从Essential Matrix估计R,T

clc
clear
t=rand(3,1)
R=rodrigues(rand(3,1))
T=[0 -t(3) t(2);
    t(3) 0 -t(1);
    -t(2) t(1) 0
];

E=T*R
[U,S,V]=svd(E);
disp('S?=?diag(1,1,0)')
S
W=[0 -1 0;
    1 0 0;
    0 0 1
];
P1=[U*W*V' U(:,3)]
P2=[U*W'*V' U(:,3)]
disp('check R..')
norm(U*W*V'-R)
norm(U*W'*V'-R)

disp('check t..')
norm(U(:,3) - t/norm(t))
norm(- U(:,3) - t/norm(t))

Decomposing the Essential matrix using Horn and Eigen 

void DecomposeEssentialUsingHorn90(double _E[9], double _R1[9], double _R2[9], double _t1[3], double _t2[3]) {
    //from : http://people.csail.mit.edu/bkph/articles/Essential.pdf
    using namespace Eigen;
 
    Matrix3d E = Map >(_E);
    Matrix3d EEt = E * E.transpose();
    Vector3d e0e1 = E.col(0).cross(E.col(1)),e1e2 = E.col(1).cross(E.col(2)),e2e0 = E.col(2).cross(E.col(2));
    Vector3d b1,b2;
 
#if 1
    //Method 1
    Matrix3d bbt = 0.5 * EEt.trace() * Matrix3d::Identity() - EEt; //Horn90 (12)
    Vector3d bbt_diag = bbt.diagonal();
    if (bbt_diag(0) > bbt_diag(1) && bbt_diag(0) > bbt_diag(2)) {
        b1 = bbt.row(0) / sqrt(bbt_diag(0));
        b2 = -b1;
    } else if (bbt_diag(1) > bbt_diag(0) && bbt_diag(1) > bbt_diag(2)) {
        b1 = bbt.row(1) / sqrt(bbt_diag(1));
        b2 = -b1;
    } else {
        b1 = bbt.row(2) / sqrt(bbt_diag(2));
        b2 = -b1;
    }
#else
    //Method 2
    if (e0e1.norm() > e1e2.norm() && e0e1.norm() > e2e0.norm()) {
        b1 = e0e1.normalized() * sqrt(0.5 * EEt.trace()); //Horn90 (18)
        b2 = -b1;
    } else if (e1e2.norm() > e0e1.norm() && e1e2.norm() > e2e0.norm()) {
        b1 = e1e2.normalized() * sqrt(0.5 * EEt.trace()); //Horn90 (18)
        b2 = -b1;
    } else {
        b1 = e2e0.normalized() * sqrt(0.5 * EEt.trace()); //Horn90 (18)
        b2 = -b1;
    }
#endif
     
    //Horn90 (19)
    Matrix3d cofactors; cofactors.col(0) = e1e2; cofactors.col(1) = e2e0; cofactors.col(2) = e0e1;
    cofactors.transposeInPlace();
     
    //B = [b]_x , see Horn90 (6) and http://en.wikipedia.org/wiki/Cross_product#Conversion_to_matrix_multiplication
    Matrix3d B1; B1 <<    0,-b1(2),b1(1),
                        b1(2),0,-b1(0),
                        -b1(1),b1(0),0;
    Matrix3d B2; B2 <<    0,-b2(2),b2(1),
                        b2(2),0,-b2(0),
                        -b2(1),b2(0),0;
 
    Map > R1(_R1),R2(_R2);
 
    //Horn90 (24)
    R2 = (cofactors.transpose() - B1*E) / b1.dot(b1);
    R1 = (cofactors.transpose() - B2*E) / b2.dot(b2);
    Map t1(_t1),t2(_t2); 
    t1 = b2; t2 = b1;
     
    cout << "Horn90 provided " << endl << R1 << endl << "and" << endl << R2 << endl;
}

http://www.morethantechnical.com/2012/08/09/decomposing-the-essential-matrix-using-horn-and-eigen-wcode/

http://www.cnblogs.com/cutepig/archive/2007/07/12/815351.html