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 boofcv.alg.sfm.structure.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.loadImage(UtilIO.pathExample("triple/"+name+"01.jpg"));
		BufferedImage buff02 = UtilImageIO.loadImage(UtilIO.pathExample("triple/"+name+"02.jpg"));
		BufferedImage buff03 = UtilImageIO.loadImage(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,BrightFeature> detDesc = FactoryDetectDescribe.surfStable(
				new ConfigFastHessian(0, 4, 1000, 1, 9, 4, 2), null,null, GrayU8.class);

		FastQueue<Point2D_F64> locations01 = new FastQueue<>(Point2D_F64::new);
		FastQueue<Point2D_F64> locations02 = new FastQueue<>(Point2D_F64::new);
		FastQueue<Point2D_F64> locations03 = new FastQueue<>(Point2D_F64::new);

		FastQueue<BrightFeature> features01 = UtilFeature.createQueue(detDesc,100);
		FastQueue<BrightFeature> features02 = UtilFeature.createQueue(detDesc,100);
		FastQueue<BrightFeature> features03 = UtilFeature.createQueue(detDesc,100);

		// 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.

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

		detDesc.detect(image01);
		for (int i = 0; i < detDesc.getNumberOfFeatures(); i++) {
			Point2D_F64 pixel = detDesc.getLocation(i);
			locations01.grow().set(pixel.x-cx,pixel.y-cy);
			features01.grow().setTo(detDesc.getDescription(i));
		}
		detDesc.detect(image02);
		for (int i = 0; i < detDesc.getNumberOfFeatures(); i++) {
			Point2D_F64 pixel = detDesc.getLocation(i);
			locations02.grow().set(pixel.x-cx,pixel.y-cy);
			features02.grow().setTo(detDesc.getDescription(i));
		}
		detDesc.detect(image03);
		for (int i = 0; i < detDesc.getNumberOfFeatures(); i++) {
			Point2D_F64 pixel = detDesc.getLocation(i);
			locations03.grow().set(pixel.x-cx,pixel.y-cy);
			features03.grow().setTo(detDesc.getDescription(i));
		}

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

		ScoreAssociation<BrightFeature> scorer = FactoryAssociation.scoreEuclidean(BrightFeature.class,true);
		AssociateDescription<BrightFeature> associate = FactoryAssociation.greedy(new ConfigAssociateGreedy(true,0.1),scorer);

		AssociateThreeByPairs<BrightFeature> associateThree = new AssociateThreeByPairs<>(associate,BrightFeature.class);

		associateThree.setFeaturesA(features01);
		associateThree.setFeaturesB(features02);
		associateThree.setFeaturesC(features03);

		associateThree.associate();

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

		ConfigRansac configRansac = new ConfigRansac();
		configRansac.iterations = 500;
		configRansac.inlierThreshold = 1;

		ConfigTrifocal configTri = new ConfigTrifocal();
		ConfigTrifocalError configError = new ConfigTrifocalError();
		configError.model = ConfigTrifocalError.Model.REPROJECTION_REFINE;

		Ransac<TrifocalTensor,AssociatedTriple> ransac =
				FactoryMultiViewRobust.trifocalRansac(configTri,configError,configRansac);

		FastQueue<AssociatedTripleIndex> associatedIdx = associateThree.getMatches();
		FastQueue<AssociatedTriple> associated = new FastQueue<>(AssociatedTriple::new);
		for (int i = 0; i < associatedIdx.size; i++) {
			AssociatedTripleIndex p = associatedIdx.get(i);
			associated.grow().set(locations01.get(p.a),locations02.get(p.b),locations03.get(p.c));
		}
		ransac.process(associated.toList());

		List<AssociatedTriple> inliers = ransac.getMatchSet();
		TrifocalTensor model = ransac.getModelParameters();
		System.out.println("Remaining after RANSAC "+inliers.size());

		// Show remaining associations from RANSAC
		AssociatedTriplePanel 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
		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.extractCameraMatrices(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!");


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

		List<CameraPinhole> listPinhole = new ArrayList<>();
		GeometricResult result = selfcalib.solve();
		if(GeometricResult.SOLVE_FAILED != result) {
			for (int i = 0; i < 3; i++) {
				Intrinsic c = selfcalib.getSolutions().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
		DMatrixRMaj H = new DMatrixRMaj(4,4); // storage for rectifying homography
		if( !MultiViewOps.absoluteQuadraticToH(selfcalib.getQ(),H) )
			throw new RuntimeException("Projective to metric failed");

		DMatrixRMaj K = new DMatrixRMaj(3,3);
		List<Se3_F64> worldToView = new ArrayList<>();
		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
		SceneStructureMetric structure = new SceneStructureMetric(false);
		structure.initialize(3,3,inliers.size());

		SceneObservations 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==0,worldToView.get(i));
			structure.connectViewToCamera(i,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
		PruneStructureFromSceneMetric pruner = new PruneStructureFromSceneMetric(structure,observations);
		pruner.pruneObservationsByErrorRank(0.7);
		pruner.pruneViews(10);
		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.getViews().data[i].worldToView.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();
		CameraPinholeBrown 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();
		CameraPinholeBrown intrinsic02 = new CameraPinholeBrown();
		intrinsic02.fsetK(cp.f,cp.f,0,cx,cy,width,height);
		intrinsic02.fsetRadial(cp.k1,cp.k2);

		Se3_F64 leftToRight = structure.views.data[1].worldToView;

		// 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.views.data[1].worldToView.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.views.data[i].worldToView;
				w2v.set(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
		DMatrixRMaj rectifiedK = new DMatrixRMaj(3, 3);
		DMatrixRMaj 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
		ConfigDisparityBMBest5 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);
	}
}