Difference between revisions of "Example Stereo Single Camera"

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A dense point cloud of an environment can be created from a single camera using two views. If the distance between the two views is not known, then the scale of the found point cloud will be arbitrary. In this example natural features are used to determine the geometric relationship between the two views.  The algorithm can be summarized as follows:
In this scenario we wish to compute a dense point cloud from two views taken with the same calibrated camera. Because the intrinsic parameters are known, it is easier to converge towards a valid solution than the entirely [[Example_Stereo_Uncalibrated|uncalibrated scenario]].
 
Because the extrinsic parameters (translation and rotation) between the two views is unknown the scene's structure can only be recovered up to a scale factor. In this example natural features are used to determine the geometric relationship between the two views.  The algorithm can be summarized as follows:


* Load camera calibration and two images
* Load camera calibration and two images
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Example File:  
Example File:  
* [https://github.com/lessthanoptimal/BoofCV/blob/v0.22/examples/src/boofcv/examples/stereo/ExampleStereoTwoViewsOneCamera.java ExampleStereoTwoViewsOneCamera.java]
* [https://github.com/lessthanoptimal/BoofCV/blob/v0.36/examples/src/main/java/boofcv/examples/stereo/ExampleStereoTwoViewsOneCamera.java ExampleStereoTwoViewsOneCamera.java]


Concepts:
Concepts:
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* Dense stereo processing
* Dense stereo processing


Relevant Applets:
Related Videos:
* [[Applet_Associate_Points| Associate Points]]
* [https://youtu.be/wOXuphyzypc Android Two View Stereo]
* [[Applet_Description_Region| Region Description]]
* [https://www.youtube.com/watch?v=8pn9Ebw90uk&t=672s Updates 0.24-0.36]
* [[Applet_Stereo_Disparity| Stereo Disparity]]


Related Tutorials/Example Code:
Related Tutorials/Example Code:
* [[Example_Stereo_Uncalibrated| Stereo Uncalibrated]]
* [[Example_Three_View_Stereo_Uncalibrated| Three View Stereo Uncalibrated]]
* [[Example_Stereo_Disparity| Stereo Disparity Example]]
* [[Example_Stereo_Disparity| Stereo Disparity Example]]
* [[Example_Rectification_Calibrated| Calibrated Stereo Rectification Example]]
* [[Example_Rectification_Calibrated| Calibrated Stereo Rectification Example]]
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// Disparity calculation parameters
// Disparity calculation parameters
private static final int minDisparity = 15;
private static final int minDisparity = 15;
private static final int maxDisparity = 100;
private static final int rangeDisparity = 85;


public static void main(String args[]) {
public static void main(String args[]) {
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// Camera parameters
// Camera parameters
IntrinsicParameters intrinsic = UtilIO.loadXML(calibDir , "intrinsic.xml");
CameraPinholeBrown intrinsic = CalibrationIO.load(new File(calibDir , "intrinsic.yaml"));


// Input images from the camera moving left to right
// Input images from the camera moving left to right
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// Input images with lens distortion
// Input images with lens distortion
ImageUInt8 distortedLeft = ConvertBufferedImage.convertFrom(origLeft, (ImageUInt8) null);
GrayU8 distortedLeft = ConvertBufferedImage.convertFrom(origLeft, (GrayU8) null);
ImageUInt8 distortedRight = ConvertBufferedImage.convertFrom(origRight, (ImageUInt8) null);
GrayU8 distortedRight = ConvertBufferedImage.convertFrom(origRight, (GrayU8) null);


// matched features between the two images
// matched features between the two images
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// Robustly estimate camera motion
// Robustly estimate camera motion
List<AssociatedPair> inliers = new ArrayList<AssociatedPair>();
List<AssociatedPair> inliers = new ArrayList<>();
Se3_F64 leftToRight = estimateCameraMotion(intrinsic, matchedCalibrated, inliers);
Se3_F64 leftToRight = estimateCameraMotion(intrinsic, matchedCalibrated, inliers);


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// Rectify and remove lens distortion for stereo processing
// Rectify and remove lens distortion for stereo processing
DenseMatrix64F rectifiedK = new DenseMatrix64F(3, 3);
DMatrixRMaj rectifiedK = new DMatrixRMaj(3, 3);
ImageUInt8 rectifiedLeft = distortedLeft.createSameShape();
DMatrixRMaj rectifiedR = new DMatrixRMaj(3, 3);
ImageUInt8 rectifiedRight = distortedRight.createSameShape();
GrayU8 rectifiedLeft = distortedLeft.createSameShape();
GrayU8 rectifiedRight = distortedRight.createSameShape();
GrayU8 rectifiedMask = distortedLeft.createSameShape();


rectifyImages(distortedLeft, distortedRight, leftToRight, intrinsic, rectifiedLeft, rectifiedRight, rectifiedK);
rectifyImages(distortedLeft, distortedRight, leftToRight, intrinsic,intrinsic,
rectifiedLeft, rectifiedRight,rectifiedMask, rectifiedK,rectifiedR);


// compute disparity
// compute disparity
StereoDisparity<ImageSInt16, ImageFloat32> disparityAlg =
ConfigDisparityBMBest5 config = new ConfigDisparityBMBest5();
FactoryStereoDisparity.regionSubpixelWta(DisparityAlgorithms.RECT_FIVE,
config.errorType = DisparityError.CENSUS;
minDisparity, maxDisparity, 5, 5, 20, 1, 0.1, ImageSInt16.class);
config.disparityMin = minDisparity;
 
config.disparityRange = rangeDisparity;
// Apply the Laplacian across the image to add extra resistance to changes in lighting or camera gain
config.subpixel = true;
ImageSInt16 derivLeft = new ImageSInt16(rectifiedLeft.width,rectifiedLeft.height);
config.regionRadiusX = config.regionRadiusY = 5;
ImageSInt16 derivRight = new ImageSInt16(rectifiedLeft.width,rectifiedLeft.height);
config.maxPerPixelError = 20;
LaplacianEdge.process(rectifiedLeft, derivLeft);
config.validateRtoL = 1;
LaplacianEdge.process(rectifiedRight,derivRight);
config.texture = 0.1;
StereoDisparity<GrayU8, GrayF32> disparityAlg =
FactoryStereoDisparity.blockMatchBest5(config, GrayU8.class, GrayF32.class);


// process and return the results
// process and return the results
disparityAlg.process(derivLeft, derivRight);
disparityAlg.process(rectifiedLeft, rectifiedRight);
ImageFloat32 disparity = disparityAlg.getDisparity();
GrayF32 disparity = disparityAlg.getDisparity();
RectifyImageOps.applyMask(disparity,rectifiedMask,0);


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


BufferedImage outLeft = ConvertBufferedImage.convertTo(rectifiedLeft, null);
BufferedImage outLeft = ConvertBufferedImage.convertTo(rectifiedLeft, null);
BufferedImage outRight = ConvertBufferedImage.convertTo(rectifiedRight, null);
BufferedImage outRight = ConvertBufferedImage.convertTo(rectifiedRight, null);


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


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


System.out.println("Total found " + matchedCalibrated.size());
System.out.println("Total found " + matchedCalibrated.size());
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* @return Found camera motion.  Note translation has an arbitrary scale
* @return Found camera motion.  Note translation has an arbitrary scale
*/
*/
public static Se3_F64 estimateCameraMotion(IntrinsicParameters intrinsic,
public static Se3_F64 estimateCameraMotion(CameraPinholeBrown intrinsic,
  List<AssociatedPair> matchedNorm, List<AssociatedPair> inliers)
  List<AssociatedPair> matchedNorm, List<AssociatedPair> inliers)
{
{
ModelMatcher<Se3_F64, AssociatedPair> epipolarMotion =
ModelMatcherMultiview<Se3_F64, AssociatedPair> epipolarMotion =
FactoryMultiViewRobust.essentialRansac(new ConfigEssential(intrinsic),new ConfigRansac(200,0.5));
FactoryMultiViewRobust.baselineRansac(new ConfigEssential(),new ConfigRansac(200,0.5));
epipolarMotion.setIntrinsic(0,intrinsic);
epipolarMotion.setIntrinsic(1,intrinsic);


if (!epipolarMotion.process(matchedNorm))
if (!epipolarMotion.process(matchedNorm))
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* Convert a set of associated point features from pixel coordinates into normalized image coordinates.
* Convert a set of associated point features from pixel coordinates into normalized image coordinates.
*/
*/
public static List<AssociatedPair> convertToNormalizedCoordinates(List<AssociatedPair> matchedFeatures, IntrinsicParameters intrinsic) {
public static List<AssociatedPair> convertToNormalizedCoordinates(List<AssociatedPair> matchedFeatures, CameraPinholeBrown intrinsic) {


PointTransform_F64 p_to_n = LensDistortionOps.transformPoint(intrinsic).undistort_F64(true, false);
Point2Transform2_F64 p_to_n = LensDistortionFactory.narrow(intrinsic).undistort_F64(true, false);


List<AssociatedPair> calibratedFeatures = new ArrayList<AssociatedPair>();
List<AssociatedPair> calibratedFeatures = new ArrayList<>();


for (AssociatedPair p : matchedFeatures) {
for (AssociatedPair p : matchedFeatures) {
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* @param distortedRight Input distorted image from right camera.
* @param distortedRight Input distorted image from right camera.
* @param leftToRight    Camera motion from left to right
* @param leftToRight    Camera motion from left to right
* @param intrinsic      Intrinsic camera parameters
* @param intrinsicLeft  Intrinsic camera parameters
* @param rectifiedLeft  Output rectified image for left camera.
* @param rectifiedLeft  Output rectified image for left camera.
* @param rectifiedRight Output rectified image for right camera.
* @param rectifiedRight Output rectified image for right camera.
* @param rectifiedMask  Mask that indicates invalid pixels in rectified image. 1 = valid, 0 = invalid
* @param rectifiedK    Output camera calibration matrix for rectified camera
* @param rectifiedK    Output camera calibration matrix for rectified camera
*/
*/
public static void rectifyImages(ImageUInt8 distortedLeft,
public static <T extends ImageBase<T>>
ImageUInt8 distortedRight,
void rectifyImages(T distortedLeft,
Se3_F64 leftToRight,
  T distortedRight,
IntrinsicParameters intrinsic,
  Se3_F64 leftToRight,
ImageUInt8 rectifiedLeft,
  CameraPinholeBrown intrinsicLeft,
ImageUInt8 rectifiedRight,
  CameraPinholeBrown intrinsicRight,
DenseMatrix64F rectifiedK) {
  T rectifiedLeft,
  T rectifiedRight,
  GrayU8 rectifiedMask,
  DMatrixRMaj rectifiedK,
  DMatrixRMaj rectifiedR) {
RectifyCalibrated rectifyAlg = RectifyImageOps.createCalibrated();
RectifyCalibrated rectifyAlg = RectifyImageOps.createCalibrated();


// original camera calibration matrices
// original camera calibration matrices
DenseMatrix64F K = PerspectiveOps.calibrationMatrix(intrinsic, null);
DMatrixRMaj K1 = PerspectiveOps.pinholeToMatrix(intrinsicLeft, (DMatrixRMaj)null);
DMatrixRMaj K2 = PerspectiveOps.pinholeToMatrix(intrinsicRight, (DMatrixRMaj)null);


rectifyAlg.process(K, new Se3_F64(), K, leftToRight);
rectifyAlg.process(K1, new Se3_F64(), K2, leftToRight);


// rectification matrix for each image
// rectification matrix for each image
DenseMatrix64F rect1 = rectifyAlg.getRect1();
DMatrixRMaj rect1 = rectifyAlg.getRect1();
DenseMatrix64F rect2 = rectifyAlg.getRect2();
DMatrixRMaj rect2 = rectifyAlg.getRect2();
rectifiedR.set(rectifyAlg.getRectifiedRotation());


// New calibration matrix,
// New calibration matrix,
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// Adjust the rectification to make the view area more useful
// Adjust the rectification to make the view area more useful
RectifyImageOps.allInsideLeft(intrinsic, rect1, rect2, rectifiedK);
ImageDimension rectShape = new ImageDimension();
RectifyImageOps.fullViewLeft(intrinsicLeft, rect1, rect2, rectifiedK, rectShape);
// RectifyImageOps.allInsideLeft(intrinsicLeft, rect1, rect2, rectifiedK, rectShape);
// Taking in account the relative rotation between the image axis and the baseline is important in
// this scenario since a person can easily hold the camera at an odd angle. If you don't adjust
// the rectified image size you might end up with a lot of wasted pixels and a low resolution model!
rectifiedLeft.reshape(rectShape.width,rectShape.height);
rectifiedRight.reshape(rectShape.width,rectShape.height);


// undistorted and rectify images
// undistorted and rectify images
ImageDistort<ImageUInt8,ImageUInt8> distortLeft =
FMatrixRMaj rect1_F32 = new FMatrixRMaj(3,3);
RectifyImageOps.rectifyImage(intrinsic, rect1, BorderType.SKIP, distortedLeft.getImageType());
FMatrixRMaj rect2_F32 = new FMatrixRMaj(3,3);
ImageDistort<ImageUInt8,ImageUInt8> distortRight =
ConvertMatrixData.convert(rect1, rect1_F32);
RectifyImageOps.rectifyImage(intrinsic, rect2, BorderType.SKIP, distortedRight.getImageType());
ConvertMatrixData.convert(rect2, rect2_F32);
 
// Extending the image prevents a harsh edge reducing false matches at the image border
// SKIP is another option, possibly a tinny bit faster, but has a harsh edge which will need to be filtered
ImageDistort<T,T> distortLeft =
RectifyImageOps.rectifyImage(intrinsicLeft, rect1_F32, BorderType.EXTENDED, distortedLeft.getImageType());
ImageDistort<T,T> distortRight =
RectifyImageOps.rectifyImage(intrinsicRight, rect2_F32, BorderType.EXTENDED, distortedRight.getImageType());


distortLeft.apply(distortedLeft, rectifiedLeft);
distortLeft.apply(distortedLeft, rectifiedLeft,rectifiedMask);
distortRight.apply(distortedRight, rectifiedRight);
distortRight.apply(distortedRight, rectifiedRight);
}
}
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* Draw inliers for debugging purposes.  Need to convert from normalized to pixel coordinates.
* Draw inliers for debugging purposes.  Need to convert from normalized to pixel coordinates.
*/
*/
public static void drawInliers(BufferedImage left, BufferedImage right, IntrinsicParameters intrinsic,
public static void drawInliers(BufferedImage left, BufferedImage right, CameraPinholeBrown intrinsic,
  List<AssociatedPair> normalized) {
  List<AssociatedPair> normalized) {
PointTransform_F64 n_to_p = LensDistortionOps.transformPoint(intrinsic).distort_F64(false,true);
Point2Transform2_F64 n_to_p = LensDistortionFactory.narrow(intrinsic).distort_F64(false,true);


List<AssociatedPair> pixels = new ArrayList<AssociatedPair>();
List<AssociatedPair> pixels = new ArrayList<>();


for (AssociatedPair n : normalized) {
for (AssociatedPair n : normalized) {
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panel.setImages(left, right);
panel.setImages(left, right);


ShowImages.showWindow(panel, "Inlier Features");
ShowImages.showWindow(panel, "Inlier Features", true);
}
}


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* Show results as a point cloud
* Show results as a point cloud
*/
*/
public static void showPointCloud(ImageSingleBand disparity, BufferedImage left,
public static void showPointCloud(ImageGray disparity, BufferedImage left,
  Se3_F64 motion, DenseMatrix64F rectifiedK ,
  Se3_F64 motion, DMatrixRMaj rectifiedK , DMatrixRMaj rectifiedR,
  int minDisparity, int maxDisparity) {
  int disparityMin, int disparityRange)
PointCloudTiltPanel gui = new PointCloudTiltPanel();
{
DisparityToColorPointCloud d2c = new DisparityToColorPointCloud();
PointCloudWriter.CloudArraysF32 cloud = new PointCloudWriter.CloudArraysF32();


double baseline = motion.getT().norm();
double baseline = motion.getT().norm();
d2c.configure(baseline, rectifiedK, rectifiedR, new DoNothing2Transform2_F64(), disparityMin, disparityRange);
d2c.process(disparity, UtilDisparitySwing.wrap(left), cloud);
CameraPinhole rectifiedPinhole = PerspectiveOps.matrixToPinhole(rectifiedK,disparity.width,disparity.height,null);
// skew the view to make the structure easier to see
Se3_F64 cameraToWorld = SpecialEuclideanOps_F64.eulerXyz(-baseline*5,0,0,0,0.2,0,null);


gui.configure(baseline, rectifiedK, new DoNothingTransform_F64(), minDisparity, maxDisparity);
PointCloudViewer pcv = VisualizeData.createPointCloudViewer();
gui.process(disparity, left);
pcv.setCameraHFov(PerspectiveOps.computeHFov(rectifiedPinhole));
gui.setPreferredSize(new Dimension(left.getWidth(), left.getHeight()));
pcv.setCameraToWorld(cameraToWorld);
pcv.setTranslationStep(baseline/3);
pcv.addCloud(cloud.cloudXyz,cloud.cloudRgb);
pcv.setDotSize(1);
pcv.setTranslationStep(baseline/10);


ShowImages.showWindow(gui, "Point Cloud");
pcv.getComponent().setPreferredSize(new Dimension(left.getWidth(), left.getHeight()));
ShowImages.showWindow(pcv.getComponent(), "Point Cloud", true);
}
}
}
}
</syntaxhighlight>
</syntaxhighlight>

Revision as of 08:39, 22 June 2020

Associated inlier features between two views
Associated inlier features between two views
Stereo disparity image
3D point cloud
Stereo disparity image 3D point cloud

In this scenario we wish to compute a dense point cloud from two views taken with the same calibrated camera. Because the intrinsic parameters are known, it is easier to converge towards a valid solution than the entirely uncalibrated scenario.

Because the extrinsic parameters (translation and rotation) between the two views is unknown the scene's structure can only be recovered up to a scale factor. In this example natural features are used to determine the geometric relationship between the two views. The algorithm can be summarized as follows:

  • Load camera calibration and two images
  • Detect, describe, and associate image features
  • Compute camera motion (Essential matrix)
  • Rectify image pair
  • Compute dense stereo disparity
  • Convert into 3D point cloud

Example File:

Concepts:

  • Point feature association
  • Epipolar geometry
  • Rectification
  • Dense stereo processing

Related Videos:

Related Tutorials/Example Code:

Example Code

/**
 * Example demonstrating how to use to images taken from a single calibrated camera to create a stereo disparity image,
 * from which a dense 3D point cloud of the scene can be computed.  For this technique to work the camera's motion
 * needs to be approximately tangential to the direction the camera is pointing.  The code below assumes that the first
 * image is to the left of the second image.
 *
 * @author Peter Abeles
 */
public class ExampleStereoTwoViewsOneCamera {

	// Disparity calculation parameters
	private static final int minDisparity = 15;
	private static final int rangeDisparity = 85;

	public static void main(String args[]) {
		// specify location of images and calibration
		String calibDir = UtilIO.pathExample("calibration/mono/Sony_DSC-HX5V_Chess/");
		String imageDir = UtilIO.pathExample("stereo/");

		// Camera parameters
		CameraPinholeBrown intrinsic = CalibrationIO.load(new File(calibDir , "intrinsic.yaml"));

		// Input images from the camera moving left to right
		BufferedImage origLeft = UtilImageIO.loadImage(imageDir , "mono_wall_01.jpg");
		BufferedImage origRight = UtilImageIO.loadImage(imageDir, "mono_wall_02.jpg");

		// Input images with lens distortion
		GrayU8 distortedLeft = ConvertBufferedImage.convertFrom(origLeft, (GrayU8) null);
		GrayU8 distortedRight = ConvertBufferedImage.convertFrom(origRight, (GrayU8) null);

		// matched features between the two images
		List<AssociatedPair> matchedFeatures = ExampleFundamentalMatrix.computeMatches(origLeft, origRight);

		// convert from pixel coordinates into normalized image coordinates
		List<AssociatedPair> matchedCalibrated = convertToNormalizedCoordinates(matchedFeatures, intrinsic);

		// Robustly estimate camera motion
		List<AssociatedPair> inliers = new ArrayList<>();
		Se3_F64 leftToRight = estimateCameraMotion(intrinsic, matchedCalibrated, inliers);

		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);
		GrayU8 rectifiedLeft = distortedLeft.createSameShape();
		GrayU8 rectifiedRight = distortedRight.createSameShape();
		GrayU8 rectifiedMask = distortedLeft.createSameShape();

		rectifyImages(distortedLeft, distortedRight, leftToRight, intrinsic,intrinsic,
				rectifiedLeft, rectifiedRight,rectifiedMask, rectifiedK,rectifiedR);

		// compute disparity
		ConfigDisparityBMBest5 config = new ConfigDisparityBMBest5();
		config.errorType = DisparityError.CENSUS;
		config.disparityMin = minDisparity;
		config.disparityRange = rangeDisparity;
		config.subpixel = true;
		config.regionRadiusX = config.regionRadiusY = 5;
		config.maxPerPixelError = 20;
		config.validateRtoL = 1;
		config.texture = 0.1;
		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,rectifiedMask,0);

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

		BufferedImage outLeft = ConvertBufferedImage.convertTo(rectifiedLeft, null);
		BufferedImage outRight = ConvertBufferedImage.convertTo(rectifiedRight, null);

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

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

		System.out.println("Total found " + matchedCalibrated.size());
		System.out.println("Total Inliers " + inliers.size());
	}

	/**
	 * Estimates the camera motion robustly using RANSAC and a set of associated points.
	 *
	 * @param intrinsic   Intrinsic camera parameters
	 * @param matchedNorm set of matched point features in normalized image coordinates
	 * @param inliers     OUTPUT: Set of inlier features from RANSAC
	 * @return Found camera motion.  Note translation has an arbitrary scale
	 */
	public static Se3_F64 estimateCameraMotion(CameraPinholeBrown intrinsic,
											   List<AssociatedPair> matchedNorm, List<AssociatedPair> inliers)
	{
		ModelMatcherMultiview<Se3_F64, AssociatedPair> epipolarMotion =
				FactoryMultiViewRobust.baselineRansac(new ConfigEssential(),new ConfigRansac(200,0.5));
		epipolarMotion.setIntrinsic(0,intrinsic);
		epipolarMotion.setIntrinsic(1,intrinsic);

		if (!epipolarMotion.process(matchedNorm))
			throw new RuntimeException("Motion estimation failed");

		// save inlier set for debugging purposes
		inliers.addAll(epipolarMotion.getMatchSet());

		return epipolarMotion.getModelParameters();
	}

	/**
	 * Convert a set of associated point features from pixel coordinates into normalized image coordinates.
	 */
	public static List<AssociatedPair> convertToNormalizedCoordinates(List<AssociatedPair> matchedFeatures, CameraPinholeBrown intrinsic) {

		Point2Transform2_F64 p_to_n = LensDistortionFactory.narrow(intrinsic).undistort_F64(true, false);

		List<AssociatedPair> calibratedFeatures = new ArrayList<>();

		for (AssociatedPair p : matchedFeatures) {
			AssociatedPair c = new AssociatedPair();

			p_to_n.compute(p.p1.x, p.p1.y, c.p1);
			p_to_n.compute(p.p2.x, p.p2.y, c.p2);

			calibratedFeatures.add(c);
		}

		return calibratedFeatures;
	}

	/**
	 * Remove lens distortion and rectify stereo images
	 *
	 * @param distortedLeft  Input distorted image from left camera.
	 * @param distortedRight Input distorted image from right camera.
	 * @param leftToRight    Camera motion from left to right
	 * @param intrinsicLeft  Intrinsic camera parameters
	 * @param rectifiedLeft  Output rectified image for left camera.
	 * @param rectifiedRight Output rectified image for right camera.
	 * @param rectifiedMask  Mask that indicates invalid pixels in rectified image. 1 = valid, 0 = invalid
	 * @param rectifiedK     Output camera calibration matrix for rectified camera
	 */
	public static <T extends ImageBase<T>>
	void rectifyImages(T distortedLeft,
					   T distortedRight,
					   Se3_F64 leftToRight,
					   CameraPinholeBrown intrinsicLeft,
					   CameraPinholeBrown intrinsicRight,
					   T rectifiedLeft,
					   T rectifiedRight,
					   GrayU8 rectifiedMask,
					   DMatrixRMaj rectifiedK,
					   DMatrixRMaj rectifiedR) {
		RectifyCalibrated rectifyAlg = RectifyImageOps.createCalibrated();

		// original camera calibration matrices
		DMatrixRMaj K1 = PerspectiveOps.pinholeToMatrix(intrinsicLeft, (DMatrixRMaj)null);
		DMatrixRMaj K2 = PerspectiveOps.pinholeToMatrix(intrinsicRight, (DMatrixRMaj)null);

		rectifyAlg.process(K1, new Se3_F64(), K2, leftToRight);

		// rectification matrix for each image
		DMatrixRMaj rect1 = rectifyAlg.getRect1();
		DMatrixRMaj rect2 = rectifyAlg.getRect2();
		rectifiedR.set(rectifyAlg.getRectifiedRotation());

		// New calibration matrix,
		rectifiedK.set(rectifyAlg.getCalibrationMatrix());

		// Adjust the rectification to make the view area more useful
		ImageDimension rectShape = new ImageDimension();
		RectifyImageOps.fullViewLeft(intrinsicLeft, rect1, rect2, rectifiedK, rectShape);
//		RectifyImageOps.allInsideLeft(intrinsicLeft, rect1, rect2, rectifiedK, rectShape);
		// Taking in account the relative rotation between the image axis and the baseline is important in
		// this scenario since a person can easily hold the camera at an odd angle. If you don't adjust
		// the rectified image size you might end up with a lot of wasted pixels and a low resolution model!
		rectifiedLeft.reshape(rectShape.width,rectShape.height);
		rectifiedRight.reshape(rectShape.width,rectShape.height);

		// undistorted and rectify images
		FMatrixRMaj rect1_F32 = new FMatrixRMaj(3,3);
		FMatrixRMaj rect2_F32 = new FMatrixRMaj(3,3);
		ConvertMatrixData.convert(rect1, rect1_F32);
		ConvertMatrixData.convert(rect2, rect2_F32);

		// Extending the image prevents a harsh edge reducing false matches at the image border
		// SKIP is another option, possibly a tinny bit faster, but has a harsh edge which will need to be filtered
		ImageDistort<T,T> distortLeft =
				RectifyImageOps.rectifyImage(intrinsicLeft, rect1_F32, BorderType.EXTENDED, distortedLeft.getImageType());
		ImageDistort<T,T> distortRight =
				RectifyImageOps.rectifyImage(intrinsicRight, rect2_F32, BorderType.EXTENDED, distortedRight.getImageType());

		distortLeft.apply(distortedLeft, rectifiedLeft,rectifiedMask);
		distortRight.apply(distortedRight, rectifiedRight);
	}

	/**
	 * Draw inliers for debugging purposes.  Need to convert from normalized to pixel coordinates.
	 */
	public static void drawInliers(BufferedImage left, BufferedImage right, CameraPinholeBrown intrinsic,
								   List<AssociatedPair> normalized) {
		Point2Transform2_F64 n_to_p = LensDistortionFactory.narrow(intrinsic).distort_F64(false,true);

		List<AssociatedPair> pixels = new ArrayList<>();

		for (AssociatedPair n : normalized) {
			AssociatedPair p = new AssociatedPair();

			n_to_p.compute(n.p1.x, n.p1.y, p.p1);
			n_to_p.compute(n.p2.x, n.p2.y, p.p2);

			pixels.add(p);
		}

		// display the results
		AssociationPanel panel = new AssociationPanel(20);
		panel.setAssociation(pixels);
		panel.setImages(left, right);

		ShowImages.showWindow(panel, "Inlier Features", true);
	}

	/**
	 * Show results as a point cloud
	 */
	public static void showPointCloud(ImageGray disparity, BufferedImage left,
									  Se3_F64 motion, DMatrixRMaj rectifiedK , DMatrixRMaj rectifiedR,
									  int disparityMin, int disparityRange)
	{
		DisparityToColorPointCloud d2c = new DisparityToColorPointCloud();
		PointCloudWriter.CloudArraysF32 cloud = new PointCloudWriter.CloudArraysF32();

		double baseline = motion.getT().norm();
		d2c.configure(baseline, rectifiedK, rectifiedR, new DoNothing2Transform2_F64(), disparityMin, disparityRange);
		d2c.process(disparity, UtilDisparitySwing.wrap(left), cloud);

		CameraPinhole rectifiedPinhole = PerspectiveOps.matrixToPinhole(rectifiedK,disparity.width,disparity.height,null);

		// skew the view to make the structure easier to see
		Se3_F64 cameraToWorld = SpecialEuclideanOps_F64.eulerXyz(-baseline*5,0,0,0,0.2,0,null);

		PointCloudViewer pcv = VisualizeData.createPointCloudViewer();
		pcv.setCameraHFov(PerspectiveOps.computeHFov(rectifiedPinhole));
		pcv.setCameraToWorld(cameraToWorld);
		pcv.setTranslationStep(baseline/3);
		pcv.addCloud(cloud.cloudXyz,cloud.cloudRgb);
		pcv.setDotSize(1);
		pcv.setTranslationStep(baseline/10);

		pcv.getComponent().setPreferredSize(new Dimension(left.getWidth(), left.getHeight()));
		ShowImages.showWindow(pcv.getComponent(), "Point Cloud", true);
	}
}