Finite element technique versus polynomial solutions in parallax bar heighting from space photography (Q1200843)

Determination of object height using stereoscopic parallax measurements on a pair of overlapping vertical aerial photography is one of the well- known practices in the science of photogrammetry. The fundamental equation used in height determination using \(x\)-parallax measurements on a photographic stereopair of aerial photography is given by: (1) \(\Delta h=H\cdot \Delta P/(b+\Delta P)\), where \(H\) is the camera height above average ground level; \(b\) the photographic base (distance between principal point of left photo and conjugate principal point of right photo); \(\Delta P\) the difference in \(x\)-parallax between a point of known height on the stereopair and the point whose height is to be determined; and \(\Delta h\) is the corresponding height difference between the two points. Because of different camera tilts around the three axes, equation (1) gives only very crude object heights. These need to be corrected in order to obtain refined heights. The objective of this paper is to investigate the accuracy of parallax bar heighting using metric space photography, as represented by the Metric Camera (a calibrated aerial survey camera), and compare the results with those obtained when correction polynomials and Shepard's formula are used. A finite element approach to correct object heights obtained by the conventional parallax-height relationship of equation (1) is used. The efficiency of the method has been tested using two stereoscopic models. The results show that high accuracy values as high as \(\pm 0.2\) 0/00 H (equivalent to \(\pm 50\) m in ground terms) could be easily obtained with film transparencies. The author concludes that such accuracy may be quite sufficient for some basic thematic applications of space photography where only modest height accuracy values are required.