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BoofCV is an open source Java library for real-time computer vision and robotics applications.
/*
* Copyright (c) 2022, Peter Abeles. All Rights Reserved.
*
* This file is part of BoofCV (http://boofcv.org).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package boofcv.alg.geo;
import boofcv.abst.geo.TriangulateNViewsMetricH;
import boofcv.abst.geo.bundle.BundleAdjustmentCamera;
import boofcv.abst.geo.bundle.SceneObservations;
import boofcv.abst.geo.bundle.SceneStructureCommon;
import boofcv.abst.geo.bundle.SceneStructureMetric;
import boofcv.alg.distort.brown.RemoveBrownPtoN_F64;
import boofcv.alg.geo.bundle.cameras.BundlePinhole;
import boofcv.alg.geo.bundle.cameras.BundlePinholeBrown;
import boofcv.alg.geo.bundle.cameras.BundlePinholeSimplified;
import boofcv.alg.geo.f.FundamentalExtractEpipoles;
import boofcv.alg.geo.f.FundamentalToProjective;
import boofcv.alg.geo.h.HomographyInducedStereo2Line;
import boofcv.alg.geo.h.HomographyInducedStereo3Pts;
import boofcv.alg.geo.h.HomographyInducedStereoLinePt;
import boofcv.alg.geo.impl.ProjectiveToIdentity;
import boofcv.alg.geo.structure.DecomposeAbsoluteDualQuadratic;
import boofcv.alg.geo.trifocal.TrifocalExtractGeometries;
import boofcv.alg.geo.trifocal.TrifocalTransfer;
import boofcv.factory.geo.ConfigTriangulation;
import boofcv.factory.geo.FactoryMultiView;
import boofcv.misc.BoofLambdas;
import boofcv.misc.BoofMiscOps;
import boofcv.struct.calib.CameraPinhole;
import boofcv.struct.geo.*;
import georegression.geometry.GeometryMath_F64;
import georegression.geometry.UtilLine2D_F64;
import georegression.geometry.UtilPoint3D_F64;
import georegression.metric.Intersection2D_F64;
import georegression.struct.GeoTuple3D_F64;
import georegression.struct.line.LineGeneral2D_F64;
import georegression.struct.point.Point2D_F64;
import georegression.struct.point.Point3D_F64;
import georegression.struct.point.Point4D_F64;
import georegression.struct.point.Vector3D_F64;
import georegression.struct.se.Se3_F64;
import georegression.transform.se.SePointOps_F64;
import org.ddogleg.struct.DogArray;
import org.ddogleg.struct.DogArray_F64;
import org.ddogleg.struct.Tuple2;
import org.ddogleg.struct.Tuple3;
import org.ejml.UtilEjml;
import org.ejml.data.DMatrix3;
import org.ejml.data.DMatrix3x3;
import org.ejml.data.DMatrix4x4;
import org.ejml.data.DMatrixRMaj;
import org.ejml.dense.fixed.CommonOps_DDF4;
import org.ejml.dense.row.CommonOps_DDRM;
import org.ejml.dense.row.NormOps_DDRM;
import org.ejml.dense.row.SingularOps_DDRM;
import org.ejml.dense.row.factory.DecompositionFactory_DDRM;
import org.ejml.interfaces.decomposition.SingularValueDecomposition_F64;
import org.jetbrains.annotations.Nullable;
import java.util.ArrayList;
import java.util.List;
import java.util.Objects;
/**
*
* Contains commonly used operations used in 2-view and 3-view 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.
*
*
* @author Peter Abeles
*/
public class MultiViewOps {
/**
*
* Creates a trifocal tensor from two camera matrices. Tijk = 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 = [I|0],
* where I is an identify matrix.
*
*
* @param P2 Camera matrix for view 2. 3x4 matrix
* @param P3 Camera matrix for view 3. 3x4 matrix
* @param ret Storage for trifocal tensor. If null a new instance will be created.
* @return The trifocal tensor
*/
public static TrifocalTensor createTrifocal( DMatrixRMaj P2, DMatrixRMaj P3,
@Nullable TrifocalTensor ret ) {
if (ret == null)
ret = new TrifocalTensor();
for (int i = 0; i < 3; i++) {
DMatrixRMaj T = ret.getT(i);
int index = 0;
for (int j = 0; j < 3; j++) {
double a_left = P2.get(j, i);
double a_right = P2.get(j, 3);
for (int k = 0; k < 3; k++) {
T.data[index++] = a_left*P3.get(k, 3) - a_right*P3.get(k, i);
}
}
}
return 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.
*
*
* @param P1 Camera matrix for view 1. 3x4 matrix
* @param P2 Camera matrix for view 2. 3x4 matrix
* @param P3 Camera matrix for view 3. 3x4 matrix
* @param ret Storage for trifocal tensor. If null a new instance will be created.
* @return The trifocal tensor
*/
public static TrifocalTensor createTrifocal( DMatrixRMaj P1, DMatrixRMaj P2, DMatrixRMaj P3,
@Nullable TrifocalTensor ret ) {
if (ret == null)
ret = new TrifocalTensor();
// invariant to scale. So pick something more reasonable and maybe reduce overflow
double scale = 1;
scale = Math.max(scale, CommonOps_DDRM.elementMaxAbs(P1));
scale = Math.max(scale, CommonOps_DDRM.elementMaxAbs(P2));
scale = Math.max(scale, CommonOps_DDRM.elementMaxAbs(P3));
DMatrixRMaj A = new DMatrixRMaj(4, 4);
double sign = 1;
for (int i = 0; i < 3; i++) {
DMatrixRMaj T = ret.getT(i);
for (int row = 0, cnt = 0; row < 3; row++) {
if (row != i) {
CommonOps_DDRM.extract(P1, row, row + 1, 0, 4, A, cnt, 0);
for (int col = 0; col < 4; col++) {
A.data[cnt*4 + col] /= scale;
}
cnt++;
}
}
for (int q = 0; q < 3; q++) {
CommonOps_DDRM.extract(P2, q, q + 1, 0, 4, A, 2, 0);
for (int col = 0; col < 4; col++) {
A.data[2*4 + col] /= scale;
}
for (int r = 0; r < 3; r++) {
CommonOps_DDRM.extract(P3, r, r + 1, 0, 4, A, 3, 0);
for (int col = 0; col < 4; col++) {
A.data[3*4 + col] /= scale;
}
double v = CommonOps_DDRM.det(A);
T.set(q, r, sign*v*scale); // scale is to the power of 2, hence the *scale here
}
}
sign *= -1;
}
return 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. [I|0]
*
*
* @param P2 Transform from view 1 to view 2.
* @param P3 Transform from view 1 to view 3.
* @param ret Storage for trifocal tensor. If null a new instance will be created.
* @return The trifocal tensor
*/
public static TrifocalTensor createTrifocal( Se3_F64 P2, Se3_F64 P3,
@Nullable TrifocalTensor ret ) {
if (ret == null)
ret = new TrifocalTensor();
DMatrixRMaj R2 = P2.getR();
DMatrixRMaj R3 = P3.getR();
Vector3D_F64 T2 = P2.getT();
Vector3D_F64 T3 = P3.getT();
for (int col = 0; col < 3; col++) {
DMatrixRMaj T = ret.getT(col);
int index = 0;
for (int i = 0; i < 3; i++) {
double a_left = R2.unsafe_get(i, col);
double a_right = T2.getIdx(i);
for (int j = 0; j < 3; j++) {
T.data[index++] = a_left*T3.getIdx(j) - a_right*R3.unsafe_get(j, col);
}
}
}
return ret;
}
/**
*
* Trifocal tensor with line-line-line correspondence:
* (l2T*[T1,T2,T3]*L2)*[l1]x = 0
*
*
* @param tensor Trifocal tensor
* @param l1 A line in the first view.
* @param l2 A line in the second view.
* @param l3 A line in the third view.
* @param ret Storage for output. If null a new instance will be declared.
* @return Result of applying the constraint. With perfect inputs will be zero.
*/
public static Vector3D_F64 constraint( TrifocalTensor tensor,
Vector3D_F64 l1, Vector3D_F64 l2, Vector3D_F64 l3,
@Nullable Vector3D_F64 ret ) {
if (ret == null)
ret = new Vector3D_F64();
double x = GeometryMath_F64.innerProd(l2, tensor.T1, l3);
double y = GeometryMath_F64.innerProd(l2, tensor.T2, l3);
double z = GeometryMath_F64.innerProd(l2, tensor.T3, l3);
GeometryMath_F64.cross(new Vector3D_F64(x, y, z), l1, ret);
return ret;
}
/**
*
* Trifocal tensor with point-line-line correspondence:
* (l2T*(sum p1i*Ti)*l3 = 0
*
*
* @param tensor Trifocal tensor
* @param p1 A point in the first view.
* @param l2 A line in the second view.
* @param l3 A line in the third view.
* @return Result of applying the constraint. With perfect inputs will be zero.
*/
public static double constraint( TrifocalTensor tensor,
Point2D_F64 p1, Vector3D_F64 l2, Vector3D_F64 l3 ) {
DMatrixRMaj sum = new DMatrixRMaj(3, 3);
CommonOps_DDRM.add(p1.x, tensor.T1, sum, sum);
CommonOps_DDRM.add(p1.y, tensor.T2, sum, sum);
CommonOps_DDRM.add(tensor.T3, sum, sum);
return GeometryMath_F64.innerProd(l2, sum, l3);
}
/**
*
* Trifocal tensor with point-line-point correspondence:
* (l2T(sum p1i*Ti)[p3]x = 0
*
*
* @param tensor Trifocal tensor
* @param p1 A point in the first view.
* @param l2 A line in the second view.
* @param p3 A point in the third view.
* @return Result of applying the constraint. With perfect inputs will be zero.
*/
public static Vector3D_F64 constraint( TrifocalTensor tensor,
Point2D_F64 p1, Vector3D_F64 l2, Point2D_F64 p3,
Vector3D_F64 ret ) {
if (ret == null)
ret = new Vector3D_F64();
DMatrixRMaj sum = new DMatrixRMaj(3, 3);
CommonOps_DDRM.add(p1.x, tensor.T1, sum, sum);
CommonOps_DDRM.add(p1.y, tensor.T2, sum, sum);
CommonOps_DDRM.add(tensor.T3, sum, sum);
Vector3D_F64 tempV = new Vector3D_F64();
GeometryMath_F64.multTran(sum, l2, tempV);
GeometryMath_F64.cross(tempV, new Vector3D_F64(p3.x, p3.y, 1), ret);
return ret;
}
/**
*
* Trifocal tensor with point-point-line correspondence:
* [p2]x(sum p1i*Ti)*l3 = 0
*
*
* @param tensor Trifocal tensor
* @param p1 A point in the first view.
* @param p2 A point in the second view.
* @param l3 A line in the third view.
* @return Result of applying the constraint. With perfect inputs will be zero.
*/
public static Vector3D_F64 constraint( TrifocalTensor tensor,
Point2D_F64 p1, Point2D_F64 p2, Vector3D_F64 l3,
Vector3D_F64 ret ) {
if (ret == null)
ret = new Vector3D_F64();
DMatrixRMaj sum = new DMatrixRMaj(3, 3);
CommonOps_DDRM.add(p1.x, tensor.T1, sum, sum);
CommonOps_DDRM.add(p1.y, tensor.T2, sum, sum);
CommonOps_DDRM.add(tensor.T3, sum, sum);
DMatrixRMaj cross2 = GeometryMath_F64.crossMatrix(p2.x, p2.y, 1, null);
DMatrixRMaj temp = new DMatrixRMaj(3, 3);
CommonOps_DDRM.mult(cross2, sum, temp);
GeometryMath_F64.mult(temp, l3, ret);
return ret;
}
/**
*
* Trifocal tensor with point-point-point correspondence:
* [p2]x(sum p1i*Ti)[p3]x = 0
*
*
* @param tensor Trifocal tensor
* @param p1 A point in the first view.
* @param p2 A point in the second view.
* @param p3 A point in the third view.
* @param ret Optional storage for output. 3x3 matrix. Modified.
* @return Result of applying the constraint. With perfect inputs will be zero.
*/
public static DMatrixRMaj constraint( TrifocalTensor tensor,
Point2D_F64 p1, Point2D_F64 p2, Point2D_F64 p3,
DMatrixRMaj ret ) {
if (ret == null)
ret = new DMatrixRMaj(3, 3);
DMatrixRMaj sum = new DMatrixRMaj(3, 3);
CommonOps_DDRM.add(p1.x, tensor.T1, p1.y, tensor.T2, sum);
CommonOps_DDRM.add(sum, tensor.T3, sum);
DMatrixRMaj cross2 = GeometryMath_F64.crossMatrix(p2.x, p2.y, 1, null);
DMatrixRMaj cross3 = GeometryMath_F64.crossMatrix(p3.x, p3.y, 1, null);
DMatrixRMaj temp = new DMatrixRMaj(3, 3);
CommonOps_DDRM.mult(cross2, sum, temp);
CommonOps_DDRM.mult(temp, cross3, ret);
return ret;
}
/**
*
* Applies the epipolar relationship constraint to an essential or fundamental matrix:
* 0 = p2T*F*p1
* Input points are in normalized image coordinates for an essential matrix and pixels for
* fundamental.
*
*
* @param F 3x3 essential or fundamental matrix.
* @param p1 Point in view 1.
* @param p2 Point in view 2.
* @return Constraint value.
*/
public static double constraint( DMatrixRMaj F, Point2D_F64 p1, Point2D_F64 p2 ) {
return GeometryMath_F64.innerProd(p2, F, p1);
}
/**
*
* 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.
*
*
* @param H Input: 3x3 Homography matrix.
* @param p1 Input: Point in view 1.
* @param outputP2 Output: storage for point in view 2.
* @return Predicted point in view 2
*/
public static Point2D_F64 constraintHomography( DMatrixRMaj H, Point2D_F64 p1, Point2D_F64 outputP2 ) {
if (outputP2 == null)
outputP2 = new Point2D_F64();
GeometryMath_F64.mult(H, p1, outputP2);
return outputP2;
}
/**
* 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
*
* @param tensor Input: Trifocal tensor
* @param line2 Input: Line in view 2. {@link LineGeneral2D_F64 General notation}.
* @param output Output: Optional storage for homography. 3x3 matrix
* @return Homography from view 1 to 3
*/
public static DMatrixRMaj inducedHomography13( TrifocalTensor tensor,
Vector3D_F64 line2,
DMatrixRMaj output ) {
if (output == null)
output = new DMatrixRMaj(3, 3);
DMatrixRMaj T = tensor.T1;
// H(:,0) = transpose(T1)*line
output.data[0] = T.data[0]*line2.x + T.data[3]*line2.y + T.data[6]*line2.z;
output.data[3] = T.data[1]*line2.x + T.data[4]*line2.y + T.data[7]*line2.z;
output.data[6] = T.data[2]*line2.x + T.data[5]*line2.y + T.data[8]*line2.z;
// H(:,1) = transpose(T2)*line
T = tensor.T2;
output.data[1] = T.data[0]*line2.x + T.data[3]*line2.y + T.data[6]*line2.z;
output.data[4] = T.data[1]*line2.x + T.data[4]*line2.y + T.data[7]*line2.z;
output.data[7] = T.data[2]*line2.x + T.data[5]*line2.y + T.data[8]*line2.z;
// H(:,2) = transpose(T3)*line
T = tensor.T3;
output.data[2] = T.data[0]*line2.x + T.data[3]*line2.y + T.data[6]*line2.z;
output.data[5] = T.data[1]*line2.x + T.data[4]*line2.y + T.data[7]*line2.z;
output.data[8] = T.data[2]*line2.x + T.data[5]*line2.y + T.data[8]*line2.z;
// Vector3D_F64 temp = new Vector3D_F64();
//
// for( int i = 0; i < 3; i++ ) {
// GeometryMath_F64.multTran(tensor.getT(i),line,temp);
// output.unsafe_set(0,i,temp.x);
// output.unsafe_set(1,i,temp.y);
// output.unsafe_set(2,i,temp.z);
// }
return 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
*
* @param tensor Input: Trifocal tensor
* @param line3 Input: Line in view 3. {@link LineGeneral2D_F64 General notation}.
* @param output Output: Optional storage for homography. 3x3 matrix
* @return Homography from view 1 to 2
*/
public static DMatrixRMaj inducedHomography12( TrifocalTensor tensor,
Vector3D_F64 line3,
DMatrixRMaj output ) {
if (output == null)
output = new DMatrixRMaj(3, 3);
// H(:,0) = T1*line
DMatrixRMaj T = tensor.T1;
output.data[0] = T.data[0]*line3.x + T.data[1]*line3.y + T.data[2]*line3.z;
output.data[3] = T.data[3]*line3.x + T.data[4]*line3.y + T.data[5]*line3.z;
output.data[6] = T.data[6]*line3.x + T.data[7]*line3.y + T.data[8]*line3.z;
// H(:,0) = T2*line
T = tensor.T2;
output.data[1] = T.data[0]*line3.x + T.data[1]*line3.y + T.data[2]*line3.z;
output.data[4] = T.data[3]*line3.x + T.data[4]*line3.y + T.data[5]*line3.z;
output.data[7] = T.data[6]*line3.x + T.data[7]*line3.y + T.data[8]*line3.z;
// H(:,0) = T3*line
T = tensor.T3;
output.data[2] = T.data[0]*line3.x + T.data[1]*line3.y + T.data[2]*line3.z;
output.data[5] = T.data[3]*line3.x + T.data[4]*line3.y + T.data[5]*line3.z;
output.data[8] = T.data[6]*line3.x + T.data[7]*line3.y + T.data[8]*line3.z;
// Vector3D_F64 temp = new Vector3D_F64();
//
// for( int i = 0; i < 3; i++ ) {
// GeometryMath_F64.mult(tensor.getT(i), line, temp);
// output.unsafe_set(0,i,temp.x);
// output.unsafe_set(1,i,temp.y);
// output.unsafe_set(2,i,temp.z);
// }
return output;
}
/**
* 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.
*
* @param F Fundamental matrix
* @param p1 Associated point observation
* @param p2 Associated point observation
* @param p3 Associated point observation
* @return The homography from view 1 to view 2 or null if it fails
* @see boofcv.alg.geo.h.HomographyInducedStereo3Pts
*/
public static @Nullable DMatrixRMaj fundamentalToHomography3Pts( DMatrixRMaj F,
AssociatedPair p1,
AssociatedPair p2,
AssociatedPair p3 ) {
HomographyInducedStereo3Pts alg = new HomographyInducedStereo3Pts();
alg.setFundamental(F, null);
if (!alg.process(p1, p2, p3))
return null;
return alg.getHomography();
}
/**
* 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.
*
* @param F Fundamental matrix
* @param line Line on the plane
* @param point Point on the plane
* @return The homography from view 1 to view 2 or null if it fails
* @see HomographyInducedStereoLinePt
*/
public static DMatrixRMaj fundamentalToHomographyLinePt( DMatrixRMaj F, PairLineNorm line, AssociatedPair point ) {
HomographyInducedStereoLinePt alg = new HomographyInducedStereoLinePt();
alg.setFundamental(F, null);
alg.process(line, point);
return alg.getHomography();
}
/**
* 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.
*
* @param F Fundamental matrix
* @param line0 Line on the plane
* @param line1 Line on the plane
* @return The homography from view 1 to view 2 or null if it fails
* @see HomographyInducedStereo2Line
*/
public static @Nullable DMatrixRMaj
fundamentalToHomography2Lines( DMatrixRMaj F, PairLineNorm line0, PairLineNorm line1 ) {
HomographyInducedStereo2Line alg = new HomographyInducedStereo2Line();
alg.setFundamental(F, null);
if (!alg.process(line0, line1))
return null;
return alg.getHomography();
}
/**
*
* 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:
*
* - e2T*F12 = 0
*
- e3T*F13 = 0
*
* where F1i is a fundamental matrix from image 1 to i.
*
*
* @param tensor Trifocal tensor. Not Modified
* @param e2 Output: Epipole in image 2. Homogeneous coordinates. Modified
* @param e3 Output: Epipole in image 3. Homogeneous coordinates. Modified
* @see TrifocalExtractGeometries
*/
public static void extractEpipoles( TrifocalTensor tensor, Point3D_F64 e2, Point3D_F64 e3 ) {
TrifocalExtractGeometries e = new TrifocalExtractGeometries();
e.setTensor(tensor);
e.extractEpipoles(e2, e3);
}
/**
*
* Extract the fundamental matrices between views 1 + 2 and views 1 + 3. The returned Fundamental
* matrices will have the following properties: xiT*Fi*x1 = 0, where i is view 2 or 3.
*
*
*
* NOTE: The first camera is assumed to have the camera matrix of P1 = [I|0]. Thus observations in pixels for
* the first camera will not meet the epipolar constraint when applied to the returned fundamental matrices.
*
*
* @param tensor Trifocal tensor. Not modified.
* @param F21 Output: Fundamental matrix for views 1 and 2. Modified.
* @param F31 Output: Fundamental matrix for views 1 and 3. Modified.
* @see TrifocalExtractGeometries
*/
public static void trifocalToFundamental( TrifocalTensor tensor, DMatrixRMaj F21, DMatrixRMaj F31 ) {
TrifocalExtractGeometries e = new TrifocalExtractGeometries();
e.setTensor(tensor);
e.extractFundmental(F21, F31);
}
/**
*
* Extract the camera matrices up to a common projective transform.
*
*
*
* NOTE: The camera matrix for the first view is assumed to be P1 = [I|0].
*
*
* @param tensor Trifocal tensor. Not modified.
* @param P2 Output: 3x4 camera matrix for views 1 to 2. Modified.
* @param P3 Output: 3x4 camera matrix for views 1 to 3. Modified.
* @see TrifocalExtractGeometries
*/
public static void trifocalToCameraMatrices( TrifocalTensor tensor, DMatrixRMaj P2, DMatrixRMaj P3 ) {
TrifocalExtractGeometries e = new TrifocalExtractGeometries();
e.setTensor(tensor);
e.extractCamera(P2, P3);
}
/**
*
* 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.
*
*
* @param R Rotation matrix.
* @param T Translation vector.
* @param E (Output) Storage for essential matrix. 3x3 matrix
* @return Essential matrix
*/
public static DMatrixRMaj createEssential( DMatrixRMaj R, Vector3D_F64 T, @Nullable DMatrixRMaj E ) {
if (E == null)
E = new DMatrixRMaj(3, 3);
DMatrixRMaj T_hat = GeometryMath_F64.crossMatrix(T, null);
CommonOps_DDRM.mult(T_hat, R, E);
return E;
}
/**
* Computes a Fundamental matrix given an Essential matrix and the camera calibration matrix.
*
* F = (K-1)T*E*K-1
*
* @param E Essential matrix
* @param K Intrinsic camera calibration matrix
* @return Fundamental matrix
*/
public static DMatrixRMaj createFundamental( DMatrixRMaj E, DMatrixRMaj K ) {
DMatrixRMaj K_inv = new DMatrixRMaj(3, 3);
CommonOps_DDRM.invert(K, K_inv);
DMatrixRMaj F = new DMatrixRMaj(3, 3);
PerspectiveOps.multTranA(K_inv, E, K_inv, F);
return F;
}
/**
* Computes a Fundamental matrix given an Essential matrix and the camera's intrinsic
* parameters.
*
* @param E Essential matrix
* @param intrinsic Intrinsic camera calibration
* @return Fundamental matrix
* @see #createFundamental(DMatrixRMaj, DMatrixRMaj)
*/
public static DMatrixRMaj createFundamental( DMatrixRMaj E, CameraPinhole intrinsic ) {
DMatrixRMaj K = PerspectiveOps.pinholeToMatrix(intrinsic, (DMatrixRMaj)null);
return createFundamental(E, K);
}
/**
* Computes a Fundamental matrix given an Essential matrix and the camera calibration matrix.
*
* F = (K2-1)T*E*K1-1
*
* @param E Essential matrix
* @param K1 Intrinsic camera calibration matrix for camera 1
* @param K2 Intrinsic camera calibration matrix for camera 2
* @return Fundamental matrix
*/
public static DMatrixRMaj createFundamental( DMatrixRMaj E,
DMatrixRMaj K1, DMatrixRMaj K2 ) {
DMatrixRMaj K1_inv = new DMatrixRMaj(3, 3);
CommonOps_DDRM.invert(K1, K1_inv);
DMatrixRMaj K2_inv = new DMatrixRMaj(3, 3);
CommonOps_DDRM.invert(K2, K2_inv);
DMatrixRMaj F = new DMatrixRMaj(3, 3);
DMatrixRMaj temp = new DMatrixRMaj(3, 3);
CommonOps_DDRM.multTransA(K2_inv, E, temp);
CommonOps_DDRM.mult(temp, K1_inv, F);
return F;
}
/**
*
* Computes an fudamental matrix from a rotation, translation, and calibration matrix. Motion
* is from the first camera frame into the second camera frame.
*
*
* @param R Rotation matrix. first to second
* @param T Translation vector. first to second
* @param K1 Intrinsic camera calibration matrix for camera 1
* @param K2 Intrinsic camera calibration matrix for camera 2
* @param F (Output) Storage for essential matrix. 3x3 matrix
* @return Essential matrix
*/
public static DMatrixRMaj createFundamental( DMatrixRMaj R, Vector3D_F64 T,
DMatrixRMaj K1, DMatrixRMaj K2, @Nullable DMatrixRMaj F ) {
if (F == null)
F = new DMatrixRMaj(3, 3);
else
F.reshape(3, 3);
createEssential(R, T, F);
F.setTo(createFundamental(F, K1, K2));
return F;
}
/**
*
* 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*NT
* Where [R,T] is the transform from camera 1 to camera 2.
*
*
* @param R Rotation matrix from camera 1 to camera 2.
* @param T Translation vector from camera 1 to camera 2.
* @param d Distance > 0 of closest point on plane to the origin of camera 1.
* @param N Normal of plane with respect to the first camera.
* @return Calibrated homography matrix
*/
public static DMatrixRMaj createHomography( DMatrixRMaj R, Vector3D_F64 T,
double d, Vector3D_F64 N ) {
DMatrixRMaj H = new DMatrixRMaj(3, 3);
GeometryMath_F64.outerProd(T, N, H);
CommonOps_DDRM.divide(H, d);
CommonOps_DDRM.addEquals(H, R);
return H;
}
/**
*
* 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*NT)*K-1
* Where [R,T] is the transform from camera 1 to camera, and K is the calibration matrix for both cameras.
*
*
* @param R Rotation matrix from camera 1 to camera 2.
* @param T Translation vector from camera 1 to camera 2.
* @param d Distance > 0 of closest point on plane to the origin of camera 1.
* @param N Normal of plane with respect to the first camera.
* @param K Intrinsic calibration matrix
* @return Uncalibrated homography matrix
*/
public static DMatrixRMaj createHomography( DMatrixRMaj R, Vector3D_F64 T,
double d, Vector3D_F64 N,
DMatrixRMaj K ) {
DMatrixRMaj temp = new DMatrixRMaj(3, 3);
DMatrixRMaj K_inv = new DMatrixRMaj(3, 3);
DMatrixRMaj H = createHomography(R, T, d, N);
// apply calibration matrix to R
CommonOps_DDRM.mult(K, H, temp);
CommonOps_DDRM.invert(K, K_inv);
CommonOps_DDRM.mult(temp, K_inv, H);
return H;
}
/**
*
* 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: e2T*F = 0
* Right: F*e1 = 0
*
*
* @param F Input: Fundamental or Essential 3x3 matrix. Not modified.
* @param e1 Output: Right epipole in homogeneous coordinates. Can be null. Modified.
* @param e2 Output: Left epipole in homogeneous coordinates. Can be null. Modified.
*/
public static void extractEpipoles( DMatrixRMaj F, Point3D_F64 e1, Point3D_F64 e2 ) {
FundamentalExtractEpipoles alg = new FundamentalExtractEpipoles();
alg.process(F, e1, e2);
}
/**
*
* 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=[I|0] and P'= [M|-M*t] = [[e']*F + e'*v^t | lambda*e']
*
* where e' is the epipole FTe' = 0, [e'] is the cross product matrix for the enclosed vector,
* v is an arbitrary 3-vector and lambda is a non-zero 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
*
*
* @param F (Input) A fundamental matrix
* @param e2 (Input) Left epipole of fundamental matrix, FT*e2 = 0.
* @param v (Input) Arbitrary 3-vector. Just pick some value, say (0,0,0).
* @param lambda (Input) A non zero scalar. Try one.
* @return The canonical camera (projection) matrix P' (3 by 4) Known up to a projective transform.
* @see #extractEpipoles
* @see FundamentalToProjective
*/
public static DMatrixRMaj fundamentalToProjective( DMatrixRMaj F, Point3D_F64 e2, Vector3D_F64 v, double lambda ) {
FundamentalToProjective f2p = new FundamentalToProjective();
DMatrixRMaj P = new DMatrixRMaj(3, 4);
f2p.twoView(F, e2, v, lambda, P);
return P;
}
/**
* Given two general camera matrices compute fundamental matrix.
*
* {@code F= [e']_x P2*P1+, where P1+ is the pseudo inverse of P1, and e' = P2*C, with P*C=0}
*
* @param P1 (Input) camera matrix for view 1
* @param P2 (Input) camera matrix for view 2
* @param F21 (Output) Fundamental matrix from view 1 to 2
* @return Fundamental matrix.
*/
public static DMatrixRMaj projectiveToFundamental( DMatrixRMaj P1, DMatrixRMaj P2, @Nullable DMatrixRMaj F21 ) {
if (F21 == null)
F21 = new DMatrixRMaj(3, 3);
ProjectiveToIdentity p2i = new ProjectiveToIdentity();
if (!p2i.process(P1))
throw new RuntimeException("Failed!");
DMatrixRMaj P1inv = p2i.getPseudoInvP();
DMatrixRMaj U = p2i.getU();
DMatrixRMaj e = new DMatrixRMaj(3, 1);
CommonOps_DDRM.mult(P2, U, e);
DMatrixRMaj tmp = new DMatrixRMaj(3, 4);
DMatrixRMaj e_skew = new DMatrixRMaj(3, 3);
GeometryMath_F64.crossMatrix(e.data[0], e.data[1], e.data[2], e_skew);
CommonOps_DDRM.mult(e_skew, P2, tmp);
CommonOps_DDRM.mult(tmp, P1inv, F21);
return F21;
}
/**
* Given an implicit P1=[I|0] camera matrix and P2 compute a fundamental matrix.
*
* {@code F= [e']_x P2*P1+, where P1+ is the pseudo inverse of P1, and e' = P2*C, with P*C=0}
*
* @param P2 (Input) camera matrix for view 2
* @param F21 (Output) Fundamental matrix from view 1 to 2
* @return Fundamental matrix.
*/
public static DMatrixRMaj projectiveToFundamental( DMatrixRMaj P2, @Nullable DMatrixRMaj F21 ) {
if (F21 == null)
F21 = new DMatrixRMaj(3, 3);
// P2 = [A|b]
// Since P1 = [I|0] F then becomes cross(b)*A
// Extract sub matrices from P2
// Do all the math by hand to avoid memory creation. This is relatively simple
double b1 = P2.unsafe_get(0, 3);
double b2 = P2.unsafe_get(1, 3);
double b3 = P2.unsafe_get(2, 3);
double a11 = P2.data[0], a12 = P2.data[1], a13 = P2.data[2];
double a21 = P2.data[4], a22 = P2.data[5], a23 = P2.data[6];
double a31 = P2.data[8], a32 = P2.data[9], a33 = P2.data[10];
// matrix multiplication below
F21.data[0] = -b3*a21 + b2*a31;
F21.data[1] = -b3*a22 + b2*a32;
F21.data[2] = -b3*a23 + b2*a33;
F21.data[3] = b3*a11 - b1*a31;
F21.data[4] = b3*a12 - b1*a32;
F21.data[5] = b3*a13 - b1*a33;
F21.data[6] = -b2*a11 + b1*a21;
F21.data[7] = -b2*a12 + b1*a22;
F21.data[8] = -b2*a13 + b1*a23;
return F21;
}
/**
*
* Given a fundamental matrix a pair of camera matrices P0 and P1 can be extracted. Same
* {@link #fundamentalToProjective(DMatrixRMaj, Point3D_F64, Vector3D_F64, double)} but with the suggested values
* for all variables filled in for you.
*
*
* @param F (Input) Fundamental Matrix
* @return The canonical camera (projection) matrix P' (3 by 4) Known up to a projective transform.
* @see FundamentalToProjective
*/
public static DMatrixRMaj fundamentalToProjective( DMatrixRMaj F ) {
FundamentalToProjective f2p = new FundamentalToProjective();
DMatrixRMaj P = new DMatrixRMaj(3, 4);
f2p.twoView(F, P);
return P;
}
/**
* 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]
*
* @param F (Input) Fundamental matrix. 3x3
* @param K (Input) Calibration matrix (3x3)
* @param outputE (Output) Found essential matrix
* @return Essential matrix
*/
public static DMatrixRMaj fundamentalToEssential( DMatrixRMaj F, DMatrixRMaj K, @Nullable DMatrixRMaj outputE ) {
return fundamentalToEssential(F, K, K, 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]
*
* @param F (Input) Fundamental matrix. 3x3
* @param K1 (Input) Calibration matrix view 1 (3x3)
* @param K2 (Input) Calibration matrix view 2 (3x3)
* @param outputE (Output) Found essential matrix
* @return Essential matrix
*/
public static DMatrixRMaj fundamentalToEssential( DMatrixRMaj F, DMatrixRMaj K1, DMatrixRMaj K2,
@Nullable DMatrixRMaj outputE ) {
if (outputE == null)
outputE = new DMatrixRMaj(3, 3);
PerspectiveOps.multTranA(K2, F, K1, outputE);
// this is unlikely to be a perfect essential matrix. reduce the error by enforcing essential constraints
SingularValueDecomposition_F64 svd = DecompositionFactory_DDRM.svd(true, true, false);
svd.decompose(outputE);
DMatrixRMaj U = svd.getU(null, false);
DMatrixRMaj W = svd.getW(null);
DMatrixRMaj V = svd.getV(null, false);
// settings value of singular values to be [1,1,0]. The first two singular values just need to be equal
// for it to be an essential matrix
SingularOps_DDRM.descendingOrder(U, false, W, V, false);
W.set(0, 0, 1);
W.set(1, 1, 1);
W.set(2, 2, 0);
PerspectiveOps.multTranC(U, W, V, outputE);
return outputE;
}
/**
* 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 in {@link FundamentalToProjective#threeView}.
*
* The first camera matrix, without loss of generality, is assumed to be P1 = [I|0].
*
*
* - Page 301 in Y. Ma, S. Soatto, J. Kosecka, and S. S. Sastry, "An Invitation to 3-D Vision"
* Springer-Verlad, 2004
*
*
* @param F21 (Input) Fundamental matrix between view 1 and 2
* @param F31 (Input) Fundamental matrix between view 1 and 3
* @param F32 (Input) Fundamental matrix between view 2 and 3
* @param P2 (Output) Camera matrix for view 2
* @param P3 (Output) Camera matrix for view 3
* @see #fundamentalCompatible3
* @see FundamentalToProjective#threeView
*/
public static void fundamentalToProjective( DMatrixRMaj F21, DMatrixRMaj F31, DMatrixRMaj F32,
DMatrixRMaj P2, DMatrixRMaj P3 ) {
FundamentalToProjective alg = new FundamentalToProjective();
alg.threeView(F21, F31, F32, P2, P3);
}
/**
* Finds the transform such that P*H = [I|0] where P is a 3x4 projective camera matrix and H is a 4x4 matrix
*
* @param P (Input) camera matrix 3x4
* @param H (Output) 4x4 matrix
*/
public static DMatrixRMaj projectiveToIdentityH( DMatrixRMaj P, @Nullable DMatrixRMaj H ) {
if (H == null)
H = new DMatrixRMaj(4, 4);
ProjectiveToIdentity alg = new ProjectiveToIdentity();
if (!alg.process(P))
throw new RuntimeException("WTF this failed?? Probably NaN in P");
alg.computeH(H);
return H;
}
/**
* Computes a homography transform which will make the first camera in the list identity and modifies
* the camera matrices using that homography
*
* @param cameraMatrices (input/output) Converts
* @param H (output + Optional) storage for homography
*/
public static void projectiveMakeFirstIdentity( List cameraMatrices, @Nullable DMatrixRMaj H ) {
BoofMiscOps.checkTrue(cameraMatrices.size() >= 1);
H = projectiveToIdentityH(cameraMatrices.get(0), H);
DMatrixRMaj tmp = new DMatrixRMaj(3, 4);
for (int i = 0; i < cameraMatrices.size(); i++) {
DMatrixRMaj P = cameraMatrices.get(i);
CommonOps_DDRM.mult(P, H, tmp);
P.setTo(tmp);
}
}
/**
*
* Checks to see if the three fundamental matrices are consistent based on their epipoles.
*
*
* e23TF21e13 = 0
* e31TF32e21 = 0
* e32TF31e12 = 0
*
*
*
* Section 15.4 in R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
*
*
* @param F21 (Input) Fundamental matrix between view 1 and 2
* @param F31 (Input) Fundamental matrix between view 1 and 3
* @param F32 (Input) Fundamental matrix between view 2 and 3
*/
public static boolean fundamentalCompatible3( DMatrixRMaj F21, DMatrixRMaj F31, DMatrixRMaj F32, double tol ) {
FundamentalExtractEpipoles extractEpi = new FundamentalExtractEpipoles();
Point3D_F64 e21 = new Point3D_F64();
Point3D_F64 e12 = new Point3D_F64();
Point3D_F64 e31 = new Point3D_F64();
Point3D_F64 e13 = new Point3D_F64();
Point3D_F64 e32 = new Point3D_F64();
Point3D_F64 e23 = new Point3D_F64();
extractEpi.process(F21, e21, e12);
extractEpi.process(F31, e31, e13);
extractEpi.process(F32, e32, e23);
// GeometryMath_F64.innerProd(e12,F21,e21)
// GeometryMath_F64.innerProd(e13,F31,e31)
double score = 0;
score += Math.abs(GeometryMath_F64.innerProd(e23, F21, e13));
score += Math.abs(GeometryMath_F64.innerProd(e31, F31, e21));
score += Math.abs(GeometryMath_F64.innerProd(e32, F32, e12));
score /= 3;
return score <= tol;
}
/**
*
* Decomposes a metric camera matrix P=K*[R|T], where A is an upper triangular camera calibration
* matrix, R is a rotation matrix, and T is a translation vector. If {@link PerspectiveOps#createCameraMatrix}
* 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.
*
*
* @param cameraMatrix Input: Camera matrix, 3 by 4
* @param K Output: Camera calibration matrix, 3 by 3.
* @param worldToView Output: The rotation and translation.
* @return true if decompose was successful
*/
public static boolean decomposeMetricCamera( DMatrixRMaj cameraMatrix, DMatrixRMaj K, Se3_F64 worldToView ) {
return new DecomposeProjectiveToMetric().decomposeMetricCamera(cameraMatrix, K, worldToView);
}
/**
* Decomposes an essential matrix into the rigid body motion which it was constructed from. Due to ambiguities
* there are four possible solutions. See {@link DecomposeEssential} 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.
*
* @param E21 An essential matrix.
* @return Four possible motions. From view 1 to view 2.
* @see DecomposeEssential
*/
public static List decomposeEssential( DMatrixRMaj E21 ) {
DecomposeEssential d = new DecomposeEssential();
d.decompose(E21);
return d.getSolutions();
}
/**
* 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*NT), 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'.
*
* @param H Homography in Euclidean space
* @return The set of four possible solutions. First param: motion (R,T). Second param: plane normal vector.
* @see DecomposeHomography
*/
public static List> decomposeHomography( DMatrixRMaj H ) {
DecomposeHomography d = new DecomposeHomography();
d.decompose(H);
List solutionsN = d.getSolutionsN();
List solutionsSe = d.getSolutionsSE();
List> ret = new ArrayList<>();
for (int i = 0; i < 4; i++) {
ret.add(new Tuple2<>(solutionsSe.get(i), solutionsN.get(i)));
}
return ret;
}
/**
* 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
*
* @param observations (Input) observations
* @param H (Input) Homography
* @param H_inv (Input) Inverse of homography. if null it will be computed internally
* @param storage (Output) storage for found errors
*/
public static void errorsHomographySymm( List observations,
DMatrixRMaj H,
@Nullable DMatrixRMaj H_inv,
DogArray_F64 storage ) {
storage.reset();
if (H_inv == null)
H_inv = new DMatrixRMaj(3, 3);
CommonOps_DDRM.invert(H, H_inv);
Point3D_F64 tmp = new Point3D_F64();
for (int i = 0; i < observations.size(); i++) {
AssociatedPair p = observations.get(i);
double dx, dy;
double error = 0;
GeometryMath_F64.mult(H, p.p1, tmp);
if (Math.abs(tmp.z) <= UtilEjml.EPS)
continue;
dx = p.p2.x - tmp.x/tmp.z;
dy = p.p2.y - tmp.y/tmp.z;
error += dx*dx + dy*dy;
GeometryMath_F64.mult(H_inv, p.p2, tmp);
if (Math.abs(tmp.z) <= UtilEjml.EPS)
continue;
dx = p.p1.x - tmp.x/tmp.z;
dy = p.p1.y - tmp.y/tmp.z;
error += dx*dx + dy*dy;
storage.add(error);
}
}
/**
* Transfers a point from the first view to the third view using a plane induced by
* a line in the second view.
*
* @param x1 (Input) point (pixel) in first view
* @param l2 (Input) line in second view
* @param T (Input) Trifocal tensor
* @param x3 (Output) Induced point (pixel) in third view. Homogenous coordinates.
* @return induced point.
*/
public static Point3D_F64 transfer_1_to_3( TrifocalTensor T, Point2D_F64 x1, Vector3D_F64 l2,
@Nullable Point3D_F64 x3 ) {
if (x3 == null)
x3 = new Point3D_F64();
GeometryMath_F64.multTran(T.T1, l2, x3);
// storage solution here to avoid the need to declare a temporary variable
double xx = x3.x*x1.x;
double yy = x3.y*x1.x;
double zz = x3.z*x1.x;
GeometryMath_F64.multTran(T.T2, l2, x3);
xx += x3.x*x1.y;
yy += x3.y*x1.y;
zz += x3.z*x1.y;
GeometryMath_F64.multTran(T.T3, l2, x3);
x3.x = xx + x3.x;
x3.y = yy + x3.y;
x3.z = zz + x3.z;
return x3;
// Commented out code is closer to tensor notation. The above was derived from it
// for (int i = 0; i < 3; i++) {
// DMatrixRMaj t = T.T1;
//
// double vx;
// switch( i ) {
// case 0: vx = x.x; break;
// case 1: vx = x.y; break;
// case 2: vx = 1; break;
// default: throw new RuntimeException("Egads");
// }
// sumX += vx*(l.x*t.get(0,0)+l.y*t.get(1,0)+l.z*t.get(2,0));
// sumY += vx*(l.x*t.get(0,1)+l.y*t.get(1,1)+l.z*t.get(2,1));
// sumZ += vx*(l.x*t.get(0,2)+l.y*t.get(1,2)+l.z*t.get(2,2));
// }
}
/**
* Transfers a point to the third view given observed locations in the first and second views
*
* @param x1 (Input) point (pixel) in first view
* @param x2 (Input) point (pixel) in second view
* @param T (Input) Trifocal tensor
* @param x3 (Output) Induced point (pixel) in third view. Homogenous coordinates.
* @return induced point.
*/
public static Point3D_F64 transfer_1_to_3( TrifocalTensor T, Point2D_F64 x1, Point2D_F64 x2,
@Nullable Point3D_F64 x3 ) {
if (x3 == null)
x3 = new Point3D_F64();
var transfer = new TrifocalTransfer();
transfer.setTrifocal(T);
transfer.transfer_1_to_3(x1.x, x1.y, x2.x, x2.y, x3);
return x3;
}
/**
* Transfers a point from the first view to the second view using a plane induced by
* a line in the third view.
*
* @param x1 (Input) point (pixel) in first view
* @param l3 (Input) line in third view
* @param T (Input) Trifocal tensor
* @param x2 (Output) Induced point (pixel) in second view. Homogenous coordinates.
* @return induced point.
*/
public static Point3D_F64 transfer_1_to_2( TrifocalTensor T, Point2D_F64 x1, Vector3D_F64 l3,
@Nullable Point3D_F64 x2 ) {
if (x2 == null)
x2 = new Point3D_F64();
GeometryMath_F64.mult(T.T1, l3, x2);
// storage solution here to avoid the need to declare a temporary variable
double xx = x2.x*x1.x;
double yy = x2.y*x1.x;
double zz = x2.z*x1.x;
GeometryMath_F64.mult(T.T2, l3, x2);
xx += x2.x*x1.y;
yy += x2.y*x1.y;
zz += x2.z*x1.y;
GeometryMath_F64.mult(T.T3, l3, x2);
x2.x = xx + x2.x;
x2.y = yy + x2.y;
x2.z = zz + x2.z;
return x2;
}
/**
* Transfers a point from the first view to the second view using the observed location in the third view
*
* @param x1 (Input) point (pixel) in first view
* @param x3 (Input) point (pixel) in third view
* @param T (Input) Trifocal tensor
* @param x2 (Output) Induced point (pixel) in second view. Homogenous coordinates.
* @return induced point.
*/
public static Point3D_F64 transfer_1_to_2( TrifocalTensor T, Point2D_F64 x1, Point2D_F64 x3,
@Nullable Point3D_F64 x2 ) {
if (x2 == null)
x2 = new Point3D_F64();
var transfer = new TrifocalTransfer();
transfer.setTrifocal(T);
transfer.transfer_1_to_2(x1.x, x1.y, x3.x, x3.y, x2);
return x2;
}
/**
* 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
*
* @param cameraMatrix (Input) camera matrix. 3x4
* @param H (Input) Rectifying homography. 4x4
* @param worldToView (Output) Transform from world to camera view
* @param K (Output) Camera calibration matrix
* @see MultiViewOps#absoluteQuadraticToH
* @see #decomposeMetricCamera(DMatrixRMaj, DMatrixRMaj, Se3_F64)
*/
public static boolean projectiveToMetric( DMatrixRMaj cameraMatrix, DMatrixRMaj H,
Se3_F64 worldToView, DMatrixRMaj K ) {
return new DecomposeProjectiveToMetric().projectiveToMetric(cameraMatrix, H, worldToView, K);
}
/**
*
* Convert the projective camera matrix into a metric transform given the rectifying homography and a
* known calibration matrix. This simplifies the math compared to {@link #projectiveToMetric} where it needs
* to extract `K`.
*
* {@code P = K*[R|T]*H} where H is the inverse of the rectifying homography.
*
* @param cameraMatrix (Input) camera matrix. 3x4
* @param H (Input) Rectifying homography. 4x4
* @param K (Input) Known calibration matrix
* @param worldToView (Output) transform from world to camera view
*/
public static boolean projectiveToMetricKnownK( DMatrixRMaj cameraMatrix,
DMatrixRMaj H, DMatrixRMaj K,
Se3_F64 worldToView ) {
return new DecomposeProjectiveToMetric().projectiveToMetricKnownK(cameraMatrix, H, K, worldToView);
}
/**
* 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])*HT and H = [K 0; -p'*K 1]
*
*
*
*
* - R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
*
*
* @param Q Approximate solution to absolute quadratic
* @see DecomposeAbsoluteDualQuadratic
*/
public static boolean enforceAbsoluteQuadraticConstraints( DMatrix4x4 Q, boolean zeroCenter, boolean zeroSkew ) {
return enforceAbsoluteQuadraticConstraints(Q, zeroCenter, zeroSkew, null);
}
public static boolean enforceAbsoluteQuadraticConstraints( DMatrix4x4 Q, boolean zeroCenter, boolean zeroSkew,
@Nullable DecomposeAbsoluteDualQuadratic alg ) {
if (alg == null)
alg = new DecomposeAbsoluteDualQuadratic();
// see if it's potentially just off by a sign
if (Q.a33 < 0)
CommonOps_DDF4.scale(-1, Q);
if (!alg.decompose(Q))
return false;
// force positive definite
DMatrix3x3 k = alg.getK();
if (zeroCenter) {
k.a13 = k.a23 = 0;
}
if (zeroSkew) {
k.a12 = 0;
}
alg.recomputeQ(Q);
return true;
}
/**
* 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*HT
* where I = diag(1 1 1 0)
*
*
* - R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
*
*
* @param Q (Input) Absolute quadratic. Typically found in auto calibration. Not modified.
* @param H (Output) 4x4 rectifying homography.
* @see DecomposeAbsoluteDualQuadratic
*/
public static boolean absoluteQuadraticToH( DMatrix4x4 Q, DMatrixRMaj H ) {
DecomposeAbsoluteDualQuadratic alg = new DecomposeAbsoluteDualQuadratic();
if (!alg.decompose(Q))
return false;
return alg.computeRectifyingHomography(H);
}
/**
* Rectifying / calibrating homography to dual absolute quadratic.
*
* Q = H*I*HT = H(:,1:3)*H(:,1:3)'
* where I = diag(1 1 1 0)
*
* @param H (Input) 4x4 rectifying homography.
* @param Q (Output) Absolute quadratic. Typically found in auto calibration. Not modified.
*/
public static void rectifyHToAbsoluteQuadratic( DMatrixRMaj H, DMatrixRMaj Q ) {
int indexQ = 0;
for (int rowA = 0; rowA < 4; rowA++) {
for (int colB = 0; colB < 4; colB++) {
int indexA = rowA*4;
int indexB = colB*4;
double sum = 0;
for (int i = 0; i < 3; i++) {
// sum += H.get(rowA,i)*H.get(colB,i);
sum += H.data[indexA++]*H.data[indexB++];
}
// Q.set(rowA,colB,sum);
Q.data[indexQ++] = sum;
}
}
}
/**
* 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 = [I|0].
*
* H=[K*K, 0; -p'*k, 1]
*
*
* - R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge 2003
*
*
* @param K (Input) 3x3 intrinsic calibration matrix
* @param planeAtInfinity (Input) Plane at infinity
* @param H (Output) rectifying homography.
*/
public static void canonicalRectifyingHomographyFromKPinf( DMatrixRMaj K, Point3D_F64 planeAtInfinity, DMatrixRMaj H ) {
H.reshape(4, 4);
CommonOps_DDRM.insert(K, H, 0, 0);
// v = -p'*K
double v1 = -(planeAtInfinity.x*K.data[0] + planeAtInfinity.y*K.data[3] + planeAtInfinity.z*K.data[6]);
double v2 = -(planeAtInfinity.x*K.data[1] + planeAtInfinity.y*K.data[4] + planeAtInfinity.z*K.data[7]);
double v3 = -(planeAtInfinity.x*K.data[2] + planeAtInfinity.y*K.data[5] + planeAtInfinity.z*K.data[8]);
H.unsafe_set(3, 0, v1);
H.unsafe_set(3, 1, v2);
H.unsafe_set(3, 2, v3);
H.unsafe_set(3, 3, 1.0);
H.unsafe_set(0, 3, 0);
H.unsafe_set(1, 3, 0);
H.unsafe_set(2, 3, 0);
}
/**
* Extracts the intrinsic camera matrix from a view given its camera matrix and the dual absolute quadratic.
*
* wi = Pi*Q*PiT, where wi = Ki*K'i
*
* @param Q (Input) Dual absolute qudratic
* @param P (Input) Camera matrix for a view
* @param intrinsic (Output) found intrinsic parameters
*/
public static void intrinsicFromAbsoluteQuadratic( DMatrixRMaj Q, DMatrixRMaj P, CameraPinhole intrinsic ) {
DMatrixRMaj tmp = new DMatrixRMaj(3, 4);
DMatrixRMaj tmp2 = new DMatrixRMaj(3, 3);
CommonOps_DDRM.mult(P, Q, tmp);
CommonOps_DDRM.multTransB(tmp, P, tmp2);
decomposeDiac(tmp2, 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.
*
* @param intrinsic (output) K extracted from w
*/
public static void decomposeDiac( double w11, double w12, double w13, double w22, double w23, double w33,
CameraPinhole intrinsic ) {
// divide by w33 to ensure that it is equal to one
double cx = w13/w33;
double cy = w23/w33;
double fy = Math.sqrt(Math.abs(w22/w33 - cy*cy));
double skew = (w12/w33 - cx*cy)/fy;
double fx = Math.sqrt(Math.abs(w11/w33 - skew*skew - cx*cx));
intrinsic.cx = cx;
intrinsic.cy = cy;
intrinsic.fx = fx;
intrinsic.fy = fy;
intrinsic.skew = skew;
}
/**
* 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.
*
* @param w (input) DIAC 3x3
* @param intrinsic (output) K extracted from w
*/
public static void decomposeDiac( DMatrixRMaj w, CameraPinhole intrinsic ) {
decomposeDiac(w.data[0], w.data[1], w.data[2], w.data[4], w.data[5], w.data[8], intrinsic);
}
/**
* 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]
*
* @param K 3x3 calibration matrix for view 1
* @param v1 plane at infinity
* @param v2 plane at infinity
* @param v3 plane at infinity
* @param lambda scaling factor
* @param H (Optional) Storage for 4x4 matrix
* @return The homography
*/
public static DMatrixRMaj createProjectiveToMetric( DMatrixRMaj K,
double v1, double v2, double v3,
double lambda,
@Nullable DMatrixRMaj H ) {
if (H == null)
H = new DMatrixRMaj(4, 4);
else
H.reshape(4, 4);
CommonOps_DDRM.insert(K, H, 0, 0);
H.set(0, 3, 0);
H.set(1, 3, 0);
H.set(2, 3, 0);
H.set(3, 0, v1);
H.set(3, 1, v2);
H.set(3, 2, v3);
H.set(3, 3, lambda);
return H;
}
/**
* Decomposes the absolute dual quadratic into the following submatrices: Q=[w -w*p;-p'*w p'*w*p]
*
* @param Q (Input) Absolute quadratic. Typically found in auto calibration. Not modified.
* @param w (Output) 3x3 symmetric matrix
* @param p (Output) 3x1 vector
* @return true if successful or false if it failed
* @see DecomposeAbsoluteDualQuadratic
*/
public static boolean decomposeAbsDualQuadratic( DMatrix4x4 Q, DMatrix3x3 w, DMatrix3 p ) {
DecomposeAbsoluteDualQuadratic alg = new DecomposeAbsoluteDualQuadratic();
if (!alg.decompose(Q))
return false;
w.setTo(alg.getW());
p.setTo(alg.getP());
return true;
}
/**
* Splits the associated pairs into two lists
*
* @param input List of associated features
* @return two lists containing each set of features
*/
public static Tuple2, List> split2( List input ) {
List list1 = new ArrayList<>();
List list2 = new ArrayList<>();
for (int i = 0; i < input.size(); i++) {
list1.add(input.get(i).p1);
list2.add(input.get(i).p2);
}
return new Tuple2<>(list1, list2);
}
/**
* Splits the associated triple into three lists
*
* @param input List of associated features
* @return three lists containing each set of features
*/
public static Tuple3, List, List> split3( List input ) {
List list1 = new ArrayList<>();
List list2 = new ArrayList<>();
List list3 = new ArrayList<>();
for (int i = 0; i < input.size(); i++) {
list1.add(input.get(i).p1);
list2.add(input.get(i).p2);
list3.add(input.get(i).p3);
}
return new Tuple3<>(list1, list2, list3);
}
/**
* Convenience function for initializing bundle adjustment parameters. Triangulates points using camera
* position and pixel observations.
*
* @param structure camera locations
* @param observations observations of features in the images
*/
public static void triangulatePoints( SceneStructureMetric structure, SceneObservations observations ) {
TriangulateNViewsMetricH triangulator = FactoryMultiView.triangulateNViewMetricH(ConfigTriangulation.GEOMETRIC());
List list_p_to_n = new ArrayList<>();
for (int i = 0; i < structure.cameras.size; i++) {
RemoveBrownPtoN_F64 p2n = new RemoveBrownPtoN_F64();
BundleAdjustmentCamera baseModel = Objects.requireNonNull(structure.cameras.data[i].model);
if (baseModel instanceof BundlePinholeSimplified) {
BundlePinholeSimplified cam = (BundlePinholeSimplified)baseModel;
p2n.setK(cam.f, cam.f, 0, 0, 0).setDistortion(new double[]{cam.k1, cam.k2}, 0, 0);
} else if (baseModel instanceof BundlePinhole) {
BundlePinhole cam = (BundlePinhole)baseModel;
p2n.setK(cam.fx, cam.fy, cam.skew, cam.cx, cam.cy).setDistortion(new double[]{0, 0}, 0, 0);
} else if (baseModel instanceof BundlePinholeBrown) {
BundlePinholeBrown cam = (BundlePinholeBrown)baseModel;
p2n.setK(cam.fx, cam.fy, cam.skew, cam.cx, cam.cy).setDistortion(cam.radial, cam.t1, cam.t2);
} else {
throw new RuntimeException("Unknown camera model! " + baseModel.getClass().getSimpleName());
}
list_p_to_n.add(p2n);
}
var normObs = new DogArray<>(Point2D_F64::new);
normObs.resize(3);
final boolean homogenous = structure.isHomogenous();
var X = new Point4D_F64();
var worldToViews = new ArrayList();
for (int i = 0; i < structure.points.size; i++) {
normObs.reset();
worldToViews.clear();
SceneStructureCommon.Point sp = structure.points.get(i);
for (int j = 0; j < sp.views.size; j++) {
int viewIdx = sp.views.get(j);
SceneStructureMetric.View v = structure.views.data[viewIdx];
worldToViews.add(structure.getParentToView(v));
// get the observation in pixels
Point2D_F64 n = normObs.grow();
int pointidx = observations.views.get(viewIdx).point.indexOf(i);
observations.views.get(viewIdx).getPixel(pointidx, n);
// convert to normalized image coordinates
list_p_to_n.get(v.camera).compute(n.x, n.y, n);
}
if (!triangulator.triangulate(normObs.toList(), worldToViews, X)) {
// this should work unless the input is bad
throw new RuntimeException("Triangulation failed. Bad input?");
}
if (homogenous)
sp.set(X.x, X.y, X.z, X.w);
else
sp.set(X.x/X.w, X.y/X.w, X.z/X.w);
}
}
/**
* Finds this scale which minimizes the difference between `a` and `b`. ||scale*a-b||
*
* @param a (Input) matrix
* @param b (Input) matrix
* @return scale factor
*/
public static double findScale( DMatrixRMaj a, DMatrixRMaj b ) {
BoofMiscOps.checkTrue(a.numRows == b.numRows);
BoofMiscOps.checkTrue(a.numCols == b.numCols);
final int N = a.getNumElements();
double sum = 0.0;
double weights = 0.0;
for (int i = 0; i < N; i++) {
double valA = a.data[i];
double valB = b.data[i];
if (valA == 0.0)
continue;
double weight = Math.abs(valB);
sum += weight*(valB/valA);
weights += weight;
}
return sum/weights;
}
/**
* Finds the scale which minimizes the difference between `a` and `b`. ||scale*a-b||
*
* @param a (Input) 3D coordinate
* @param b (Input) 3D coordinate
* @return scale factor
*/
public static double findScale( GeoTuple3D_F64 a, GeoTuple3D_F64 b ) {
int which = UtilPoint3D_F64.axisLargestAbs(a);
double bottom = a.getIdx(which);
if (bottom == 0.0)
return 0.0;
return b.getIdx(which)/bottom;
}
/**
* Lists a list of {@link AssociatedTriple} into a list of observations for each camera independently.
*
* @param src (Input) list of {@link AssociatedTriple}
* @param dst (Output) list of lists. Can be null.
* @return list of lists.
*/
public static List>
splits3Lists( List src, @Nullable List> dst ) {
// Ensure dst is a list that contains 3 empty lists
if (dst == null) {
dst = new ArrayList<>();
}
if (dst.size() != 3) {
dst.clear();
for (int i = 0; i < 3; i++) {
dst.add(new ArrayList<>());
}
} else {
for (int i = 0; i < 3; i++) {
dst.get(i).clear();
}
}
for (int i = 0; i < src.size(); i++) {
AssociatedTriple a = src.get(i);
dst.get(0).add(a.p1);
dst.get(1).add(a.p2);
dst.get(2).add(a.p3);
}
return dst;
}
/**
* Converts a list of associated {@link AssociatedTriple} in a {@link DogArray} of {@link AssociatedTuple}
*
* @param src (Input) List of AssociatedTriple
* @param dst (Output) Array of AssociatedTuple. Array is reset.
*/
public static void convertTr( List src, DogArray dst ) {
dst.resize(src.size());
if (src.size() == 0)
return;
BoofMiscOps.checkTrue(dst.get(0).size() == 3);
for (int i = 0; i < src.size(); i++) {
AssociatedTriple a = src.get(i);
AssociatedTuple b = dst.get(i);
b.set(0, a.p1);
b.set(1, a.p2);
b.set(2, a.p3);
}
}
/**
* Converts a list of associated {@link AssociatedTriple} in a {@link DogArray} of {@link AssociatedPair}
*
* @param src (Input) List of AssociatedTriple
* @param idx0 (Input) which feature in the triple is p1 in the pair
* @param idx1 (Input) which feature in the triple is p2 in the pair
* @param dst (Output) Array of AssociatedPair. Array is reset.
*/
public static void convertTr( List src, int idx0, int idx1,
DogArray dst ) {
dst.resize(src.size());
if (src.size() == 0)
return;
for (int i = 0; i < src.size(); i++) {
AssociatedTriple a = src.get(i);
dst.get(i).setTo(a.get(idx0), a.get(idx1));
}
}
/**
* Converts a list of associated {@link AssociatedTuple} in a {@link DogArray} of {@link AssociatedPair}
*
* @param src (Input) List of AssociatedTuple
* @param idx0 (Input) which feature in the tuple is p1 in the pair
* @param idx1 (Input) which feature in the tuple is p2 in the pair
* @param dst (Output) Array of AssociatedPair. Array is reset.
*/
public static void convertTu( List src, int idx0, int idx1,
DogArray dst ) {
dst.resize(src.size());
if (src.size() == 0)
return;
BoofMiscOps.checkTrue(src.get(0).size() == 3);
for (int i = 0; i < src.size(); i++) {
AssociatedTuple a = src.get(i);
dst.get(i).setTo(a.get(idx0), a.get(idx1));
}
}
/**
* 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.
*/
public static double disparityToRange( double disparity, double focalLength, double baseline ) {
if (disparity == 0.0)
return Double.POSITIVE_INFINITY;
if (disparity < 0.0)
throw new IllegalArgumentException("Disparity can't be less than zero");
return focalLength*baseline/disparity;
}
/**
* 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
*
*
* @param scene (Input) Metric scene
* @param viewIdx (Input) Index of view for which points are projected
* @param function (Output) Called with results (index, 3D camera location, pixel)
*/
public static void scenePointsToPixels( SceneStructureMetric scene, int viewIdx,
BoofLambdas.ProcessIndex2 function ) {
Se3_F64 world_to_view = new Se3_F64();
SceneStructureMetric.View view = scene.views.get(viewIdx);
scene.getWorldToView(view, world_to_view, null);
BundleAdjustmentCamera camera = Objects.requireNonNull(scene.getViewCamera(view).model);
Point3D_F64 camPoint = new Point3D_F64();
Point2D_F64 pixel = new Point2D_F64();
for (int pointIdx = 0; pointIdx < scene.points.size; pointIdx++) {
SceneStructureCommon.Point point = scene.points.get(pointIdx);
double x = point.coordinate[0];
double y = point.coordinate[1];
double z = point.coordinate[2];
double w = scene.isHomogenous() ? point.coordinate[3] : 1.0;
// Project the pixel while being careful for points at infinity
SePointOps_F64.transformV(world_to_view, x, y, z, w, camPoint);
camera.project(camPoint.x, camPoint.y, camPoint.z, pixel);
function.process(pointIdx, camPoint, pixel);
}
}
/**
* 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.
*
* @param scene (Input) The scene
* @param tol (Input) Only used if the scene is in homogenous coordinates.
* Tolerance for points being at infinity. Smaller values means more tolerant. Try 1e-8.
* @param func (Output) Results are passed in to this function with their index and 3D point.
*/
public static void sceneToCloud3( SceneStructureMetric scene, double tol,
BoofLambdas.ProcessIndex func ) {
Point3D_F64 out = new Point3D_F64();
final boolean homogenous = scene.isHomogenous();
for (int pointIdx = 0; pointIdx < scene.points.size; pointIdx++) {
SceneStructureCommon.Point point = scene.points.get(pointIdx);
double x = point.coordinate[0];
double y = point.coordinate[1];
double z = point.coordinate[2];
if (homogenous) {
double r = Math.sqrt(x*x + y*y + z*z);
double w = point.coordinate[3];
// Make sure the point isn't at infinity
if (r*tol > Math.abs(w)) {
continue;
}
x /= w;
y /= w;
z /= w;
}
out.setTo(x, y, z);
func.process(pointIdx, out);
}
}
/**
* 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.
*
* @param scene (Input) The scene
* @param func (Output) Results are passed in to this function with their index and 3D point.
*/
public static void sceneToCloudH( SceneStructureMetric scene, BoofLambdas.ProcessIndex func ) {
Point4D_F64 out = new Point4D_F64();
final boolean homogenous = scene.isHomogenous();
for (int pointIdx = 0; pointIdx < scene.points.size; pointIdx++) {
SceneStructureCommon.Point point = scene.points.get(pointIdx);
double x = point.coordinate[0];
double y = point.coordinate[1];
double z = point.coordinate[2];
double w = homogenous ? point.coordinate[3] : 1.0;
out.setTo(x, y, z, w);
func.process(pointIdx, out);
}
}
/**
* 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
*
*
* @param F (Input) Fundamental matrix
* @param H (Input) Homography
* @return A number close to zero if compatible
*/
public static double compatibleHomography( DMatrixRMaj F, DMatrixRMaj H ) {
DMatrixRMaj tmp0 = new DMatrixRMaj(3, 3);
DMatrixRMaj tmp1 = new DMatrixRMaj(3, 3);
CommonOps_DDRM.multTransA(H, F, tmp0);
CommonOps_DDRM.multTransA(F, H, tmp1);
CommonOps_DDRM.add(tmp0, tmp1, tmp1);
return NormOps_DDRM.normF(tmp1);
}
/**
* 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
*
*
* @param H21 (Input) known homography
* @param pairs (Input) two or more point observations which do not lie on the plane
* @param F21 (Output) found homography matrix
* @return true if no errors were encountered
*/
public static boolean homographyToFundamental( DMatrixRMaj H21, List pairs, DMatrixRMaj F21 ) {
List epipolarLines = new ArrayList<>();
Point2D_F64 h2 = new Point2D_F64();
for (int i = 0; i < pairs.size(); i++) {
AssociatedPair p = pairs.get(i);
GeometryMath_F64.mult(H21, p.p1, h2);
epipolarLines.add(UtilLine2D_F64.convert(p.p2, h2, (LineGeneral2D_F64)null));
}
// Epipole in the second view, homogenous coordinates
Point3D_F64 epipole = Intersection2D_F64.intersection(epipolarLines, null);
// F=cross_matrix(e)*H
GeometryMath_F64.multCrossA(epipole, H21, F21);
// In the future an alternative implementation might require error checking, so this is staying
return true;
}
/**
* Creates a pixel homography from a rotation matrix and the intrinsic calibration matrices. H = K2*R21*inv(K1)
*
* @param R21 (Input) Rotation matrix
* @param K1 (Input) Intrinsic camera matrix 1
* @param K2 (Input) Intrinsic camera matrix 2
* @return The homography
*/
public static DMatrixRMaj homographyFromRotation( DMatrixRMaj R21, DMatrixRMaj K1, DMatrixRMaj K2,
@Nullable DMatrixRMaj H21 ) {
if (H21 == null)
H21 = new DMatrixRMaj(3, 3);
DMatrixRMaj K1_inv = new DMatrixRMaj(3, 3);
DMatrixRMaj KR = new DMatrixRMaj(3, 3);
PerspectiveOps.invertCalibrationMatrix(K1, K1_inv);
CommonOps_DDRM.mult(K2, R21, KR);
CommonOps_DDRM.mult(KR, K1_inv, H21);
return H21;
}
}
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