I am trying to map image coordinates to world coordinates for a particular dataset. I have the camera parameters available (both intrinsic and extrinsic). According to the equation, I need to take an inverse of the Homography matrix. However, when I try to do so, it fails as the Homography matrix for the camera turns out to be singular (non invertible).
H = K [ r1 | r2 | T ]
p(img) = H x p(w)
p(w) = H-1 x p(img)
The reason for using this form of Homography matrix is that I am finding Road coordinates, hence Z=0 Here, x is sign for matrix multiplication, H is the homography, K is the Intrinsic matrix, T is the Translational matrix , r1 and r2 are the first and second columns of the Rotational Matrix. p(img) are the image coordinates and p(img) are the world coordinates.
Getting values for the intrinsic and extrinsic parameters (https://github.com/ori-mrg/robotcar-dataset-sdk/blob/master/models/stereo_narrow_left.txt)
The homography matrix we get is singular: Homography matrix
Is there another way to map image to world coordinates?