Geo-location Estimation From Two Shadow Trajectories

Estimating tools for geo-locating and geo-orientating static camera is a key step in creating a useful global imaging network from cameras attached to the network. The position of a world point's solar shadow depends on its geographical location, the geometrical relationship between the orientation of the sunshine and the ground plane where the shadow casts. It is often the case in practice that lines and planes giving rise to vanishing points are orthogonal. In this case there are particularly simple relationships amongst their vanishing points and lines involving the Image and Absolute Conic, and furthermore these relations can be used to determine the Image and Absolute Conic, and consequently the camera calibration. This paper investigates the property of solar shadow trajectories on a planar surface and shows that camera parameters, latitude, longitude and shadow casting objects'relative height ratios can be estimated from two observed shadow trajectories. One contribution is to recover the horizon line and metric rectification matrix from four observations of two shadow tips. The other contribution is that we use the design of an analemmatic sundial to get the shadow conic and furthermore recover the camera's geographical location. The proposed method does not require the shadow casting objects or a vertical object to be visible in the recovery of camera calibration. This approach is thoroughly validated on both synthetic and real data, and tested against various sources of errors including noise, number of observations, objects locations, and camera orientations.