Automatic camera orientation estimation for a partially calibrated camera above a plane with a line at known planar distance

We present a derivation for estimating the roll and pitch orientation of a partially calibrated camera mounted above a planar surface, using minimal scene information. Specifically, we assume known intrinsic parameters and a fixed height between the camera and the observed plane. By detecting a single straight reference line at a known planar distance -- such as the edge between a floor and a wall -- we estimate the roll and pitch angles via inverse projection geometry. The method leverages geometric constraints and the camera model, including lens distortion correction. This approach is suitable for scenarios where full calibration is impractical and offers a lightweight alternative for multi-camera systems operating in constrained environments.