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BoofCV is an open source Java library for real-time computer vision and robotics applications.
/*
* Copyright (c) 2011-2013, 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.rectify;
import boofcv.alg.geo.MultiViewOps;
import boofcv.struct.geo.AssociatedPair;
import georegression.geometry.GeometryMath_F64;
import georegression.struct.point.Point2D_F64;
import georegression.struct.point.Point3D_F64;
import georegression.struct.point.Vector3D_F64;
import org.ejml.data.DenseMatrix64F;
import org.ejml.simple.SimpleMatrix;
import java.util.List;
/**
*
* Rectifies a stereo pair given a fundamental or essential matrix. The rectification ensures that
* the epipolar lines project to infinity along the x-axis. The computed transforms are designed to
* minimize the range of disparity between the two images. For this technique to work
* the epipoles must lie outside of both images. See [1] for algorithmic details.
*
*
*
* WARNING: On paper this technique sounds straight forward. In practice it requires a very
* precise fundamental matrix estimate to be of practical use. Using the epipolar constraint alone is not
* sufficient to remove outliers because a point far away that lands on the epipolar line will have a small
* error. Removing lens distortion from the image is recommended.
*
*
*
* [1] R. Hartley, "Theory and Practice of Projective Rectification", International Journal of Computer Vision,
* vol 35, no 2, pages 115-127, 1999.
*
*
* @author Peter Abeles
*/
public class RectifyFundamental {
// rectifying transform for left and right images
private DenseMatrix64F rect1 = new DenseMatrix64F(3,3);
private DenseMatrix64F rect2 = new DenseMatrix64F(3,3);
// storage for epipoles
private Point3D_F64 epipole1 = new Point3D_F64();
private Point3D_F64 epipole2 = new Point3D_F64();
/**
* Compute rectification transforms for the stereo pair given a fundamental matrix and its observations.
*
* @param F Fundamental matrix
* @param observations Observations used to compute F
* @param width Width of first image.
* @param height Height of first image.
*/
public void process( DenseMatrix64F F , List observations ,
int width , int height ) {
int centerX = width/2;
int centerY = height/2;
MultiViewOps.extractEpipoles(F, epipole1, epipole2);
checkEpipoleInside(width, height);
// compute the transform H which will send epipole2 to infinity
SimpleMatrix R = rotateEpipole(epipole2,centerX,centerY);
SimpleMatrix T = translateToOrigin(centerX,centerY);
SimpleMatrix G = computeG(epipole2,centerX,centerY);
SimpleMatrix H = G.mult(R).mult(T);
//Find the two matching transforms
SimpleMatrix Hzero = computeHZero(F,epipole2,H);
SimpleMatrix Ha = computeAffineH(observations,H.getMatrix(),Hzero.getMatrix());
rect1.set(Ha.mult(Hzero).getMatrix());
rect2.set(H.getMatrix());
}
/**
* The epipoles need to be outside the image
*/
private void checkEpipoleInside(int width, int height) {
double x1 = epipole1.x/epipole1.z;
double y1 = epipole1.y/epipole1.z;
double x2 = epipole2.x/epipole2.z;
double y2 = epipole2.y/epipole2.z;
if( x1 >= 0 && x1 < width && y1 >= 0 && y1 < height )
throw new IllegalArgumentException("First epipole is inside the image");
if( x2 >= 0 && x2 < width && y2 >= 0 && y2 < height )
throw new IllegalArgumentException("Second epipole is inside the image");
}
/**
* Create a transform which will move the specified point to the origin
*/
private SimpleMatrix translateToOrigin( int x0 , int y0 ) {
SimpleMatrix T = SimpleMatrix.identity(3);
T.set(0, 2, -x0);
T.set(1, 2, -y0);
return T;
}
/**
* Apply a rotation such that the epipole is equal to [f,0,1)\
*/
private SimpleMatrix rotateEpipole( Point3D_F64 epipole , int x0 , int y0 )
{
// compute rotation which will set
// x * sin(theta) + y * cos(theta) = 0
double x = epipole.x/epipole.z-x0;
double y = epipole.y/epipole.z-y0;
double theta = Math.atan2(-y,x);
double c = Math.cos(theta);
double s = Math.sin(theta);
SimpleMatrix R = new SimpleMatrix(3,3);
R.setRow(0, 0, c,-s);
R.setRow(1, 0, s, c);
R.set(2, 2, 1);
return R;
}
private SimpleMatrix computeG( Point3D_F64 epipole , int x0 , int y0 ) {
double x = epipole.x/epipole.z - x0;
double y = epipole.y/epipole.z - y0;
double f = Math.sqrt(x*x + y*y);
SimpleMatrix G = SimpleMatrix.identity(3);
G.set(2,0,-1.0/f);
return G;
}
/**
* Finds the values of a,b,c which minimize
*
* sum (a*x(+)_i + b*y(+)_i + c - x(-)_i)^2
*
* See page 306
*
* @return Affine transform
*/
private SimpleMatrix computeAffineH( List observations ,
DenseMatrix64F H , DenseMatrix64F Hzero ) {
SimpleMatrix A = new SimpleMatrix(observations.size(),3);
SimpleMatrix b = new SimpleMatrix(A.numRows(),1);
Point2D_F64 c = new Point2D_F64();
Point2D_F64 k = new Point2D_F64();
for( int i = 0; i < observations.size(); i++ ) {
AssociatedPair a = observations.get(i);
GeometryMath_F64.mult(Hzero, a.p1, k);
GeometryMath_F64.mult(H,a.p2,c);
A.setRow(i,0,k.x,k.y,1);
b.set(i,0,c.x);
}
SimpleMatrix x = A.solve(b);
SimpleMatrix Ha = SimpleMatrix.identity(3);
Ha.setRow(0,0,x.getMatrix().data);
return Ha;
}
/**
* H0 = H*M
* P=[M|m] from canonical camera
*/
private SimpleMatrix computeHZero( DenseMatrix64F F , Point3D_F64 e2 ,
SimpleMatrix H ) {
Vector3D_F64 v = new Vector3D_F64(.1,0.5,.2);
// need to make sure M is not singular for this technique to work
SimpleMatrix P = SimpleMatrix.wrap(MultiViewOps.canonicalCamera(F, e2, v, 1));
SimpleMatrix M = P.extractMatrix(0, 3, 0, 3);
return H.mult(M);
}
/**
* Rectification transform for first camera
*/
public DenseMatrix64F getRect1() {
return rect1;
}
/**
* Rectification transform for second camera
*/
public DenseMatrix64F getRect2() {
return rect2;
}
}