The macroscopic shapes, rotational states, and scattering parameters of atmosphereless bodies can be deduced from photometric measurements of total brightnesses in different viewing/illumination geometries. The problem is solved with nonlinear optimization techniques; the use of positive definite quantities effectively removes the apparent ill-posedness of the problem. Since the parameters of scattering laws such as the Hapke model cannot be unambiguously determined from photometric data only, we propose a simple empirical scattering model for the purpose. Our methods can obtain convex hull-like shapes even for strongly nonconvex objects; a conception of the major concavities can also be formed.
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