A new differential geometric method to rectify digital images of the Earth's surface using isothermal coordinates

Abstract

A new method to rectify monoscopic digital images and generate orthoimages of the Earth's surface is described. It replaces the standard procedure, which transfers the perspective projection of a frame photograph to an orthographic projection of pixels onto a reference plane using corresponding corrections. Instead, the perspective forward projection is kept but every pixel is vertically mapped along the surface normal onto a curved reference surface, for example, the ellipsoid of the World Geodetic System 1984 under the condition that a precise enough surface elevation model is available. The gained ellipsoidal coordinates (latitude, longitude and height) of each pixel are then transformed into isothermal coordinates like the Universal Transverse Mercator coordinates. Their differential geometric characteristics allow mapping every pixel to a reference plane producing, after some interpolation between irregularly spaced pixels, a photomap with the same geometric properties as any other topographic map. The suitability of the method is demonstrated by two photomaps from Ankara, Turkey, which are compared to high-quality topographic maps whereby the average position errors are about 2-3 pixels.