Radarclinometry of the Earth and Venus from SpaceShuttle and Venera15 Imagery
Abstract
The project to develop a lineintegral approach to 2dimensional radarclinometry and to bring it to the status of producing topographic maps from real radar images has been concluded. The final developments of the theory itself have involved a trialanderror resolution of the curvature decision process at each integration step over range as follows: (1) Locally Indeterminate AzimuthAzimuth Curvature is invoked if the rangedirected path of integration is within 1 ‡ in angle of the tangent to a local characteristic curve of the partial differential equation of radarclinometry (equivalent to a lapse in the necessity for an auxiliary curvature assumption); (2) Local Cylindricity is invoked if the local image isophote has a radiusofcurvature greater than 50 pixels; (3) LeastSquared Local Sphericity is invoked if the characteristic curve trends at greater than 70 ‡ to the range direction (the auxiliary curvature assumption is becoming a sufficiently strong influence as to warrant the overconstraint), and (4) the default hypothesis, which is invoked most often, is the localization through the Euler/Lagrange equation from the calculus of variations of the global principle of minimization of the surface area of the terrain. The development of the set of line integrals into a 2dimensional topographic surface is not practically achieved by branching the line integral at the range threshold, because the radarclinometry equations are too frequently coupled but weakly to the slope component in the direction of radarazimuth, and under circumstances for which the powerfully influential auxiliary curvature assumption is too unrealistic. In other words, a line integration in radarazimuth is far more frequently directed orthogonally to the local characteristic curve than is one carried out over range. Such orthogonality results in stepping the strike under the exclusive control of the curvature assumption. Instead, a quasisurfaceintegration step is taken by modeling the dependence on initial strike of the gravitational potential energy of the vertical slab of terrain under the rangeprofile. The adopted starting strike for the range integral is the one which minimizes the gravitational potential energy. This radarclinometric method, in combination with my recently published method for determining an effective radar backscattering function from onedimensional slope statistics and image pixelsignal statistics, was applied to three images. First, to separate theoretical difficulties from experimental impediments, an artificial radar image was generated from a topographic map of the Lake Champlain West quadrangle in the Adirondack Mountains. Except for the regional trend in elevation, to which radarclinometry is insensitive by design, the agreement between the original and derived topography appears good. The morphologies agree and the range of relief is the same to within 4%. As an example of data of the highest quality available from spaceborne radar at the present time, a SIRB image of very rugged terrain in the coastal mountains of Oregon was similarly processed. The result, after filtering to redistribute photoclinometric errors about the twodimensional spatial spectrum, agrees with ground truth almost as well. As an example of the worst possible data, in terms of signaltonoise ratio and radar incidence angle (no detraction from the praise due the first high resolution spaceborne radarimaging of Venus intended), a Venera15 image segment in Sedna Planitia just northeast of Sapho was processed, using Venera altimetry and Pioneer roughness data for slope statistics, in spite of the resolution mismatch. Considerably more trialanderror filtering was required. The result appears plausible, but an error check is, of course, impossible.
 Publication:

Earth Moon and Planets
 Pub Date:
 March 1990
 DOI:
 10.1007/BF00113857
 Bibcode:
 1990EM&P...48..197W
 Keywords:

 Earth Surface;
 Photogrammetry;
 Radar Maps;
 Relief Maps;
 Remote Sensing;
 Venus Surface;
 Earth Observations (From Space);
 Image Processing;
 Radar Imagery;
 Shuttle Imaging Radar;
 Space Based Radar;
 Venera Satellites;
 Lunar and Planetary Exploration