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Shows how to compute a trifocal tensor after it has been computed. Trifocal tensors compactly represent 3-view geometry and just computing them will remove many outliers which made their way through robust 2-view tests. Once known they can be used to predict the locations of points in different views and when decomposed can be used to easily create consistent projective reconstructions.

Example Code:


  • Three view geometry
  • Reconstruction

Related Examples:

Example Code

 * Shows a few example uses of the trifocal tensor.
public class ExampleTrifocalTensorUses {
	public static void main( String[] args ) {
		// Load three images/views
		String name = "rock_leaves_";
		GrayU8 gray01 = UtilImageIO.loadImage(UtilIO.pathExample("triple/" + name + "01.jpg"), GrayU8.class);
		GrayU8 gray02 = UtilImageIO.loadImage(UtilIO.pathExample("triple/" + name + "02.jpg"), GrayU8.class);
		GrayU8 gray03 = UtilImageIO.loadImage(UtilIO.pathExample("triple/" + name + "03.jpg"), GrayU8.class);

		// Get the trifocal tensor for these three images
		var tensor = new TrifocalTensor();
		List<AssociatedTriple> inliers = ExampleComputeTrifocalTensor.imagesToTrifocal(gray01, gray02, gray03, tensor);
		// The inlier set from robustly fitting a trifocal tensor is one of its more helpful uses.
		// It has fewer degenerate situations than a straight forward application of fundamental/essential matrices.
		// Unlike with two views where you find the distance from the epipolar line, if you use three views there is
		// a unique pixel in each view and that will improve the efficiency of many SFM applications. Yes, if you
		// know what you are doing it's possible to use multiple stereo pairs. However, most people do that incorrectly
		// which will yield worse results.

		// Trifocal tensor to 3 compatible camera matrices
		// Camera matrix for view-1, P1, is going to be identity
		DMatrixRMaj P2 = new DMatrixRMaj(3, 4);
		DMatrixRMaj P3 = new DMatrixRMaj(3, 4);
		MultiViewOps.trifocalToCameraMatrices(tensor, P2, P3);
		// These camera matrices are useful if doing a projective reconstruction.

		// One thing that you can do with a trifocal tensor is transfer points from one view onto another
		// Similar to what you would do with a homography.
		AssociatedTriple match = inliers.get(4);
		Point3D_F64 predicted3 = new Point3D_F64(); // pixel, but in homogenous coordinates
		MultiViewOps.transfer_1_to_3(tensor, match.p1, match.p2, predicted3);

		System.out.printf("Predicted x3=(%.1f, %.1f)  actual=(%.1f, %.1f)\n",
				predicted3.x/predicted3.z, predicted3.y/predicted3.z, match.p3.x, match.p3.y);

		// You can get two fundamental matrices from the trifocal tensor
		DMatrixRMaj F21 = new DMatrixRMaj(3, 3);
		DMatrixRMaj F31 = new DMatrixRMaj(3, 3);
		MultiViewOps.trifocalToFundamental(tensor, F21, F31);

		// Scale is arbitrary so let's make it norm of 1
		CommonOps_DDRM.divide(F21, NormOps_DDRM.normF(F21));
		CommonOps_DDRM.divide(F31, NormOps_DDRM.normF(F31));

		// Demonstration the epipolar constraint works here. This should be close to zero
		System.out.println("x2'*F21*X1 = " + MultiViewOps.constraint(F21, match.p1, match.p2));
		System.out.println("x3'*F31*X1 = " + MultiViewOps.constraint(F31, match.p1, match.p3));

		// For examples of how a trifocal tensor can be used in self calibration see
		// ExampleTrifocalStereoUncalibrated