/**
* Method to calculate alpha and t as indices from the radon transformed image of a view.
* Neccessary are the inverse projection image (as SimpleMatrix) and the epipolar plane E
*
* @param E: epipolar plane E as SimpleVector (4 entries)
* @return: line integral value as double
*/
private double getValueByAlphaAndT(SimpleVector E) {
// compute corresponding epipolar lines //
// (epipolar lines are of 3x1 = 3x4 * 4x1)
SimpleVector l_kappa = SimpleOperators.multiply(this.P_Inverse.transposed(), E);
// init the coordinate shift //
int t_u = this.projectionWidth / 2;
int t_v = this.projectionHeight / 2;
// compute angle alpha and distance to origin t //
double l0 = l_kappa.getElement(0);
double l1 = l_kappa.getElement(1);
double l2 = l_kappa.getElement(2);
double alpha_kappa_RAD = Math.atan2(-l0, l1) + Math.PI / 2;
double t_kappa = -l2 / Math.sqrt(l0 * l0 + l1 * l1);
// correct the coordinate shift //
t_kappa -= t_u * Math.cos(alpha_kappa_RAD) + t_v * Math.sin(alpha_kappa_RAD);
// correct some alpha falling out of the radon window //
if (alpha_kappa_RAD < 0) {
alpha_kappa_RAD *= -1.0;
} else if (alpha_kappa_RAD > Math.PI) {
alpha_kappa_RAD = 2.0 * Math.PI - alpha_kappa_RAD;
}
// write back to l_kappa //
l_kappa.setElementValue(0, Math.cos(alpha_kappa_RAD));
l_kappa.setElementValue(1, Math.sin(alpha_kappa_RAD));
l_kappa.setElementValue(2, -t_kappa);
// calculate x and y coordinates for derived radon transformed image //
double x = t_kappa * this.lineIncrement + 0.5 * this.radonWidth;
double y = alpha_kappa_RAD * this.angleIncrement;
// get intensity value out of radon transformed image //
// (interpolation needed)
return InterpolationOperators.interpolateLinear(this.radon, x, y);
}
/**
* method to compute the epipolar line integrals that state the epipolar consistency conditions by
* comparison of two views
*
* @param kappa_RAD: angle of epipolar plane
* @return double[] array containing two values (one for each view's line integral)
*/
public double[] computeEpipolarLineIntegrals(double kappa_RAD) {
// compute points on unit-circle (3x1) //
SimpleVector x_kappa = new SimpleVector(Math.cos(kappa_RAD), Math.sin(kappa_RAD), 1);
// compute epipolar plane E_kappa (4x1 = 4x3 * 3x1) //
SimpleVector E_kappa = SimpleOperators.multiply(this.K, x_kappa);
// compute line integral out of derived radon transform //
double value1 = view1.getValueByAlphaAndT(E_kappa);
double value2 = view2.getValueByAlphaAndT(E_kappa);
// both values are returned //
return new double[] {value1, value2};
}
