# In which way do image transformations change camera extrinsics?

Given a pinhole camera model, we have an image and according camera intrinsics K and extrinsic parameters R.

When we scale the image or crop it, the corresponding camera intrinsics K change in ways that can be found in literature.

However, assume we transform or distort the image using a projective projection Q. How do the intrinsic parameters K of the camera change?

For further reference, Q is generated by K * U * K^-1, where U is a rotation matrix.

The projective transformation is illustrated in the two images below:

The transformation used in this example is a slight rotation around the vertical axis.