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Theoretical models of light-curve inversion that can be used in photomorphography, i.e., determination of the 3D shape and/or the light-scattering behavior of the surface of a body from disk-integrated photometry. These methods can be applied to atmosphereless bodies, mainly asteroids and planetary satellites, in the solar system. The inversion comprises three steps. First, a function containing data on the shape and the albedo variegation of an asteroid is determined. In the second step, separate expressions for the inverse of the Gaussian curvature and the albedo distribution are derived from the information obtained in the first step. In the third step, the nontrivial problem of determining the radius vector of the surface from the Gaussian curvature is solved by using iterative optimization procedures.

We have developed methods of inversion that can be used in the determination of the three-dimensional shape or the albedo distribution of the surface of a body from disk-integrated photometry, assuming the shape to be strictly convex. In addition to the theory of inversion methods, we have studied the practical aspects of the inversion problem and applied our methods to lightcurve data of 39 Laetitia and 16 Psyche.