Photogrammetric Texture Mapping onto Planar Polygons

This paper presents a mathematical description of texture mapping onto planar polygons from a photogrammetry viewpoint. In principle, this approach can accommodate textures acquired from a variety of camera systems including panoramic, strip, pushbroom, multispectral scanners and synthetic aperture radar, as well as the common frame (snap-shot) camera. The main focus of this paper, however, is the frame camera. When this type of camera photographs an object obliquely, the transformation between polygon and texture is characterized by a perspective projection rather than an affine transformation. In particular, we derive the rational linear texture mapping transformation equation and show how to compute its coefficients in two ways using known values for the relevant camera parameters. We also show that the denominator term in this transformation is not equivalent to perspective depth as it is when the textures are face-on to the polygon surface. Although the specific case of perspective texture projection onto planar polygons has been discussed before using techniques based upon homogeneous coordinates, we believe that this paper will be interesting and beneficial due to the intuitive basis of the photogrammetry concepts.