基本矩阵分解:验证 R 和 T 的四种可能解决方案

My problem is that I have 2 possible solutions for R and 2 possible solutions for T which leads to 4 solutions for the overall pose, where only one of the 4 solutions is the right one. How can I find the correct solution?

这是我的代码:

private void calculateRT(Mat E, Mat R, Mat T){

    Mat w = new Mat();
    Mat u = new Mat();
    Mat vt = new Mat();

    Mat diag = new Mat(3,3,CvType.CV_64FC1);
    double[] diagVal = {1,0,0,0,1,0,0,0,1};
    diag.put(0, 0, diagVal);

    Mat newE = new Mat(3,3,CvType.CV_64FC1);

    Core.SVDecomp(E, w, u, vt, Core.DECOMP_SVD); 

    Core.gemm(u, diag, 1, vt, 1, newE);

    Core.SVDecomp(newE, w, u, vt, Core.DECOMP_SVD);

    publishProgress("U: " + u.dump());
    publishProgress("W: " + w.dump());
    publishProgress("vt:" + vt.dump());

    double[] W_Values = {0,-1,0,1,0,0,0,0,1};
    Mat W = new Mat(new Size(3,3), CvType.CV_64FC1);
    W.put(0, 0, W_Values);

    double[] Wt_values = {0,1,0-1,0,0,0,0,1};
    Mat Wt = new Mat(new Size(3,3), CvType.CV_64FC1);
    Wt.put(0,0,Wt_values);


    Mat R1 = new Mat();
    Mat R2 = new Mat();

    // u * W * vt = R 
    Core.gemm(u, Wt, 1, vt, 1, R2);
    Core.gemm(u, W, 1, vt, 1, R1);

    publishProgress("R: " + R.dump());


    // +- T (2 possible solutions for T)
    Mat T1 = new Mat();
    Mat T2 = new Mat();
    // T = u.t
    u.col(2).copyTo(T1);

    publishProgress("T : " + T.dump());

    Core.multiply(T, new Scalar(-1.0, -1.0, -1.0), T2);

    // TODO Here I have to find the correct combination for R1 R2 and T1 T2

}

推荐答案

从两个相机的基本矩阵重建相对欧几里得姿势时存在理论歧义.这种模糊性与以下事实有关:给定图像中的 2D 点，经典针孔相机模型无法分辨相应的 3D 点是在相机前面还是在相机后面.为了消除这种歧义，您需要知道图像中的一个点对应关系:因为这两个 2D 点被假定为位于两个相机前面的单个 3D 点的投影(因为它在两个图像中都可见)，这将能够选择正确的 R 和 T.

[e]x = [0,-e_3,e_2; e_3,0,-e_1; -e_2,e_1,0]