Difference between revisions of "Example Fundamental Matrix"

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The Fundamental matrix is a 3 by 3 matrix which describes the geometric (epipolar) relationship between two images.  In the example below, features are automatically found and the fundamental matrix computed using two different techniques.  The robust technique uses RANSAC to remove incorrect image pairs (see image above) followed by non-linear optimization.  The simple technique assumes that all the image pairs are correct (not true in this scenario) and apply a fast to compute linear algorithm.
The Fundamental matrix is a 3 by 3 matrix which describes the geometric (epipolar) relationship between two images.  In the example below, features are automatically found and the fundamental matrix computed using two different techniques.  The robust technique uses RANSAC to remove incorrect image pairs (see image above) followed by non-linear optimization.  The simple technique assumes that all the image pairs are correct (not true in this scenario) and apply a fast to compute linear algorithm.


Example File: [https://github.com/lessthanoptimal/BoofCV/blob/v0.36/examples/src/main/java/boofcv/examples/stereo/ExampleFundamentalMatrix.java ExampleFundamentalMatrix.java]
Example File: [https://github.com/lessthanoptimal/BoofCV/blob/v0.37/examples/src/main/java/boofcv/examples/stereo/ExampleFundamentalMatrix.java ExampleFundamentalMatrix.java]


Concepts:
Concepts:
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<syntaxhighlight lang="java">
<syntaxhighlight lang="java">
/**
/**
  * A Fundamental matrix describes the epipolar relationship between two images. If two points, one from
  * A Fundamental matrix describes the epipolar relationship between two images. If two points, one from
  * each image, match, then the inner product around the Fundamental matrix will be zero. If a fundamental
  * each image, match, then the inner product around the Fundamental matrix will be zero. If a fundamental
  * matrix is known, then information about the scene and its structure can be extracted.
  * matrix is known, then information about the scene and its structure can be extracted.
  *
  *
  * Below are two examples of how a Fundamental matrix can be computed using different.
  * Below are two examples of how a Fundamental matrix can be computed using different.
  * The robust technique attempts to find the best fit Fundamental matrix to the data while removing noisy
  * The robust technique attempts to find the best fit Fundamental matrix to the data while removing noisy
  * matches, The simple version just assumes that all the matches are correct. Similar techniques can be used
  * matches, The simple version just assumes that all the matches are correct. Similar techniques can be used
  * to fit various other types of motion or structural models to observations.
  * to fit various other types of motion or structural models to observations.
  *
  *
  * The input image and associated features are displayed in a window. In another window, inlier features
  * The input image and associated features are displayed in a window. In another window, inlier features
  * from robust model fitting are shown.
  * from robust model fitting are shown.
  *
  *
Line 37: Line 37:
  */
  */
public class ExampleFundamentalMatrix {
public class ExampleFundamentalMatrix {
/**
/**
* Given a set of noisy observations, compute the Fundamental matrix while removing
* Given a set of noisy observations, compute the Fundamental matrix while removing the noise.
* the noise.
*
*
* @param matches List of associated features between the two images
* @param matches List of associated features between the two images
Line 46: Line 44:
* @return The found fundamental matrix.
* @return The found fundamental matrix.
*/
*/
public static DMatrixRMaj robustFundamental( List<AssociatedPair> matches ,
public static DMatrixRMaj robustFundamental( List<AssociatedPair> matches,
List<AssociatedPair> inliers , double inlierThreshold ) {
List<AssociatedPair> inliers, double inlierThreshold ) {
 
ConfigRansac configRansac = new ConfigRansac();
ConfigRansac configRansac = new ConfigRansac();
configRansac.inlierThreshold = inlierThreshold;
configRansac.inlierThreshold = inlierThreshold;
Line 61: Line 58:


ModelMatcher<DMatrixRMaj, AssociatedPair> ransac =
ModelMatcher<DMatrixRMaj, AssociatedPair> ransac =
FactoryMultiViewRobust.fundamentalRansac(configFundamental,configRansac);
FactoryMultiViewRobust.fundamentalRansac(configFundamental, configRansac);


// Estimate the fundamental matrix while removing outliers
// Estimate the fundamental matrix while removing outliers
if( !ransac.process(matches) )
if (!ransac.process(matches))
throw new IllegalArgumentException("Failed");
throw new IllegalArgumentException("Failed");


Line 71: Line 68:


// Improve the estimate of the fundamental matrix using non-linear optimization
// Improve the estimate of the fundamental matrix using non-linear optimization
DMatrixRMaj F = new DMatrixRMaj(3,3);
DMatrixRMaj F = new DMatrixRMaj(3, 3);
ModelFitter<DMatrixRMaj,AssociatedPair> refine =
ModelFitter<DMatrixRMaj, AssociatedPair> refine =
FactoryMultiView.fundamentalRefine(1e-8, 400, EpipolarError.SAMPSON);
FactoryMultiView.fundamentalRefine(1e-8, 400, EpipolarError.SAMPSON);
if( !refine.fitModel(inliers, ransac.getModelParameters(), F) )
if (!refine.fitModel(inliers, ransac.getModelParameters(), F))
throw new IllegalArgumentException("Failed");
throw new IllegalArgumentException("Failed");


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/**
/**
* If the set of associated features are known to be correct, then the fundamental matrix can
* If the set of associated features are known to be correct, then the fundamental matrix can
* be computed directly with a lot less code. The down side is that this technique is very
* be computed directly with a lot less code. The down side is that this technique is very
* sensitive to noise.
* sensitive to noise.
*/
*/
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Estimate1ofEpipolar estimateF = FactoryMultiView.fundamental_1(EnumFundamental.LINEAR_8, 0);
Estimate1ofEpipolar estimateF = FactoryMultiView.fundamental_1(EnumFundamental.LINEAR_8, 0);


DMatrixRMaj F = new DMatrixRMaj(3,3);
DMatrixRMaj F = new DMatrixRMaj(3, 3);
if( !estimateF.process(matches,F) )
if (!estimateF.process(matches, F))
throw new IllegalArgumentException("Failed");
throw new IllegalArgumentException("Failed");


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* fundamental matrix.
* fundamental matrix.
*/
*/
public static List<AssociatedPair> computeMatches( BufferedImage left , BufferedImage right ) {
public static List<AssociatedPair> computeMatches( BufferedImage left, BufferedImage right ) {
DetectDescribePoint detDesc = FactoryDetectDescribe.surfStable(
DetectDescribePoint detDesc = FactoryDetectDescribe.surfStable(
new ConfigFastHessian(0, 2, 400, 1, 9, 4, 4), null,null, GrayF32.class);
new ConfigFastHessian(0, 2, 400, 1, 9, 4, 4), null, null, GrayF32.class);
// DetectDescribePoint detDesc = FactoryDetectDescribe.sift(null,new ConfigSiftDetector(2,0,200,5),null,null);
// DetectDescribePoint detDesc = FactoryDetectDescribe.sift(null,new ConfigSiftDetector(2,0,200,5),null,null);


ScoreAssociation<BrightFeature> scorer = FactoryAssociation.scoreEuclidean(BrightFeature.class,true);
ScoreAssociation<TupleDesc_F64> scorer = FactoryAssociation.scoreEuclidean(TupleDesc_F64.class, true);
AssociateDescription<BrightFeature> associate = FactoryAssociation.greedy(new ConfigAssociateGreedy(true,0.1),scorer);
AssociateDescription<TupleDesc_F64> associate = FactoryAssociation.greedy(new ConfigAssociateGreedy(true, 0.1), scorer);


ExampleAssociatePoints<GrayF32,BrightFeature> findMatches =
ExampleAssociatePoints<GrayF32, TupleDesc_F64> findMatches =
new ExampleAssociatePoints<>(detDesc, associate, GrayF32.class);
new ExampleAssociatePoints<>(detDesc, associate, GrayF32.class);


findMatches.associate(left,right);
findMatches.associate(left, right);


List<AssociatedPair> matches = new ArrayList<>();
List<AssociatedPair> matches = new ArrayList<>();
FastAccess<AssociatedIndex> matchIndexes = associate.getMatches();
FastAccess<AssociatedIndex> matchIndexes = associate.getMatches();


for( int i = 0; i < matchIndexes.size; i++ ) {
for (int i = 0; i < matchIndexes.size; i++) {
AssociatedIndex a = matchIndexes.get(i);
AssociatedIndex a = matchIndexes.get(i);
AssociatedPair p = new AssociatedPair(findMatches.pointsA.get(a.src) , findMatches.pointsB.get(a.dst));
AssociatedPair p = new AssociatedPair(findMatches.pointsA.get(a.src), findMatches.pointsB.get(a.dst));
matches.add( p);
matches.add(p);
}
}


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}
}


public static void main( String args[] ) {
public static void main( String[] args ) {
 
String dir = UtilIO.pathExample("structure/");
String dir = UtilIO.pathExample("structure/");


BufferedImage imageA = UtilImageIO.loadImage(dir , "undist_cyto_01.jpg");
BufferedImage imageA = UtilImageIO.loadImage(dir, "undist_cyto_01.jpg");
BufferedImage imageB = UtilImageIO.loadImage(dir , "undist_cyto_02.jpg");
BufferedImage imageB = UtilImageIO.loadImage(dir, "undist_cyto_02.jpg");


List<AssociatedPair> matches = computeMatches(imageA,imageB);
List<AssociatedPair> matches = computeMatches(imageA, imageB);


// Where the fundamental matrix is stored
// Where the fundamental matrix is stored
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AssociationPanel panel = new AssociationPanel(20);
AssociationPanel panel = new AssociationPanel(20);
panel.setAssociation(inliers);
panel.setAssociation(inliers);
panel.setImages(imageA,imageB);
panel.setImages(imageA, imageB);


ShowImages.showWindow(panel, "Inlier Pairs");
ShowImages.showWindow(panel, "Inlier Pairs");

Revision as of 19:47, 21 December 2020

The Fundamental matrix is a 3 by 3 matrix which describes the geometric (epipolar) relationship between two images. In the example below, features are automatically found and the fundamental matrix computed using two different techniques. The robust technique uses RANSAC to remove incorrect image pairs (see image above) followed by non-linear optimization. The simple technique assumes that all the image pairs are correct (not true in this scenario) and apply a fast to compute linear algorithm.

Example File: ExampleFundamentalMatrix.java

Concepts:

  • Epipolar constraint
  • Fundamental matrix
  • Stereo Vision

Related Examples:

Example Code

/**
 * A Fundamental matrix describes the epipolar relationship between two images. If two points, one from
 * each image, match, then the inner product around the Fundamental matrix will be zero. If a fundamental
 * matrix is known, then information about the scene and its structure can be extracted.
 *
 * Below are two examples of how a Fundamental matrix can be computed using different.
 * The robust technique attempts to find the best fit Fundamental matrix to the data while removing noisy
 * matches, The simple version just assumes that all the matches are correct. Similar techniques can be used
 * to fit various other types of motion or structural models to observations.
 *
 * The input image and associated features are displayed in a window. In another window, inlier features
 * from robust model fitting are shown.
 *
 * @author Peter Abeles
 */
public class ExampleFundamentalMatrix {
	/**
	 * Given a set of noisy observations, compute the Fundamental matrix while removing the noise.
	 *
	 * @param matches List of associated features between the two images
	 * @param inliers List of feature pairs that were determined to not be noise.
	 * @return The found fundamental matrix.
	 */
	public static DMatrixRMaj robustFundamental( List<AssociatedPair> matches,
												 List<AssociatedPair> inliers, double inlierThreshold ) {
		ConfigRansac configRansac = new ConfigRansac();
		configRansac.inlierThreshold = inlierThreshold;
		configRansac.iterations = 1000;
		ConfigFundamental configFundamental = new ConfigFundamental();
		configFundamental.which = EnumFundamental.LINEAR_7;
		configFundamental.numResolve = 2;
		configFundamental.errorModel = ConfigFundamental.ErrorModel.GEOMETRIC;
		// geometric error is the most accurate error metric, but also the slowest to compute. See how the
		// results change if you switch to sampson and how much faster it is. You also should adjust
		// the inlier threshold.

		ModelMatcher<DMatrixRMaj, AssociatedPair> ransac =
				FactoryMultiViewRobust.fundamentalRansac(configFundamental, configRansac);

		// Estimate the fundamental matrix while removing outliers
		if (!ransac.process(matches))
			throw new IllegalArgumentException("Failed");

		// save the set of features that were used to compute the fundamental matrix
		inliers.addAll(ransac.getMatchSet());

		// Improve the estimate of the fundamental matrix using non-linear optimization
		DMatrixRMaj F = new DMatrixRMaj(3, 3);
		ModelFitter<DMatrixRMaj, AssociatedPair> refine =
				FactoryMultiView.fundamentalRefine(1e-8, 400, EpipolarError.SAMPSON);
		if (!refine.fitModel(inliers, ransac.getModelParameters(), F))
			throw new IllegalArgumentException("Failed");

		// Return the solution
		return F;
	}

	/**
	 * If the set of associated features are known to be correct, then the fundamental matrix can
	 * be computed directly with a lot less code. The down side is that this technique is very
	 * sensitive to noise.
	 */
	public static DMatrixRMaj simpleFundamental( List<AssociatedPair> matches ) {
		// Use the 8-point algorithm since it will work with an arbitrary number of points
		Estimate1ofEpipolar estimateF = FactoryMultiView.fundamental_1(EnumFundamental.LINEAR_8, 0);

		DMatrixRMaj F = new DMatrixRMaj(3, 3);
		if (!estimateF.process(matches, F))
			throw new IllegalArgumentException("Failed");

		// while not done here, this initial linear estimate can be refined using non-linear optimization
		// as was done above.
		return F;
	}

	/**
	 * Use the associate point feature example to create a list of {@link AssociatedPair} for use in computing the
	 * fundamental matrix.
	 */
	public static List<AssociatedPair> computeMatches( BufferedImage left, BufferedImage right ) {
		DetectDescribePoint detDesc = FactoryDetectDescribe.surfStable(
				new ConfigFastHessian(0, 2, 400, 1, 9, 4, 4), null, null, GrayF32.class);
//		DetectDescribePoint detDesc = FactoryDetectDescribe.sift(null,new ConfigSiftDetector(2,0,200,5),null,null);

		ScoreAssociation<TupleDesc_F64> scorer = FactoryAssociation.scoreEuclidean(TupleDesc_F64.class, true);
		AssociateDescription<TupleDesc_F64> associate = FactoryAssociation.greedy(new ConfigAssociateGreedy(true, 0.1), scorer);

		ExampleAssociatePoints<GrayF32, TupleDesc_F64> findMatches =
				new ExampleAssociatePoints<>(detDesc, associate, GrayF32.class);

		findMatches.associate(left, right);

		List<AssociatedPair> matches = new ArrayList<>();
		FastAccess<AssociatedIndex> matchIndexes = associate.getMatches();

		for (int i = 0; i < matchIndexes.size; i++) {
			AssociatedIndex a = matchIndexes.get(i);
			AssociatedPair p = new AssociatedPair(findMatches.pointsA.get(a.src), findMatches.pointsB.get(a.dst));
			matches.add(p);
		}

		return matches;
	}

	public static void main( String[] args ) {
		String dir = UtilIO.pathExample("structure/");

		BufferedImage imageA = UtilImageIO.loadImage(dir, "undist_cyto_01.jpg");
		BufferedImage imageB = UtilImageIO.loadImage(dir, "undist_cyto_02.jpg");

		List<AssociatedPair> matches = computeMatches(imageA, imageB);

		// Where the fundamental matrix is stored
		DMatrixRMaj F;
		// List of matches that matched the model
		List<AssociatedPair> inliers = new ArrayList<>();

		// estimate and print the results using a robust and simple estimator
		// The results should be difference since there are many false associations in the simple model
		// Also note that the fundamental matrix is only defined up to a scale factor.
		F = robustFundamental(matches, inliers, 0.5);
		System.out.println("Robust");
		CommonOps_DDRM.divide(F, NormOps_DDRM.normF(F)); // scale to make comparision easier
		F.print();

		F = simpleFundamental(matches);
		System.out.println("Simple");
		CommonOps_DDRM.divide(F, NormOps_DDRM.normF(F));
		F.print();

		// display the inlier matches found using the robust estimator
		AssociationPanel panel = new AssociationPanel(20);
		panel.setAssociation(inliers);
		panel.setImages(imageA, imageB);

		ShowImages.showWindow(panel, "Inlier Pairs");
	}
}