Inserting 3D models in a photo

I finally found an interesting article which goes through what needs to be done when placing 3D models on a photo, to make it look like they belong.

• Of course, you need to know some camera parameters, which are separated into extrinsic (camera rotation and center) and intrinsic (focal length, skew and the principal point) parameters. The skew of modern cameras is most often 0, or close enough to set it as 0.
• Furthermore, projection parameters need to be known when going from 3D space to 2D images. This is due to the fact that we "remove one dimension" from the equation, leaving us with a flat image of objects projected from 3D. The parameters of the camera are found as follows:
  
• Determining the vanishing points - at least two out of the three vanishing points must be detected, whereafter the third can be computed if necessary.
• Recovering the projection matrix. This is done using the vanishing points and the image of the origin of the world coordinta system. The origin is selected arbitrarily, and aligned with the principal axis.
• Determining the extrinsic camera parameters. This is computed analytically.
• World coordinate calculations can be made if we know that the point lies on a known world plane - thereby having a homography between the image point and the corresponding 3D world coordinate.

This is a very short description, which I'll dive into further later, digging into more details of the methods.