Example Three View Stereo Uncalibrated

Left is disparity image and Right is found 3D Point Cloud

Given three views from an unknown camera compute a dense 3D point cloud. Similar to the uncalibrated two view example, but much more stable. With three view's its possible to prune many more false associations because there is a unique projection in each view. A Trifocal Tensor fit to the associations with RANSAC instead of a Fundamental matrix in the two view case.

See code comments below for a summary of all the processing steps involved.

Example File:

• ExampleTrifocalStereoUncalibrated.java

Videos:

• Theoretical Explanation
• Three View Stereo

Concepts:

• Self calibration / Automatic Calibration
• Projective Geometry
• Metric Geometry
• Bundle Adjustment
• Three View Feature Association
• Trifocal Tensor
• Rectification
• Dense stereo processing

Related Tutorials/Example Code:

• Stereo Single Calibrated Camera
• Stereo Uncalibrated
• Bundle Adjustment
• Stereo Disparity Example
• Calibrated Stereo Rectification Example
• Camera Calibration Tutorial

Example Code

/**
 * In this example three uncalibrated images are used to compute a point cloud. Extrinsic as well as all intrinsic
 * parameters (e.g. focal length and lens distortion) are found. Stereo disparity is computed between two of
 * the three views and the point cloud derived from that. To keep the code (relatively) simple, extra steps which
 * improve convergence have been omitted. See {@link ThreeViewEstimateMetricScene} for
 * a more robust version of what has been presented here. Even with these simplifications this example can be
 * difficult to fully understand.
 *
 * Three images produce a more stable "practical" algorithm when dealing with uncalibrated images.
 * With just two views its impossible to remove all false matches since an image feature can lie any where
 * along an epipolar line in other other view. Even with three views, results are not always stable or 100% accurate
 * due to scene geometry and here the views were captured. In general you want a well textured scene with objects
 * up close and far away, and images taken with translational
 * motion. Pure rotation and planar scenes are impossible to estimate the structure from.
 *
 * Steps:
 * <ol>
 *     <li>Feature Detection (e.g. SURF)</li>
 *     <li>Two view association</li>
 *     <li>Find 3 View Tracks</li>
 *     <li>Fit Trifocal tensor using RANSAC</li>
 *     <li>Get and refine camera matrices</li>
 *     <li>Compute dual absolute quadratic</li>
 *     <li>Estimate intrinsic parameters from DAC</li>
 *     <li>Estimate metric scene structure</li>
 *     <li>Sparse bundle adjustment</li>
 *     <li>Rectify two of the images</li>
 *     <li>Compute stereo disparity</li>
 *     <li>Convert into a point cloud</li>
 * </ol>
 *
 * For a more stable and accurate version this example see {@link ThreeViewEstimateMetricScene}.
 *
 * @author Peter Abeles
 */
public class ExampleTrifocalStereoUncalibrated {
	public static void main( String[] args ) {
		String name = "rock_leaves_";
//		String name = "mono_wall_";
//		String name = "minecraft_cave1_";
//		String name = "minecraft_distant_";
//		String name = "bobcats_";
//		String name = "chicken_";
//		String name = "turkey_";
//		String name = "rockview_";
//		String name = "pebbles_";
//		String name = "books_";
//		String name = "skull_";
//		String name = "triflowers_";

		BufferedImage buff01 = UtilImageIO.loadImageNotNull(UtilIO.pathExample("triple/" + name + "01.jpg"));
		BufferedImage buff02 = UtilImageIO.loadImageNotNull(UtilIO.pathExample("triple/" + name + "02.jpg"));
		BufferedImage buff03 = UtilImageIO.loadImageNotNull(UtilIO.pathExample("triple/" + name + "03.jpg"));

		Planar<GrayU8> color01 = ConvertBufferedImage.convertFrom(buff01, true, ImageType.pl(3, GrayU8.class));
		Planar<GrayU8> color02 = ConvertBufferedImage.convertFrom(buff02, true, ImageType.pl(3, GrayU8.class));
		Planar<GrayU8> color03 = ConvertBufferedImage.convertFrom(buff03, true, ImageType.pl(3, GrayU8.class));

		GrayU8 image01 = ConvertImage.average(color01, null);
		GrayU8 image02 = ConvertImage.average(color02, null);
		GrayU8 image03 = ConvertImage.average(color03, null);

		// using SURF features. Robust and fairly fast to compute
		DetectDescribePoint<GrayU8, TupleDesc_F64> detDesc = FactoryDetectDescribe.surfStable(
				new ConfigFastHessian(0, 4, 1000, 1, 9, 4, 2), null, null, GrayU8.class);

		// Associate features across all three views using previous example code
		var associateThree = new ExampleAssociateThreeView();
		associateThree.initialize(detDesc);
		associateThree.detectFeatures(image01, 0);
		associateThree.detectFeatures(image02, 1);
		associateThree.detectFeatures(image03, 2);

		System.out.println("features01.size = " + associateThree.features01.size);
		System.out.println("features02.size = " + associateThree.features02.size);
		System.out.println("features03.size = " + associateThree.features03.size);

		int width = image01.width, height = image01.height;
		System.out.println("Image Shape " + width + " x " + height);
		double cx = width/2;
		double cy = height/2;

		// The self calibration step requires that the image coordinate system be in the image center
		associateThree.locations01.forEach(p -> p.setTo(p.x - cx, p.y - cy));
		associateThree.locations02.forEach(p -> p.setTo(p.x - cx, p.y - cy));
		associateThree.locations03.forEach(p -> p.setTo(p.x - cx, p.y - cy));

		// Converting data formats for the found features into what can be processed by SFM algorithms
		// Notice how the image center is subtracted from the coordinates? In many cases a principle point
		// of zero is assumed. This is a reasonable assumption in almost all modern cameras. Errors in
		// the principle point tend to materialize as translations and are non fatal.

		// Associate features in the three views using image information alone
		DogArray<AssociatedTripleIndex> associatedIdx = associateThree.threeViewPairwiseAssociate();

		// Convert the matched indexes into AssociatedTriple which contain the actual pixel coordinates
		var associated = new DogArray<>(AssociatedTriple::new);
		associatedIdx.forEach(p -> associated.grow().setTo(
				associateThree.locations01.get(p.a),
				associateThree.locations02.get(p.b),
				associateThree.locations03.get(p.c)));

		System.out.println("Total Matched Triples = " + associated.size);

		var model = new TrifocalTensor();
		List<AssociatedTriple> inliers = ExampleComputeTrifocalTensor.computeTrifocal(associated, model);

		System.out.println("Remaining after RANSAC " + inliers.size());

		// Show remaining associations from RANSAC
		var triplePanel = new AssociatedTriplePanel();
		triplePanel.setPixelOffset(cx, cy);
		triplePanel.setImages(buff01, buff02, buff03);
		triplePanel.setAssociation(inliers);
		ShowImages.showWindow(triplePanel, "Associations", true);

		// estimate using all the inliers
		// No need to re-scale the input because the estimator automatically adjusts the input on its own
		var configTri = new ConfigTrifocal();
		configTri.which = EnumTrifocal.ALGEBRAIC_7;
		configTri.converge.maxIterations = 100;
		Estimate1ofTrifocalTensor trifocalEstimator = FactoryMultiView.trifocal_1(configTri);
		if (!trifocalEstimator.process(inliers, model))
			throw new RuntimeException("Estimator failed");
		model.print();

		DMatrixRMaj P1 = CommonOps_DDRM.identity(3, 4);
		DMatrixRMaj P2 = new DMatrixRMaj(3, 4);
		DMatrixRMaj P3 = new DMatrixRMaj(3, 4);
		MultiViewOps.trifocalToCameraMatrices(model, P2, P3);

		// Most of the time this refinement step makes little difference, but in some edges cases it appears
		// to help convergence
		System.out.println("Refining projective camera matrices");
		RefineThreeViewProjective refineP23 = FactoryMultiView.threeViewRefine(null);
		if (!refineP23.process(inliers, P2, P3, P2, P3))
			throw new RuntimeException("Can't refine P2 and P3!");


		var selfcalib = new SelfCalibrationLinearDualQuadratic(1.0);
		selfcalib.addCameraMatrix(P1);
		selfcalib.addCameraMatrix(P2);
		selfcalib.addCameraMatrix(P3);

		var listPinhole = new ArrayList<CameraPinhole>();
		GeometricResult result = selfcalib.solve();
		if (GeometricResult.SOLVE_FAILED != result) {
			for (int i = 0; i < 3; i++) {
				Intrinsic c = selfcalib.getIntrinsics().get(i);
				CameraPinhole p = new CameraPinhole(c.fx, c.fy, 0, 0, 0, width, height);
				listPinhole.add(p);
			}
		} else {
			System.out.println("Self calibration failed!");
			for (int i = 0; i < 3; i++) {
				CameraPinhole p = new CameraPinhole(width/2, width/2, 0, 0, 0, width, height);
				listPinhole.add(p);
			}
		}

		// print the initial guess for focal length. Focal length is a crtical and difficult to estimate
		// parameter
		for (int i = 0; i < 3; i++) {
			CameraPinhole r = listPinhole.get(i);
			System.out.println("fx=" + r.fx + " fy=" + r.fy + " skew=" + r.skew);
		}

		System.out.println("Projective to metric");
		// convert camera matrix from projective to metric
		var H = new DMatrixRMaj(4, 4); // storage for rectifying homography
		if (!MultiViewOps.absoluteQuadraticToH(selfcalib.getQ(), H))
			throw new RuntimeException("Projective to metric failed");

		var K = new DMatrixRMaj(3, 3);
		var worldToView = new ArrayList<Se3_F64>();
		for (int i = 0; i < 3; i++) {
			worldToView.add(new Se3_F64());
		}

		// ignore K since we already have that
		MultiViewOps.projectiveToMetric(P1, H, worldToView.get(0), K);
		MultiViewOps.projectiveToMetric(P2, H, worldToView.get(1), K);
		MultiViewOps.projectiveToMetric(P3, H, worldToView.get(2), K);

		// scale is arbitrary. Set max translation to 1
		adjustTranslationScale(worldToView);

		// Construct bundle adjustment data structure
		var structure = new SceneStructureMetric(false);
		structure.initialize(3, 3, inliers.size());

		var observations = new SceneObservations();
		observations.initialize(3);

		for (int i = 0; i < listPinhole.size(); i++) {
			BundlePinholeSimplified bp = new BundlePinholeSimplified();
			bp.f = listPinhole.get(i).fx;
			structure.setCamera(i, false, bp);
			structure.setView(i, i, i == 0, worldToView.get(i));
		}
		for (int i = 0; i < inliers.size(); i++) {
			AssociatedTriple t = inliers.get(i);

			observations.getView(0).add(i, (float)t.p1.x, (float)t.p1.y);
			observations.getView(1).add(i, (float)t.p2.x, (float)t.p2.y);
			observations.getView(2).add(i, (float)t.p3.x, (float)t.p3.y);

			structure.connectPointToView(i, 0);
			structure.connectPointToView(i, 1);
			structure.connectPointToView(i, 2);
		}

		// Initial estimate for point 3D locations
		triangulatePoints(structure, observations);

		ConfigLevenbergMarquardt configLM = new ConfigLevenbergMarquardt();
		configLM.dampeningInitial = 1e-3;
		configLM.hessianScaling = false;
		ConfigBundleAdjustment configSBA = new ConfigBundleAdjustment();
		configSBA.configOptimizer = configLM;

		// Create and configure the bundle adjustment solver
		BundleAdjustment<SceneStructureMetric> bundleAdjustment = FactoryMultiView.bundleSparseMetric(configSBA);
		// prints out useful debugging information that lets you know how well it's converging
//		bundleAdjustment.setVerbose(System.out,0);
		bundleAdjustment.configure(1e-6, 1e-6, 100); // convergence criteria

		bundleAdjustment.setParameters(structure, observations);
		bundleAdjustment.optimize(structure);

		// See if the solution is physically possible. If not fix and run bundle adjustment again
		checkBehindCamera(structure, observations, bundleAdjustment);

		// It's very difficult to find the best solution due to the number of local minimum. In the three view
		// case it's often the problem that a small translation is virtually identical to a small rotation.
		// Convergence can be improved by considering that possibility

		// Now that we have a decent solution, prune the worst outliers to improve the fit quality even more
		var pruner = new PruneStructureFromSceneMetric(structure, observations);
		pruner.pruneObservationsByErrorRank(0.7);
		pruner.pruneViews(10);
		pruner.pruneUnusedMotions();
		pruner.prunePoints(1);
		bundleAdjustment.setParameters(structure, observations);
		bundleAdjustment.optimize(structure);

		System.out.println("Final Views");
		for (int i = 0; i < 3; i++) {
			BundlePinholeSimplified cp = structure.getCameras().get(i).getModel();
			Vector3D_F64 T = structure.getParentToView(i).T;
			System.out.printf("[ %d ] f = %5.1f T=%s\n", i, cp.f, T.toString());
		}

		System.out.println("\n\nComputing Stereo Disparity");
		BundlePinholeSimplified cp = structure.getCameras().get(0).getModel();
		var intrinsic01 = new CameraPinholeBrown();
		intrinsic01.fsetK(cp.f, cp.f, 0, cx, cy, width, height);
		intrinsic01.fsetRadial(cp.k1, cp.k2);

		cp = structure.getCameras().get(1).getModel();
		var intrinsic02 = new CameraPinholeBrown();
		intrinsic02.fsetK(cp.f, cp.f, 0, cx, cy, width, height);
		intrinsic02.fsetRadial(cp.k1, cp.k2);

		Se3_F64 leftToRight = structure.getParentToView(1);

		// TODO dynamic max disparity
		computeStereoCloud(image01, image02, color01, color02, intrinsic01, intrinsic02, leftToRight, 0, 250);
	}

	private static void adjustTranslationScale( List<Se3_F64> worldToView ) {
		double maxT = 0;
		for (Se3_F64 p : worldToView) {
			maxT = Math.max(maxT, p.T.norm());
		}
		for (Se3_F64 p : worldToView) {
			p.T.scale(1.0/maxT);
			p.print();
		}
	}

	// TODO Do this correction without running bundle adjustment again
	private static void checkBehindCamera( SceneStructureMetric structure, SceneObservations observations, BundleAdjustment<SceneStructureMetric> bundleAdjustment ) {

		int totalBehind = 0;
		Point3D_F64 X = new Point3D_F64();
		for (int i = 0; i < structure.points.size; i++) {
			structure.points.data[i].get(X);
			if (X.z < 0)
				totalBehind++;
		}
		structure.getParentToView(1).T.print();
		if (totalBehind > structure.points.size/2) {
			System.out.println("Flipping because it's reversed. score = " + bundleAdjustment.getFitScore());
			for (int i = 1; i < structure.views.size; i++) {
				Se3_F64 w2v = structure.getParentToView(i);
				w2v.setTo(w2v.invert(null));
			}
			triangulatePoints(structure, observations);

			bundleAdjustment.setParameters(structure, observations);
			bundleAdjustment.optimize(structure);
			System.out.println("  after = " + bundleAdjustment.getFitScore());
		} else {
			System.out.println("Points not behind camera. " + totalBehind + " / " + structure.points.size);
		}
	}

	public static void computeStereoCloud( GrayU8 distortedLeft, GrayU8 distortedRight,
										   Planar<GrayU8> colorLeft, Planar<GrayU8> colorRight,
										   CameraPinholeBrown intrinsicLeft,
										   CameraPinholeBrown intrinsicRight,
										   Se3_F64 leftToRight,
										   int minDisparity, int rangeDisparity ) {

//		drawInliers(origLeft, origRight, intrinsic, inliers);

		// Rectify and remove lens distortion for stereo processing
		var rectifiedK = new DMatrixRMaj(3, 3);
		var rectifiedR = new DMatrixRMaj(3, 3);

		// rectify a colored image
		Planar<GrayU8> rectColorLeft = colorLeft.createSameShape();
		Planar<GrayU8> rectColorRight = colorLeft.createSameShape();
		GrayU8 rectMask = new GrayU8(colorLeft.width, colorLeft.height);

		rectifyImages(colorLeft, colorRight, leftToRight, intrinsicLeft, intrinsicRight,
				rectColorLeft, rectColorRight, rectMask, rectifiedK, rectifiedR);

		if (rectifiedK.get(0, 0) < 0)
			throw new RuntimeException("Egads");

		System.out.println("Rectified K");
		rectifiedK.print();

		System.out.println("Rectified R");
		rectifiedR.print();

		GrayU8 rectifiedLeft = distortedLeft.createSameShape();
		GrayU8 rectifiedRight = distortedRight.createSameShape();
		ConvertImage.average(rectColorLeft, rectifiedLeft);
		ConvertImage.average(rectColorRight, rectifiedRight);

		// compute disparity
		var config = new ConfigDisparityBMBest5();
		config.errorType = DisparityError.CENSUS;
		config.disparityMin = minDisparity;
		config.disparityRange = rangeDisparity;
		config.subpixel = true;
		config.regionRadiusX = config.regionRadiusY = 6;
		config.validateRtoL = 1;
		config.texture = 0.2;
		StereoDisparity<GrayU8, GrayF32> disparityAlg =
				FactoryStereoDisparity.blockMatchBest5(config, GrayU8.class, GrayF32.class);

		// process and return the results
		disparityAlg.process(rectifiedLeft, rectifiedRight);
		GrayF32 disparity = disparityAlg.getDisparity();
		RectifyImageOps.applyMask(disparity, rectMask, 0);

		// show results
		BufferedImage visualized = VisualizeImageData.disparity(disparity, null, rangeDisparity, 0);

		BufferedImage outLeft = ConvertBufferedImage.convertTo(rectColorLeft, null, true);
		BufferedImage outRight = ConvertBufferedImage.convertTo(rectColorRight, null, true);

		ShowImages.showWindow(new RectifiedPairPanel(true, outLeft, outRight), "Rectification", true);
		ShowImages.showWindow(visualized, "Disparity", true);

		showPointCloud(disparity, outLeft, leftToRight, rectifiedK, rectifiedR, minDisparity, rangeDisparity);
	}
}