Theoretical Analysis of the Iterative Photogrammetric Method to Determining Ground Coordinates from Photo Coordinates and a DEM

It is necessary to determine ground coordinates from a single aerial image and a digital elevation model (DEM). A widely used method in photogrammetry is to iteratively calculate the coordinates based on the inverse collinearity equations. The iterative photogrammetric method may be divergent when the terrain surface becomes complicated. However, there is a lack of theoretical analysis of this method. This paper theoretically analyzes the convergence condition and the convergence speed of the method, and validates the theory using a simulated surface containing various slope conditions. The elevation angle θ of the view ray and the inclination angle a of the profile, intersected by the terrain surface and the vertical view plane, play a critical role in the method. The necessary and sufficient condition for convergence is a < 6. The convergence speed is quantified as a function of a, 6, the convergence threshold AT and the offset ΔZ 0 of initial elevation estimate.