Sensor pose inference from airborne videos by decomposing homography estimates

Airborne videos are gaining increasing importance. Video cameras are taking huge amounts of measurements for low costs. Their low weight and low requirement for energy makes them particularly attractive for small airborne carriers with low payload. Such carriers are discussed for military as well as for civil applications, e.g. traffic-surveillance. Often video cameras are used for documentation and reference in connection with other sensor systems. In addition to panchromatic or ordinary colour videos, nowadays also cameras operating in the thermal spectral domain gain attention. For the utilization of any stream of measurements taken from a moving platform the pose of the sensor in orientation and position has to be constantly determined. For airborne platforms often GPS and INS are used to acquire this information. However, the video stream itself provides also possibilities to estimate pose parameters. In this contribution we restrict our investigation to almost flat scenes but we allow oblique views both forward looking and side looking. The optical flow of the scene fixed structure on the world plane is estimated by a planar projective homography. This requires at least four point or line correspondences that can be traced over an appropriate number of frames. If the focal length is not changed and the camera has not been rotated, the proper transform will be restricted to a planar homology with five degrees of freedom. For this case pose parameters were estimated by the analysis of the eigenvectors of the transform. The axis of the homology (corresponding to its double eigenvalue) is the horizon, from which we obtain the rotational part of the pose. The sensor translation is obtained from the vertex (corresponding to its single eigenvalue) and the cross ratio of the homology. Situations where the vertex is close to the horizon needs special treatment (this mapping is called elation). If the camera has rotated between the frames the homography will be decomposed into a homology and an orthogonal rotation matrix. The five degrees of freedom of the homology and the three degrees of freedom of the orthogonal rotation matrix sum up to eight, which is exactly the same number of degrees of freedom that a planar homography has. There is a set of analytic solutions to this equation system, of which the correct solution can be picked by heuristic considerations. We also investigate the propagation of measurement errors through these calculations. Examples for such estimations are shown for a thermal video.
Michaelsen E, Kirchhof M, Stilla U (2004) Sensor pose inference from airborne videos by decomposing homography estimates. In: Altan MO (ed) International Archives of Photogrammetry and Remote Sensing. Vol. 35, Part B3, 1-6
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