UAS displacement measurement using a three point homography method with potential bridge monitoring applications

Measuring bridge displacements using Unmanned Aerial Systems (UAS) is an emerging field offering the advantage of a remote non -contact approach for measuring bridge displacements. Unfortunately, UAS measurements contain the motion of the UAS which needs to be compensated for to get true bridge displacements. So far, UAS bridge displacement studies have compensated the unwanted motion of the UAS from measurements by tracking a minimum of 4 stationary points required as the minimal solution to calculate a Projective homography between two UAS camera views. While this has been shown to be effective, a reduction in the minimal solution would make these methods more robust to factors such as loss of stabilising points or temporary occlusion to an object entering the scene. In this paper, by combining recent advances to the Perspective -3 -Point problem that make camera pose calculation from 3 points reliable and calculating a Euclidean homography instead of a Projective homography, we show in a laboratory experiment that structural displacements can successfully be made to submillimetre accuracy using only 3 points instead of the traditional 4 points. This is done with only visual information from video feed without the need for any additional sensors.