/**
* 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};
}
/**
* 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 compute the metric for the epipolar consistency conditions between two views with
* varying angle kappa from lowerBorderAngle to upperBorderAngle with an increment of
* angleIncrement
*
* @param lowerBorderAngle
* @param upperBorderAngle
* @param angleIncrement
* @return: 2D-array containing the line integral values of two different views of all angles
* running in the range defined by the input parameters the stored format is [angle,
* valueView1, valueView2] in the first dimension, increasing/decreasing angle in the second
*/
public double[][] evaluateConsistency(
double lowerBorderAngle, double upperBorderAngle, double angleIncrement) {
// compute the mapping matrix to the epipolar plane //
createMappingToEpipolarPlane();
// (K is a 4x3 matrix)
// calculate inverses of projection matrices and save to view //
this.view1.P_Inverse = this.view1.P.inverse(InversionType.INVERT_SVD);
this.view2.P_Inverse = this.view2.P.inverse(InversionType.INVERT_SVD);
// get number of decimal places of the angleIncrement //
String[] split = Double.toString(angleIncrement).split("\\.");
int decimalPlaces = split[1].length();
// obtain size parameter for results array //
int height = (int) ((upperBorderAngle - lowerBorderAngle) / angleIncrement + 1);
// results are saved in an array in the format [angle,valueView1,valueView2]
double[][] results = new double[height][3];
int count = 0;
// go through angles //
for (double kappa = lowerBorderAngle; kappa <= upperBorderAngle; kappa += angleIncrement) {
double kappa_RAD = kappa / 180.0 * Math.PI;
// get values for line integrals that fulfill the epipolar consistency conditions //
double[] values = computeEpipolarLineIntegrals(kappa_RAD);
// store values in results array //
results[count][0] =
Math.round(kappa * Math.pow(10, decimalPlaces)) / (Math.pow(10, decimalPlaces) + 0.0);
results[count][1] = values[0];
results[count][2] = values[1];
count++;
}
// show results //
for (int i = 0; i < results.length; i++) {
System.out.println(
"at angle kappa: " + results[i][0] + " P1: " + results[i][1] + " P2: " + results[i][2]);
}
return results;
}
/**
* method to compute the squared radon transformed and derived image for one view the derivation
* is done in t-direction (distance to origin)
*
* @param data: Grid2D which represents the projection
* @param radonSize: value to determine the size of the squared radon transformed and derived
* image
* @return: radon transformed image as Grid2D (its size is radonSize x radonSize)
*/
public static Grid2D computeRadonTrafoAndDerive(Grid2D data, int radonSize) {
Grid2D radon = null;
// optional: preprocessing can be done here
// for example:
/*
float value;
for (int i = 0; i < data.getWidth(); i++) {
for (int j = 0; j < data.getHeight(); j++) {
if (j < 10 || j > data.getHeight() - 11) {
// set border to zero
value = 0.0f;
} else {
value = (float)(-Math.log(data.getAtIndex(i, j) / 0.842f));
}
data.setAtIndex(i, j, value);
}
}
data.show("preprocessed image");
*/
// * get some dimensions out of data (projection) *//
int projSizeX = data.getWidth();
int projSizeY = data.getHeight();
double projectionDiag = Math.sqrt(projSizeX * projSizeX + projSizeY * projSizeY);
double deltaS = projectionDiag / radonSize;
double deltaTheta = Math.PI / radonSize;
// * create a parallel projector in order to compute the radon transformation *//
ParallelProjector2D projector =
new ParallelProjector2D(Math.PI, deltaTheta, projectionDiag, deltaS);
// * create radon transformation *//
radon = projector.projectRayDriven(data);
// for a faster GPU implementation use: (possibly not working):
// radon = projector.projectRayDrivenCL(data);
// * derivative by Sobel operator in t-direction *//
final int size = 1024;
SobelKernel1D kernel = new SobelKernel1D(size, 9);
kernel.applyToGrid(radon);
// * optional: save file in tiff-format *//
/*
FileSaver saveRadon = new FileSaver(ImageUtil.wrapGrid(radon, ""));
saveRadon.saveAsTiff();
*/
return radon;
}
/**
* 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);
}
