Class MultiViewOps
Contains commonly used operations used in 2view and 3view perspective geometry.
LINES: lines on the image place are represented in homogeneous or generic form as a 3D vector. If a point in homogeneous coordinates is on a line and the dot product is computed the result will be zero.

Constructor Summary

Method Summary
Modifier and TypeMethodDescriptionstatic boolean
Decomposes the absolute quadratic to extract the rectifying homogrpahy H.static void
canonicalRectifyingHomographyFromKPinf
(DMatrixRMaj K, Point3D_F64 planeAtInfinity, DMatrixRMaj H) Constructs a canonical rectifying homography from its components, 3x3 intrinsic matrix K and p the plane at infinity.static double
IF a homography is compatible with a fundamental matrix then norm(H'*F + F'*H) = 0.static DMatrixRMaj
constraint
(TrifocalTensor tensor, Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3, DMatrixRMaj ret) Trifocal tensor with pointpointpoint correspondence:
[p2]_{x}(sum p1^{i}*T_{i})[p3]_{x} = 0static Vector3D_F64
constraint
(TrifocalTensor tensor, Point2D_F64 p1, Point2D_F64 p2, Vector3D_F64 l3, Vector3D_F64 ret) Trifocal tensor with pointpointline correspondence:
[p2]_{x}(sum p1^{i}*T_{i})*l3 = 0static Vector3D_F64
constraint
(TrifocalTensor tensor, Point2D_F64 p1, Vector3D_F64 l2, Point2D_F64 p3, Vector3D_F64 ret) Trifocal tensor with pointlinepoint correspondence:
(l2^{T}(sum p1^{i}*T_{i})[p3]_{x} = 0static double
constraint
(TrifocalTensor tensor, Point2D_F64 p1, Vector3D_F64 l2, Vector3D_F64 l3) Trifocal tensor with pointlineline correspondence:
(l2^{T}*(sum p1^{i}*T_{i})*l3 = 0static Vector3D_F64
constraint
(TrifocalTensor tensor, Vector3D_F64 l1, Vector3D_F64 l2, Vector3D_F64 l3, @Nullable Vector3D_F64 ret) Trifocal tensor with linelineline correspondence:
(l2^{T}*[T1,T2,T3]*L2)*[l1]_{x} = 0static double
constraint
(DMatrixRMaj F, Point2D_F64 p1, Point2D_F64 p2) Applies the epipolar relationship constraint to an essential or fundamental matrix:
0 = p2^{T}*F*p1
Input points are in normalized image coordinates for an essential matrix and pixels for fundamental.static Point2D_F64
constraintHomography
(DMatrixRMaj H, Point2D_F64 p1, Point2D_F64 outputP2) Applies the homography constraints to two points:
z*p2 = H*p1
where z is a scale factor and (p1,p2) are point observations.static void
convertTr
(List<AssociatedTriple> src, int idx0, int idx1, DogArray<AssociatedPair> dst) static void
convertTr
(List<AssociatedTriple> src, DogArray<AssociatedTuple> dst) static void
convertTu
(List<AssociatedTuple> src, int idx0, int idx1, DogArray<AssociatedPair> dst) static DMatrixRMaj
createEssential
(DMatrixRMaj R, Vector3D_F64 T, @Nullable DMatrixRMaj E) Computes an essential matrix from a rotation and translation.static DMatrixRMaj
createFundamental
(DMatrixRMaj E, CameraPinhole intrinsic) Computes a Fundamental matrix given an Essential matrix and the camera's intrinsic parameters.static DMatrixRMaj
createFundamental
(DMatrixRMaj R, Vector3D_F64 T, DMatrixRMaj K1, DMatrixRMaj K2, @Nullable DMatrixRMaj F) Computes an fudamental matrix from a rotation, translation, and calibration matrix.static DMatrixRMaj
Computes a Fundamental matrix given an Essential matrix and the camera calibration matrix.static DMatrixRMaj
createFundamental
(DMatrixRMaj E, DMatrixRMaj K1, DMatrixRMaj K2) Computes a Fundamental matrix given an Essential matrix and the camera calibration matrix.static DMatrixRMaj
createHomography
(DMatrixRMaj R, Vector3D_F64 T, double d, Vector3D_F64 N) Computes a homography matrix from a rotation, translation, plane normal and plane distance:
x[2] = H*x[1]
where x[1] is the point on the first camera and x[2] the location in the second camera.
H = R+(1/d)*T*N^{T}
Where [R,T] is the transform from camera 1 to camera 2.static DMatrixRMaj
createHomography
(DMatrixRMaj R, Vector3D_F64 T, double d, Vector3D_F64 N, DMatrixRMaj K) Computes a homography matrix from a rotation, translation, plane normal, plane distance, and calibration matrix:
x[2] = H*x[1]
where x[1] is the point on the first camera and x[2] the location in the second camera.
H = K*(R+(1/d)*T*N^{T})*K^{1}
Where [R,T] is the transform from camera 1 to camera, and K is the calibration matrix for both cameras.static DMatrixRMaj
createProjectiveToMetric
(DMatrixRMaj K, double v1, double v2, double v3, double lambda, @Nullable DMatrixRMaj H) Given the calibration matrix for the first view, plane at infinity, and lambda (scaling factor) compute the rectifying homography for changing a projective camera matrix into a metric one.static TrifocalTensor
createTrifocal
(Se3_F64 P2, Se3_F64 P3, @Nullable TrifocalTensor ret) Creates a trifocal tensor from two rigid body motions.static TrifocalTensor
createTrifocal
(DMatrixRMaj P2, DMatrixRMaj P3, @Nullable TrifocalTensor ret) Creates a trifocal tensor from two camera matrices.static TrifocalTensor
createTrifocal
(DMatrixRMaj P1, DMatrixRMaj P2, DMatrixRMaj P3, @Nullable TrifocalTensor ret) Creates a trifocal tensor from three camera matrices.static boolean
Decomposes the absolute dual quadratic into the following submatrices: Q=[w w*p;p'*w p'*w*p]static void
decomposeDiac
(double w11, double w12, double w13, double w22, double w23, double w33, CameraPinhole intrinsic) Extracts the camera calibration matrix on the dual image of the absolute conic (DIAC).static void
decomposeDiac
(DMatrixRMaj w, CameraPinhole intrinsic) Extracts the camera calibration matrix on the dual image of the absolute conic (DIAC).Decomposes an essential matrix into the rigid body motion which it was constructed from.static List<Tuple2<Se3_F64,
Vector3D_F64>> Decomposes a homography matrix that's in Euclidean space (computed from features in normalized image coordinates).static boolean
decomposeMetricCamera
(DMatrixRMaj cameraMatrix, DMatrixRMaj K, Se3_F64 worldToView) Decomposes a metric camera matrix P=K*[RT], where A is an upper triangular camera calibration matrix, R is a rotation matrix, and T is a translation vector.static double
disparityToRange
(double disparity, double focalLength, double baseline) Applies stereo disparity equation to compute the distance of an object.static boolean
enforceAbsoluteQuadraticConstraints
(DMatrix4x4 Q, boolean zeroCenter, boolean zeroSkew) If the solution to the absolute quadratic was computed using a linear methods it will not exactly have the required structure.static boolean
enforceAbsoluteQuadraticConstraints
(DMatrix4x4 Q, boolean zeroCenter, boolean zeroSkew, @Nullable DecomposeAbsoluteDualQuadratic alg) static void
errorsHomographySymm
(List<AssociatedPair> observations, DMatrixRMaj H, @Nullable DMatrixRMaj H_inv, DogArray_F64 storage) Computes symmetric Euclidean error for each observation and puts it into the storage.static void
extractEpipoles
(TrifocalTensor tensor, Point3D_F64 e2, Point3D_F64 e3) Computes the epipoles of the first camera in the second and third images.static void
extractEpipoles
(DMatrixRMaj F, Point3D_F64 e1, Point3D_F64 e2) Extracts the epipoles from an essential or fundamental matrix.static double
findScale
(GeoTuple3D_F64<?> a, GeoTuple3D_F64<?> b) Finds the scale which minimizes the difference between `a` and `b`.static double
findScale
(DMatrixRMaj a, DMatrixRMaj b) Finds this scale which minimizes the difference between `a` and `b`.static boolean
fundamentalCompatible3
(DMatrixRMaj F21, DMatrixRMaj F31, DMatrixRMaj F32, double tol) Checks to see if the three fundamental matrices are consistent based on their epipoles.static DMatrixRMaj
fundamentalToEssential
(DMatrixRMaj F, DMatrixRMaj K, @Nullable DMatrixRMaj outputE) Given the calibration matrix, convert the fundamental matrix into an essential matrix.static DMatrixRMaj
fundamentalToEssential
(DMatrixRMaj F, DMatrixRMaj K1, DMatrixRMaj K2, @Nullable DMatrixRMaj outputE) Given the calibration matrix, convert the fundamental matrix into an essential matrix.static @Nullable DMatrixRMaj
fundamentalToHomography2Lines
(DMatrixRMaj F, PairLineNorm line0, PairLineNorm line1) Computes the homography induced from a planar surface when viewed from two views using correspondences of two lines.static @Nullable DMatrixRMaj
Computes the homography induced from a planar surface when viewed from two views using correspondences of three points.static DMatrixRMaj
fundamentalToHomographyLinePt
(DMatrixRMaj F, PairLineNorm line, AssociatedPair point) Computes the homography induced from a planar surface when viewed from two views using correspondences of a line and a point.static DMatrixRMaj
Given a fundamental matrix a pair of camera matrices P0 and P1 can be extracted.static DMatrixRMaj
fundamentalToProjective
(DMatrixRMaj F, Point3D_F64 e2, Vector3D_F64 v, double lambda) Given a fundamental matrix a pair of camera matrices P and P1' are extracted.static void
fundamentalToProjective
(DMatrixRMaj F21, DMatrixRMaj F31, DMatrixRMaj F32, DMatrixRMaj P2, DMatrixRMaj P3) Given three fundamental matrices that describing the relationship between three views, compute a consistent set of projective camera matrices.static DMatrixRMaj
homographyFromRotation
(DMatrixRMaj R21, DMatrixRMaj K1, DMatrixRMaj K2, @Nullable DMatrixRMaj H21) Creates a pixel homography from a rotation matrix and the intrinsic calibration matrices.static boolean
homographyToFundamental
(DMatrixRMaj H21, List<AssociatedPair> pairs, DMatrixRMaj F21) Given a homography, compute the Fundamental matrix between the two views.static DMatrixRMaj
inducedHomography12
(TrifocalTensor tensor, Vector3D_F64 line3, DMatrixRMaj output) Computes the homography induced from view 1 to 2 by a line in view 3.static DMatrixRMaj
inducedHomography13
(TrifocalTensor tensor, Vector3D_F64 line2, DMatrixRMaj output) Computes the homography induced from view 1 to 3 by a line in view 2.static void
intrinsicFromAbsoluteQuadratic
(DMatrixRMaj Q, DMatrixRMaj P, CameraPinhole intrinsic) Extracts the intrinsic camera matrix from a view given its camera matrix and the dual absolute quadratic.static void
projectiveMakeFirstIdentity
(List<DMatrixRMaj> cameraMatrices, @Nullable DMatrixRMaj H) Computes a homography transform which will make the first camera in the list identity and modifies the camera matrices using that homographystatic DMatrixRMaj
projectiveToFundamental
(DMatrixRMaj P2, @Nullable DMatrixRMaj F21) Given an implicit P1=[I0] camera matrix and P2 compute a fundamental matrix.static DMatrixRMaj
projectiveToFundamental
(DMatrixRMaj P1, DMatrixRMaj P2, @Nullable DMatrixRMaj F21) Given two general camera matrices compute fundamental matrix.static DMatrixRMaj
projectiveToIdentityH
(DMatrixRMaj P, @Nullable DMatrixRMaj H) Finds the transform such that P*H = [I0] where P is a 3x4 projective camera matrix and H is a 4x4 matrixstatic boolean
projectiveToMetric
(DMatrixRMaj cameraMatrix, DMatrixRMaj H, Se3_F64 worldToView, DMatrixRMaj K) Elevates a projective camera matrix into a metric one using the rectifying homography.static boolean
projectiveToMetricKnownK
(DMatrixRMaj cameraMatrix, DMatrixRMaj H, DMatrixRMaj K, Se3_F64 worldToView) Convert the projective camera matrix into a metric transform given the rectifying homography and a known calibration matrix.static void
Rectifying / calibrating homography to dual absolute quadratic.static void
scenePointsToPixels
(SceneStructureMetric scene, int viewIdx, BoofLambdas.ProcessIndex2<Point3D_F64, Point2D_F64> function) Projects points in the scene onto the specified image.static void
sceneToCloud3
(SceneStructureMetric scene, double tol, BoofLambdas.ProcessIndex<Point3D_F64> func) Converts the points in the scene into a 3D point cloud.static void
sceneToCloudH
(SceneStructureMetric scene, BoofLambdas.ProcessIndex<Point4D_F64> func) Converts the points in the scene into a homogenous point cloud.static Tuple2<List<Point2D_F64>,
List<Point2D_F64>> split2
(List<AssociatedPair> input) Splits the associated pairs into two listsstatic Tuple3<List<Point2D_F64>,
List<Point2D_F64>, List<Point2D_F64>> split3
(List<AssociatedTriple> input) Splits the associated triple into three listsstatic List<List<Point2D_F64>>
splits3Lists
(List<AssociatedTriple> src, @Nullable List<List<Point2D_F64>> dst) Lists a list ofAssociatedTriple
into a list of observations for each camera independently.static Point3D_F64
transfer_1_to_2
(TrifocalTensor T, Point2D_F64 x1, Point2D_F64 x3, @Nullable Point3D_F64 x2) Transfers a point from the first view to the second view using the observed location in the third viewstatic Point3D_F64
transfer_1_to_2
(TrifocalTensor T, Point2D_F64 x1, Vector3D_F64 l3, @Nullable Point3D_F64 x2) Transfers a point from the first view to the second view using a plane induced by a line in the third view.static Point3D_F64
transfer_1_to_3
(TrifocalTensor T, Point2D_F64 x1, Point2D_F64 x2, @Nullable Point3D_F64 x3) Transfers a point to the third view given observed locations in the first and second viewsstatic Point3D_F64
transfer_1_to_3
(TrifocalTensor T, Point2D_F64 x1, Vector3D_F64 l2, @Nullable Point3D_F64 x3) Transfers a point from the first view to the third view using a plane induced by a line in the second view.static void
triangulatePoints
(SceneStructureMetric structure, SceneObservations observations) Convenience function for initializing bundle adjustment parameters.static void
trifocalToCameraMatrices
(TrifocalTensor tensor, DMatrixRMaj P2, DMatrixRMaj P3) Extract the camera matrices up to a common projective transform.static void
trifocalToFundamental
(TrifocalTensor tensor, DMatrixRMaj F21, DMatrixRMaj F31) Extract the fundamental matrices between views 1 + 2 and views 1 + 3.

Constructor Details

MultiViewOps
public MultiViewOps()


Method Details

createTrifocal
public static TrifocalTensor createTrifocal(DMatrixRMaj P2, DMatrixRMaj P3, @Nullable @Nullable TrifocalTensor ret) Creates a trifocal tensor from two camera matrices. T_{i}^{jk} = a[j,i]*b[k,3]  a[j,3]*b[k,i], where a=P2 and b=P3.
IMPORTANT: It is assumed that the first camera has the following camera matrix P1 = [I0], where I is an identify matrix.
 Parameters:
P2
 Camera matrix for view 2. 3x4 matrixP3
 Camera matrix for view 3. 3x4 matrixret
 Storage for trifocal tensor. If null a new instance will be created. Returns:
 The trifocal tensor

createTrifocal
public static TrifocalTensor createTrifocal(DMatrixRMaj P1, DMatrixRMaj P2, DMatrixRMaj P3, @Nullable @Nullable TrifocalTensor ret) Creates a trifocal tensor from three camera matrices. The
Page 415 in R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
WARNING: This method of creating a trifocal tensor might be numerically less accurate. A unit test had to be changed which used this method to use another approach to constructing the tensor because it was failing even with perfect data. With some thought this issue could be fixed.
 Parameters:
P1
 Camera matrix for view 1. 3x4 matrixP2
 Camera matrix for view 2. 3x4 matrixP3
 Camera matrix for view 3. 3x4 matrixret
 Storage for trifocal tensor. If null a new instance will be created. Returns:
 The trifocal tensor

createTrifocal
public static TrifocalTensor createTrifocal(Se3_F64 P2, Se3_F64 P3, @Nullable @Nullable TrifocalTensor ret) Creates a trifocal tensor from two rigid body motions. This is for the calibrated camera case.
NOTE: View 1 is the world coordinate system, i.e. [I0]
 Parameters:
P2
 Transform from view 1 to view 2.P3
 Transform from view 1 to view 3.ret
 Storage for trifocal tensor. If null a new instance will be created. Returns:
 The trifocal tensor

constraint
public static Vector3D_F64 constraint(TrifocalTensor tensor, Vector3D_F64 l1, Vector3D_F64 l2, Vector3D_F64 l3, @Nullable @Nullable Vector3D_F64 ret) Trifocal tensor with linelineline correspondence:
(l2^{T}*[T1,T2,T3]*L2)*[l1]_{x} = 0 Parameters:
tensor
 Trifocal tensorl1
 A line in the first view.l2
 A line in the second view.l3
 A line in the third view.ret
 Storage for output. If null a new instance will be declared. Returns:
 Result of applying the constraint. With perfect inputs will be zero.

constraint
public static double constraint(TrifocalTensor tensor, Point2D_F64 p1, Vector3D_F64 l2, Vector3D_F64 l3) Trifocal tensor with pointlineline correspondence:
(l2^{T}*(sum p1^{i}*T_{i})*l3 = 0 Parameters:
tensor
 Trifocal tensorp1
 A point in the first view.l2
 A line in the second view.l3
 A line in the third view. Returns:
 Result of applying the constraint. With perfect inputs will be zero.

constraint
public static Vector3D_F64 constraint(TrifocalTensor tensor, Point2D_F64 p1, Vector3D_F64 l2, Point2D_F64 p3, Vector3D_F64 ret) Trifocal tensor with pointlinepoint correspondence:
(l2^{T}(sum p1^{i}*T_{i})[p3]_{x} = 0 Parameters:
tensor
 Trifocal tensorp1
 A point in the first view.l2
 A line in the second view.p3
 A point in the third view. Returns:
 Result of applying the constraint. With perfect inputs will be zero.

constraint
public static Vector3D_F64 constraint(TrifocalTensor tensor, Point2D_F64 p1, Point2D_F64 p2, Vector3D_F64 l3, Vector3D_F64 ret) Trifocal tensor with pointpointline correspondence:
[p2]_{x}(sum p1^{i}*T_{i})*l3 = 0 Parameters:
tensor
 Trifocal tensorp1
 A point in the first view.p2
 A point in the second view.l3
 A line in the third view. Returns:
 Result of applying the constraint. With perfect inputs will be zero.

constraint
public static DMatrixRMaj constraint(TrifocalTensor tensor, Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3, DMatrixRMaj ret) Trifocal tensor with pointpointpoint correspondence:
[p2]_{x}(sum p1^{i}*T_{i})[p3]_{x} = 0 Parameters:
tensor
 Trifocal tensorp1
 A point in the first view.p2
 A point in the second view.p3
 A point in the third view.ret
 Optional storage for output. 3x3 matrix. Modified. Returns:
 Result of applying the constraint. With perfect inputs will be zero.

constraint
Applies the epipolar relationship constraint to an essential or fundamental matrix:
0 = p2^{T}*F*p1
Input points are in normalized image coordinates for an essential matrix and pixels for fundamental. Parameters:
F
 3x3 essential or fundamental matrix.p1
 Point in view 1.p2
 Point in view 2. Returns:
 Constraint value.

constraintHomography
Applies the homography constraints to two points:
z*p2 = H*p1
where z is a scale factor and (p1,p2) are point observations. Note that since 2D points are inputted translation and normalization to homogeneous coordinates with z=1 is automatically handled. Parameters:
H
 Input: 3x3 Homography matrix.p1
 Input: Point in view 1.outputP2
 Output: storage for point in view 2. Returns:
 Predicted point in view 2

inducedHomography13
public static DMatrixRMaj inducedHomography13(TrifocalTensor tensor, Vector3D_F64 line2, DMatrixRMaj output) Computes the homography induced from view 1 to 3 by a line in view 2. The provided line in view 2 must contain the view 2 observation. p3 = H13*p1 Parameters:
tensor
 Input: Trifocal tensorline2
 Input: Line in view 2.General notation
.output
 Output: Optional storage for homography. 3x3 matrix Returns:
 Homography from view 1 to 3

inducedHomography12
public static DMatrixRMaj inducedHomography12(TrifocalTensor tensor, Vector3D_F64 line3, DMatrixRMaj output) Computes the homography induced from view 1 to 2 by a line in view 3. The provided line in view 3 must contain the view 3 observation. p2 = H12*p1 Parameters:
tensor
 Input: Trifocal tensorline3
 Input: Line in view 3.General notation
.output
 Output: Optional storage for homography. 3x3 matrix Returns:
 Homography from view 1 to 2

fundamentalToHomography3Pts
@Nullable public static @Nullable DMatrixRMaj fundamentalToHomography3Pts(DMatrixRMaj F, AssociatedPair p1, AssociatedPair p2, AssociatedPair p3) Computes the homography induced from a planar surface when viewed from two views using correspondences of three points. Observations must be on the planar surface.WARNING: As implemented, it seems to have stability issues or a bug. See code for comments. Please fix and update unit test.
 Parameters:
F
 Fundamental matrixp1
 Associated point observationp2
 Associated point observationp3
 Associated point observation Returns:
 The homography from view 1 to view 2 or null if it fails
 See Also:

fundamentalToHomographyLinePt
public static DMatrixRMaj fundamentalToHomographyLinePt(DMatrixRMaj F, PairLineNorm line, AssociatedPair point) Computes the homography induced from a planar surface when viewed from two views using correspondences of a line and a point. Observations must be on the planar surface. Parameters:
F
 Fundamental matrixline
 Line on the planepoint
 Point on the plane Returns:
 The homography from view 1 to view 2 or null if it fails
 See Also:

fundamentalToHomography2Lines
@Nullable public static @Nullable DMatrixRMaj fundamentalToHomography2Lines(DMatrixRMaj F, PairLineNorm line0, PairLineNorm line1) Computes the homography induced from a planar surface when viewed from two views using correspondences of two lines. Observations must be on the planar surface. Parameters:
F
 Fundamental matrixline0
 Line on the planeline1
 Line on the plane Returns:
 The homography from view 1 to view 2 or null if it fails
 See Also:

extractEpipoles
Computes the epipoles of the first camera in the second and third images. Epipoles are found in homogeneous coordinates and have a norm of 1.
Properties:
 e2^{T}*F12 = 0
 e3^{T}*F13 = 0
 Parameters:
tensor
 Trifocal tensor. Not Modifiede2
 Output: Epipole in image 2. Homogeneous coordinates. Modifiede3
 Output: Epipole in image 3. Homogeneous coordinates. Modified See Also:

trifocalToFundamental
Extract the fundamental matrices between views 1 + 2 and views 1 + 3. The returned Fundamental matrices will have the following properties: x_{i}^{T}*Fi*x_{1} = 0, where i is view 2 or 3.
NOTE: The first camera is assumed to have the camera matrix of P1 = [I0]. Thus observations in pixels for the first camera will not meet the epipolar constraint when applied to the returned fundamental matrices.
 Parameters:
tensor
 Trifocal tensor. Not modified.F21
 Output: Fundamental matrix for views 1 and 2. Modified.F31
 Output: Fundamental matrix for views 1 and 3. Modified. See Also:

trifocalToCameraMatrices
Extract the camera matrices up to a common projective transform.
NOTE: The camera matrix for the first view is assumed to be P1 = [I0].
 Parameters:
tensor
 Trifocal tensor. Not modified.P2
 Output: 3x4 camera matrix for views 1 to 2. Modified.P3
 Output: 3x4 camera matrix for views 1 to 3. Modified. See Also:

createEssential
public static DMatrixRMaj createEssential(DMatrixRMaj R, Vector3D_F64 T, @Nullable @Nullable DMatrixRMaj E) Computes an essential matrix from a rotation and translation. This motion is the motion from the first camera frame into the second camera frame. The essential matrix 'E' is defined as:
E = hat(T)*R
where hat(T) is the skew symmetric cross product matrix for vector T. Parameters:
R
 Rotation matrix.T
 Translation vector.E
 (Output) Storage for essential matrix. 3x3 matrix Returns:
 Essential matrix

createFundamental
Computes a Fundamental matrix given an Essential matrix and the camera calibration matrix. F = (K^{1})^{T}*E*K^{1} Parameters:
E
 Essential matrixK
 Intrinsic camera calibration matrix Returns:
 Fundamental matrix

createFundamental
Computes a Fundamental matrix given an Essential matrix and the camera's intrinsic parameters. Parameters:
E
 Essential matrixintrinsic
 Intrinsic camera calibration Returns:
 Fundamental matrix
 See Also:

createFundamental
Computes a Fundamental matrix given an Essential matrix and the camera calibration matrix. F = (K2^{1})^{T}*E*K1^{1} Parameters:
E
 Essential matrixK1
 Intrinsic camera calibration matrix for camera 1K2
 Intrinsic camera calibration matrix for camera 2 Returns:
 Fundamental matrix

createFundamental
public static DMatrixRMaj createFundamental(DMatrixRMaj R, Vector3D_F64 T, DMatrixRMaj K1, DMatrixRMaj K2, @Nullable @Nullable DMatrixRMaj F) Computes an fudamental matrix from a rotation, translation, and calibration matrix. Motion is from the first camera frame into the second camera frame.
 Parameters:
R
 Rotation matrix. first to secondT
 Translation vector. first to secondK1
 Intrinsic camera calibration matrix for camera 1K2
 Intrinsic camera calibration matrix for camera 2F
 (Output) Storage for essential matrix. 3x3 matrix Returns:
 Essential matrix

createHomography
Computes a homography matrix from a rotation, translation, plane normal and plane distance:
x[2] = H*x[1]
where x[1] is the point on the first camera and x[2] the location in the second camera.
H = R+(1/d)*T*N^{T}
Where [R,T] is the transform from camera 1 to camera 2. Parameters:
R
 Rotation matrix from camera 1 to camera 2.T
 Translation vector from camera 1 to camera 2.d
 Distance > 0 of closest point on plane to the origin of camera 1.N
 Normal of plane with respect to the first camera. Returns:
 Calibrated homography matrix

createHomography
public static DMatrixRMaj createHomography(DMatrixRMaj R, Vector3D_F64 T, double d, Vector3D_F64 N, DMatrixRMaj K) Computes a homography matrix from a rotation, translation, plane normal, plane distance, and calibration matrix:
x[2] = H*x[1]
where x[1] is the point on the first camera and x[2] the location in the second camera.
H = K*(R+(1/d)*T*N^{T})*K^{1}
Where [R,T] is the transform from camera 1 to camera, and K is the calibration matrix for both cameras. Parameters:
R
 Rotation matrix from camera 1 to camera 2.T
 Translation vector from camera 1 to camera 2.d
 Distance > 0 of closest point on plane to the origin of camera 1.N
 Normal of plane with respect to the first camera.K
 Intrinsic calibration matrix Returns:
 Uncalibrated homography matrix

extractEpipoles
Extracts the epipoles from an essential or fundamental matrix. The epipoles are extracted from the left and right null space of the provided matrix. Note that the found epipoles are in homogeneous coordinates. If the epipole is at infinity then z=0
Left: e_{2}^{T}*F = 0
Right: F*e_{1} = 0 Parameters:
F
 Input: Fundamental or Essential 3x3 matrix. Not modified.e1
 Output: Right epipole in homogeneous coordinates. Can be null. Modified.e2
 Output: Left epipole in homogeneous coordinates. Can be null. Modified.

fundamentalToProjective
public static DMatrixRMaj fundamentalToProjective(DMatrixRMaj F, Point3D_F64 e2, Vector3D_F64 v, double lambda) Given a fundamental matrix a pair of camera matrices P and P1' are extracted. The camera matrices are 3 by 4 and used to project a 3D homogenous point onto the image plane. These camera matrices will only be known up to a projective transform, thus there are multiple solutions, The canonical camera matrix is defined as:
P=[I0] and P'= [MM*t] = [[e']*F + e'*v^t  lambda*e']
where e' is the epipole F^{T}e' = 0, [e'] is the cross product matrix for the enclosed vector, v is an arbitrary 3vector and lambda is a nonzero scalar.NOTE: Additional information is needed to upgrade this projective transform into a metric transform.
Page 256 in R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
F
 (Input) A fundamental matrixe2
 (Input) Left epipole of fundamental matrix, F^{T}*e2 = 0.v
 (Input) Arbitrary 3vector. Just pick some value, say (0,0,0).lambda
 (Input) A non zero scalar. Try one. Returns:
 The canonical camera (projection) matrix P' (3 by 4) Known up to a projective transform.
 See Also:

projectiveToFundamental
public static DMatrixRMaj projectiveToFundamental(DMatrixRMaj P1, DMatrixRMaj P2, @Nullable @Nullable DMatrixRMaj F21) Given two general camera matrices compute fundamental matrix.
F= [e']_x P2*P1+, where P1+ is the pseudo inverse of P1, and e' = P2*C, with P*C=0
 Parameters:
P1
 (Input) camera matrix for view 1P2
 (Input) camera matrix for view 2F21
 (Output) Fundamental matrix from view 1 to 2 Returns:
 Fundamental matrix.

projectiveToFundamental
public static DMatrixRMaj projectiveToFundamental(DMatrixRMaj P2, @Nullable @Nullable DMatrixRMaj F21) Given an implicit P1=[I0] camera matrix and P2 compute a fundamental matrix.
F= [e']_x P2*P1+, where P1+ is the pseudo inverse of P1, and e' = P2*C, with P*C=0
 Parameters:
P2
 (Input) camera matrix for view 2F21
 (Output) Fundamental matrix from view 1 to 2 Returns:
 Fundamental matrix.

fundamentalToProjective
Given a fundamental matrix a pair of camera matrices P0 and P1 can be extracted. Same
fundamentalToProjective(DMatrixRMaj, Point3D_F64, Vector3D_F64, double)
but with the suggested values for all variables filled in for you. Parameters:
F
 (Input) Fundamental Matrix Returns:
 The canonical camera (projection) matrix P' (3 by 4) Known up to a projective transform.
 See Also:

fundamentalToEssential
public static DMatrixRMaj fundamentalToEssential(DMatrixRMaj F, DMatrixRMaj K, @Nullable @Nullable DMatrixRMaj outputE) Given the calibration matrix, convert the fundamental matrix into an essential matrix. E = K'*F*k. The singular values of the resulting E matrix are forced to be [1,1,0] Parameters:
F
 (Input) Fundamental matrix. 3x3K
 (Input) Calibration matrix (3x3)outputE
 (Output) Found essential matrix Returns:
 Essential matrix

fundamentalToEssential
public static DMatrixRMaj fundamentalToEssential(DMatrixRMaj F, DMatrixRMaj K1, DMatrixRMaj K2, @Nullable @Nullable DMatrixRMaj outputE) Given the calibration matrix, convert the fundamental matrix into an essential matrix. E = K[2]^{T}*F*k[1]. The singular values of the resulting E matrix are forced to be [1,1,0] Parameters:
F
 (Input) Fundamental matrix. 3x3K1
 (Input) Calibration matrix view 1 (3x3)K2
 (Input) Calibration matrix view 2 (3x3)outputE
 (Output) Found essential matrix Returns:
 Essential matrix

fundamentalToProjective
public static void fundamentalToProjective(DMatrixRMaj F21, DMatrixRMaj F31, DMatrixRMaj F32, DMatrixRMaj P2, DMatrixRMaj P3) Given three fundamental matrices that describing the relationship between three views, compute a consistent set of projective camera matrices. Consistent means that the camera matrices will give back the same fundamental matrices, see [1]. This function is of dubious practical value, see discussion inFundamentalToProjective.threeView(org.ejml.data.DMatrixRMaj, org.ejml.data.DMatrixRMaj, org.ejml.data.DMatrixRMaj, org.ejml.data.DMatrixRMaj, org.ejml.data.DMatrixRMaj)
. The first camera matrix, without loss of generality, is assumed to be P1 = [I0]. Page 301 in Y. Ma, S. Soatto, J. Kosecka, and S. S. Sastry, "An Invitation to 3D Vision" SpringerVerlad, 2004
 Parameters:
F21
 (Input) Fundamental matrix between view 1 and 2F31
 (Input) Fundamental matrix between view 1 and 3F32
 (Input) Fundamental matrix between view 2 and 3P2
 (Output) Camera matrix for view 2P3
 (Output) Camera matrix for view 3 See Also:

projectiveToIdentityH
Finds the transform such that P*H = [I0] where P is a 3x4 projective camera matrix and H is a 4x4 matrix Parameters:
P
 (Input) camera matrix 3x4H
 (Output) 4x4 matrix

projectiveMakeFirstIdentity
public static void projectiveMakeFirstIdentity(List<DMatrixRMaj> cameraMatrices, @Nullable @Nullable DMatrixRMaj H) Computes a homography transform which will make the first camera in the list identity and modifies the camera matrices using that homography Parameters:
cameraMatrices
 (input/output) ConvertsH
 (output + Optional) storage for homography

fundamentalCompatible3
public static boolean fundamentalCompatible3(DMatrixRMaj F21, DMatrixRMaj F31, DMatrixRMaj F32, double tol) Checks to see if the three fundamental matrices are consistent based on their epipoles.
e_{23}^{T}F_{21}e_{13} = 0
e_{31}^{T}F_{32}e_{21} = 0
e_{32}^{T}F_{31}e_{12} = 0
Section 15.4 in R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
F21
 (Input) Fundamental matrix between view 1 and 2F31
 (Input) Fundamental matrix between view 1 and 3F32
 (Input) Fundamental matrix between view 2 and 3

decomposeMetricCamera
public static boolean decomposeMetricCamera(DMatrixRMaj cameraMatrix, DMatrixRMaj K, Se3_F64 worldToView) Decomposes a metric camera matrix P=K*[RT], where A is an upper triangular camera calibration matrix, R is a rotation matrix, and T is a translation vector. If
PerspectiveOps.createCameraMatrix(org.ejml.data.DMatrixRMaj, georegression.struct.point.Vector3D_F64, org.ejml.data.DMatrixRMaj, org.ejml.data.DMatrixRMaj)
is called using the returned value you will get an equivalent camera matrix. NOTE: There are multiple valid solutions to this problem and only one solution is returned.
 NOTE: The camera center will be on the plane at infinity.
 Parameters:
cameraMatrix
 Input: Camera matrix, 3 by 4K
 Output: Camera calibration matrix, 3 by 3.worldToView
 Output: The rotation and translation. Returns:
 true if decompose was successful

decomposeEssential
Decomposes an essential matrix into the rigid body motion which it was constructed from. Due to ambiguities there are four possible solutions. SeeDecomposeEssential
for the details. The correct solution can be found using triangulation and the positive depth constraint, e.g. the objects must be in front of the camera to be seen. Also note that the scale of the translation is lost, even with perfect data. Parameters:
E21
 An essential matrix. Returns:
 Four possible motions. From view 1 to view 2.
 See Also:

decomposeHomography
Decomposes a homography matrix that's in Euclidean space (computed from features in normalized image coordinates). The homography is defined as H = (R + (1/d)*T*N^{T}), where R is a 3x3 rotation matrix, d is the distance of the plane, N is the plane's normal (unit vector), T is the translation vector. If the homography is from view 'a' to 'b' then transform (R,T) will be from reference 'a' to 'b'. Note that the returned 'T' is divided by 'd'. Parameters:
H
 Homography in Euclidean space Returns:
 The set of four possible solutions. First param: motion (R,T). Second param: plane normal vector.
 See Also:

errorsHomographySymm
public static void errorsHomographySymm(List<AssociatedPair> observations, DMatrixRMaj H, @Nullable @Nullable DMatrixRMaj H_inv, DogArray_F64 storage) Computes symmetric Euclidean error for each observation and puts it into the storage. If the homography projects the point into the plane at infinity (z=0) then it is skipped
error[i] = (H*x1  x2')**2 + (inv(H)*x2  x1')**2 Parameters:
observations
 (Input) observationsH
 (Input) HomographyH_inv
 (Input) Inverse of homography. if null it will be computed internallystorage
 (Output) storage for found errors

transfer_1_to_3
public static Point3D_F64 transfer_1_to_3(TrifocalTensor T, Point2D_F64 x1, Vector3D_F64 l2, @Nullable @Nullable Point3D_F64 x3) Transfers a point from the first view to the third view using a plane induced by a line in the second view. Parameters:
x1
 (Input) point (pixel) in first viewl2
 (Input) line in second viewT
 (Input) Trifocal tensorx3
 (Output) Induced point (pixel) in third view. Homogenous coordinates. Returns:
 induced point.

transfer_1_to_3
public static Point3D_F64 transfer_1_to_3(TrifocalTensor T, Point2D_F64 x1, Point2D_F64 x2, @Nullable @Nullable Point3D_F64 x3) Transfers a point to the third view given observed locations in the first and second views Parameters:
x1
 (Input) point (pixel) in first viewx2
 (Input) point (pixel) in second viewT
 (Input) Trifocal tensorx3
 (Output) Induced point (pixel) in third view. Homogenous coordinates. Returns:
 induced point.

transfer_1_to_2
public static Point3D_F64 transfer_1_to_2(TrifocalTensor T, Point2D_F64 x1, Vector3D_F64 l3, @Nullable @Nullable Point3D_F64 x2) Transfers a point from the first view to the second view using a plane induced by a line in the third view. Parameters:
x1
 (Input) point (pixel) in first viewl3
 (Input) line in third viewT
 (Input) Trifocal tensorx2
 (Output) Induced point (pixel) in second view. Homogenous coordinates. Returns:
 induced point.

transfer_1_to_2
public static Point3D_F64 transfer_1_to_2(TrifocalTensor T, Point2D_F64 x1, Point2D_F64 x3, @Nullable @Nullable Point3D_F64 x2) Transfers a point from the first view to the second view using the observed location in the third view Parameters:
x1
 (Input) point (pixel) in first viewx3
 (Input) point (pixel) in third viewT
 (Input) Trifocal tensorx2
 (Output) Induced point (pixel) in second view. Homogenous coordinates. Returns:
 induced point.

projectiveToMetric
public static boolean projectiveToMetric(DMatrixRMaj cameraMatrix, DMatrixRMaj H, Se3_F64 worldToView, DMatrixRMaj K) Elevates a projective camera matrix into a metric one using the rectifying homography. Extracts calibration and Se3 pose.P'=P*H K,R,t = decompose(P')
where P is the camera matrix, H is the homography, (K,R,t) are the intrinsic calibration matrix, rotation, and translation Parameters:
cameraMatrix
 (Input) camera matrix. 3x4H
 (Input) Rectifying homography. 4x4worldToView
 (Output) Transform from world to camera viewK
 (Output) Camera calibration matrix See Also:

projectiveToMetricKnownK
public static boolean projectiveToMetricKnownK(DMatrixRMaj cameraMatrix, DMatrixRMaj H, DMatrixRMaj K, Se3_F64 worldToView) Convert the projective camera matrix into a metric transform given the rectifying homography and a known calibration matrix. This simplifies the math compared to
projectiveToMetric(org.ejml.data.DMatrixRMaj, org.ejml.data.DMatrixRMaj, georegression.struct.se.Se3_F64, org.ejml.data.DMatrixRMaj)
where it needs to extract `K`.P = K*[RT]*H
where H is the inverse of the rectifying homography. Parameters:
cameraMatrix
 (Input) camera matrix. 3x4H
 (Input) Rectifying homography. 4x4K
 (Input) Known calibration matrixworldToView
 (Output) transform from world to camera view

enforceAbsoluteQuadraticConstraints
public static boolean enforceAbsoluteQuadraticConstraints(DMatrix4x4 Q, boolean zeroCenter, boolean zeroSkew) If the solution to the absolute quadratic was computed using a linear methods it will not exactly have the required structure. This forces the structure to match. Positive diagonal elements
 (Optional) zero principle point
 (Optional) zero skew
 Q = H*diag([1 1 1 0])*H^{T} and H = [K 0; p'*K 1]
 R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
Q
 Approximate solution to absolute quadratic See Also:

enforceAbsoluteQuadraticConstraints
public static boolean enforceAbsoluteQuadraticConstraints(DMatrix4x4 Q, boolean zeroCenter, boolean zeroSkew, @Nullable @Nullable DecomposeAbsoluteDualQuadratic alg) 
absoluteQuadraticToH
Decomposes the absolute quadratic to extract the rectifying homogrpahy H. This is used to go from a projective to metric (calibrated) geometry. See pg 464 in [1].Q = H*I*H^{T}
where I = diag(1 1 1 0)
 R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
Q
 (Input) Absolute quadratic. Typically found in auto calibration. Not modified.H
 (Output) 4x4 rectifying homography. See Also:

rectifyHToAbsoluteQuadratic
Rectifying / calibrating homography to dual absolute quadratic.Q = H*I*H^{T} = H(:,1:3)*H(:,1:3)'
where I = diag(1 1 1 0)
 Parameters:
H
 (Input) 4x4 rectifying homography.Q
 (Output) Absolute quadratic. Typically found in auto calibration. Not modified.

canonicalRectifyingHomographyFromKPinf
public static void canonicalRectifyingHomographyFromKPinf(DMatrixRMaj K, Point3D_F64 planeAtInfinity, DMatrixRMaj H) Constructs a canonical rectifying homography from its components, 3x3 intrinsic matrix K and p the plane at infinity. See 19.2 page 460 in [1]. This assumes that camera matrix P1 = [I0].H=[K*K, 0; p'*k, 1]
 R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
K
 (Input) 3x3 intrinsic calibration matrixplaneAtInfinity
 (Input) Plane at infinityH
 (Output) rectifying homography.

intrinsicFromAbsoluteQuadratic
public static void intrinsicFromAbsoluteQuadratic(DMatrixRMaj Q, DMatrixRMaj P, CameraPinhole intrinsic) Extracts the intrinsic camera matrix from a view given its camera matrix and the dual absolute quadratic.w_{i} = P_{i}*Q*P_{i}^{T}, where w_{i} = K_{i}*K'_{i}
 Parameters:
Q
 (Input) Dual absolute qudraticP
 (Input) Camera matrix for a viewintrinsic
 (Output) found intrinsic parameters

decomposeDiac
public static void decomposeDiac(double w11, double w12, double w13, double w22, double w23, double w33, CameraPinhole intrinsic) Extracts the camera calibration matrix on the dual image of the absolute conic (DIAC). Elements which could cause problems if negative have the absolute value taken to avoid NaN. The upper triangular elements in w (DIAC) are passed in. Parameters:
intrinsic
 (output) K extracted from w

decomposeDiac
Extracts the camera calibration matrix on the dual image of the absolute conic (DIAC). Elements which could cause problems if negative have the absolute value taken to avoid NaN. Parameters:
w
 (input) DIAC 3x3intrinsic
 (output) K extracted from w

createProjectiveToMetric
public static DMatrixRMaj createProjectiveToMetric(DMatrixRMaj K, double v1, double v2, double v3, double lambda, @Nullable @Nullable DMatrixRMaj H) Given the calibration matrix for the first view, plane at infinity, and lambda (scaling factor) compute the rectifying homography for changing a projective camera matrix into a metric one.H = [K 0;v' &lambda]
 Parameters:
K
 3x3 calibration matrix for view 1v1
 plane at infinityv2
 plane at infinityv3
 plane at infinitylambda
 scaling factorH
 (Optional) Storage for 4x4 matrix Returns:
 The homography

decomposeAbsDualQuadratic
Decomposes the absolute dual quadratic into the following submatrices: Q=[w w*p;p'*w p'*w*p] Parameters:
Q
 (Input) Absolute quadratic. Typically found in auto calibration. Not modified.w
 (Output) 3x3 symmetric matrixp
 (Output) 3x1 vector Returns:
 true if successful or false if it failed
 See Also:

split2
Splits the associated pairs into two lists Parameters:
input
 List of associated features Returns:
 two lists containing each set of features

split3
public static Tuple3<List<Point2D_F64>,List<Point2D_F64>, split3List<Point2D_F64>> (List<AssociatedTriple> input) Splits the associated triple into three lists Parameters:
input
 List of associated features Returns:
 three lists containing each set of features

triangulatePoints
public static void triangulatePoints(SceneStructureMetric structure, SceneObservations observations) Convenience function for initializing bundle adjustment parameters. Triangulates points using camera position and pixel observations. Parameters:
structure
 camera locationsobservations
 observations of features in the images

findScale
Finds this scale which minimizes the difference between `a` and `b`. scale*ab Parameters:
a
 (Input) matrixb
 (Input) matrix Returns:
 scale factor

findScale
Finds the scale which minimizes the difference between `a` and `b`. scale*ab Parameters:
a
 (Input) 3D coordinateb
 (Input) 3D coordinate Returns:
 scale factor

splits3Lists
public static List<List<Point2D_F64>> splits3Lists(List<AssociatedTriple> src, @Nullable @Nullable List<List<Point2D_F64>> dst) Lists a list ofAssociatedTriple
into a list of observations for each camera independently. Parameters:
src
 (Input) list ofAssociatedTriple
dst
 (Output) list of lists. Can be null. Returns:
 list of lists.

convertTr
 Parameters:
src
 (Input) List of AssociatedTripledst
 (Output) Array of AssociatedTuple. Array is reset.

convertTr
public static void convertTr(List<AssociatedTriple> src, int idx0, int idx1, DogArray<AssociatedPair> dst)  Parameters:
src
 (Input) List of AssociatedTripleidx0
 (Input) which feature in the triple is p1 in the pairidx1
 (Input) which feature in the triple is p2 in the pairdst
 (Output) Array of AssociatedPair. Array is reset.

convertTu
public static void convertTu(List<AssociatedTuple> src, int idx0, int idx1, DogArray<AssociatedPair> dst)  Parameters:
src
 (Input) List of AssociatedTupleidx0
 (Input) which feature in the tuple is p1 in the pairidx1
 (Input) which feature in the tuple is p2 in the pairdst
 (Output) Array of AssociatedPair. Array is reset.

disparityToRange
public static double disparityToRange(double disparity, double focalLength, double baseline) Applies stereo disparity equation to compute the distance of an object. Simple equation but if you use this equation you know you didn't screw it up. 
scenePointsToPixels
public static void scenePointsToPixels(SceneStructureMetric scene, int viewIdx, BoofLambdas.ProcessIndex2<Point3D_F64, Point2D_F64> function) Projects points in the scene onto the specified image. Results are returned using a lambda that provides the points index, the point's 3D location in the camera frame, and the projected pixels. No checks are done for the following: Was the feature observed by this view
 Does the feature appear behind the camera
 Is the projected pixel inside the image
 Parameters:
scene
 (Input) Metric sceneviewIdx
 (Input) Index of view for which points are projectedfunction
 (Output) Called with results (index, 3D camera location, pixel)

sceneToCloud3
public static void sceneToCloud3(SceneStructureMetric scene, double tol, BoofLambdas.ProcessIndex<Point3D_F64> func) Converts the points in the scene into a 3D point cloud. A lambda is used pass in the results. This function will work if it's homogenous or 3D coordinates. Parameters:
scene
 (Input) The scenetol
 (Input) Only used if the scene is in homogenous coordinates. Tolerance for points being at infinity. Smaller values means more tolerant. Try 1e8.func
 (Output) Results are passed in to this function with their index and 3D point.

sceneToCloudH
public static void sceneToCloudH(SceneStructureMetric scene, BoofLambdas.ProcessIndex<Point4D_F64> func) Converts the points in the scene into a homogenous point cloud. Results are passed in to the lambda. It will work with a scene in homogenous or 3D coordinates. Parameters:
scene
 (Input) The scenefunc
 (Output) Results are passed in to this function with their index and 3D point.

compatibleHomography
IF a homography is compatible with a fundamental matrix then norm(H'*F + F'*H) = 0. A homography is compatible with F, if H is generated from a plane.Page 327 in R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
F
 (Input) Fundamental matrixH
 (Input) Homography Returns:
 A number close to zero if compatible

homographyToFundamental
public static boolean homographyToFundamental(DMatrixRMaj H21, List<AssociatedPair> pairs, DMatrixRMaj F21) Given a homography, compute the Fundamental matrix between the two views. This requires at least 2 points which are not on the plane to work. Using this function it is possible to compute a fundamental matrix from 6 points.Page 335 in R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
 Parameters:
H21
 (Input) known homographypairs
 (Input) two or more point observations which do not lie on the planeF21
 (Output) found homography matrix Returns:
 true if no errors were encountered

homographyFromRotation
public static DMatrixRMaj homographyFromRotation(DMatrixRMaj R21, DMatrixRMaj K1, DMatrixRMaj K2, @Nullable @Nullable DMatrixRMaj H21) Creates a pixel homography from a rotation matrix and the intrinsic calibration matrices. H = K2*R21*inv(K1) Parameters:
R21
 (Input) Rotation matrixK1
 (Input) Intrinsic camera matrix 1K2
 (Input) Intrinsic camera matrix 2 Returns:
 The homography
