  Reconstructing 3D distributions from their 2D projections is a ubiquitous
problem in various scientific fields, particularly so in observational
astronomy. In this work, we present a new approach to solving this problem: a
Vienna inverse-Abel-transform based object reconstruction algorithm AVIATOR.
The reconstruction that it performs is based on the assumption that the
distribution along the line of sight is similar to the distribution in the
plane of projection, which requires a morphological analysis of the structures
in the projected image. The output of the AVIATOR algorithm is an estimate of
the 3D distribution in the form of a reconstruction volume that is calculated
without the problematic requirements that commonly occur in other
reconstruction methods such as symmetry in the plane of projection or modelling
of radial profiles. We demonstrate the robustness of the technique to different
geometries, density profiles, and noise by applying the AVIATOR algorithm to
several model objects. In addition, the algorithm is applied to real data: We
reconstruct the density and temperature distributions of two dense molecular
cloud cores and find that they are in excellent agreement with profiles
reported in the literature. The AVIATOR algorithm is thus capable of
reconstructing 3D distributions of physical quantities consistently using an
intuitive set of assumptions.
