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?