Topography from single radar images.
A mathematical theory and a corresponding numerical procedure have been developed to produce digital topography from radar images as digital photometric arrays. Thus, as radargrammetry is to photogrammetry, so radarclinometry is to photoclinometry. Photoclinometry encompasses a fundamental indeterminacy principle even for terrain that is homogeneous in normal albedo, because the surface normal consistent with a given reflected specific intensity is not unique. A geometric locus of such normal directions is implied, which generates a surface. For microwave backscatter, in specific application to radarclinometry, this surface is a cone whose half-angle is the incidence angle, whose axis contains the radar, and whose apex coincides with the terrain point. Although the indeterminacy can be removed if a properly directed profile of ground truth is available as a constraint, such is seldom the case. In its absence, an auxiliary assumption, such as that the strike line runs perpendicular to the illumination line, is needed. If metric integrity is a goal, then this is an absurd assumption. Herein, "the hypothesis of local cylindricity" has been assumed, a premise regarding the nature of topographic curvature that seems more realistic and that makes possible the production of topography as a set of parallel line integrals.
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