Camera calibration from orthogonally projected coordinates with noisy-RANSAC

We introduce a formulation for ¿orthogonal calibration¿ which is to extract camera calibration parameters from the world coordinates with unknown heights. Such coordinates can be obtained from an aerial photograph or a GPS device. A typical approach would be to introduce a planar surface assumption and apply the plane homography. However, the planar assumption often fails; moreover, the camera parameters recovered from a homography matrix is highly sensitive to noise. We introduce a formulation for the orthogonal calibration which is similar to the fundamental matrix equation. Based on the formulation, we introduce a 6-point algorithm to recover the rotation and translation and a 7-point algorithm to recover the focal lengths in addition. Then, we introduce a noisy-RANSAC method which enables robust parameter recovery from a small number of point correspondences. The noisy-RANSAC naturally incorporates the orthogonal calibration and any available information on the scene structure, which delivers much improved estimates. Experimental results on synthetic datasets and an example application to a real image are presented.