How to compute camera pose from Homography matrix?

Question

Say I use only one calibrated camera. From this camera, I get images A and B. I know the homography between A and B, computed through OpenCV's findHomography().

I know the pose (rotation matrix R and translation vector t) of image A, and I need the pose of image B. Once I get it, I suppose I'll be able to compute every further poses of following images.

Do you know an implementation of computing B's pose? I found several articles on the web, but I couldn't find an easily implementable solution...

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I found a nice implementation, using OpenCV: http://nghiaho.com/?p=1298

Answer 1

Even if my answer comes too late for you, maybe other people find this useful. I have the codes for an openCV Pose from Homography. I found the method at this really useful website, euclideanspace.

void cameraPoseFromHomography(const Mat& H, Mat& pose)
{
    pose = Mat::eye(3, 4, CV_64FC1); //3x4 matrix
    float norm1 = (float)norm(H.col(0)); 
    float norm2 = (float)norm(H.col(1));
    float tnorm = (norm1 + norm2) / 2.0f;

    Mat v1 = H.col(0);
    Mat v2 = pose.col(0);

    cv::normalize(v1, v2); // Normalize the rotation

    v1 = H.col(1);
    v2 = pose.col(1);

    cv::normalize(v1, v2);

    v1 = pose.col(0);
    v2 = pose.col(1);

    Mat v3 = v1.cross(v2);  //Computes the cross-product of v1 and v2
    Mat c2 = pose.col(2);
    v3.copyTo(c2);      

    pose.col(3) = H.col(2) / tnorm; //vector t [R|t]
}

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Answer 2

You can use Homography decomposition method implemented in Opencv 3.0+

decomposeHomographyMat

• Opencv’s function returns set of possible rotations, camera normals and translation matrices.
• You have to select correct set among them by comparing camera normals with camera normal of camera when first image was captured