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

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 co- ordinates. 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.