Translating and Rotating an Image in 3D using OpenCV

Question

Given a 3 x 3 rotation matrix,R, and a 3 x 1 translation matrix,T, I am wondering how to multiply the T and R matrices to an image?

Lets say the Iplimage img is 640 x 48

Answer 1

The function you are searching for is probably warpPerspective() : this is a use case...

// Projection 2D -> 3D matrix
        Mat A1 = (Mat_(4,3) <<
            1, 0, -w/2,
            0, 1, -h/2,
            0, 0,    0,
            0, 0,    1);

// Rotation matrices around the X axis
        Mat R = (Mat_(4, 4) <<
            1,          0,           0, 0,
            0, cos(alpha), -sin(alpha), 0,
            0, sin(alpha),  cos(alpha), 0,
            0,          0,           0, 1);

// Translation matrix on the Z axis 
        Mat T = (Mat_(4, 4) <<
            1, 0, 0, 0,
            0, 1, 0, 0,
            0, 0, 1, dist,
            0, 0, 0, 1);

// Camera Intrisecs matrix 3D -> 2D
        Mat A2 = (Mat_(3,4) <<
            f, 0, w/2, 0,
            0, f, h/2, 0,
            0, 0,   1, 0);

Mat transfo = A2 * (T * (R * A1));

Mat source;
Mat destination;

warpPerspective(source, destination, transfo, source.size(), INTER_CUBIC | WARP_INVERSE_MAP);

I hope it could help you,

Julien

PS : I gave the example with a projection from 2D to 3D but you can use directly transfo = T* R;