (4x3 = 4x4 * 4x3) //
this.K = SimpleOperators.multiplyMatrixProd(SimpleOperators.getPlueckerMatrixDual(B), A);
}