Constrained inverse volume rendering for planetary nebulae

Determining the three-dimensional structure of distant astronomical objects is a challenging task, given that terrestrial observations provide only one viewpoint. For this task, bipolar planetary nebulae are interesting objects of study because of their pronounced axial symmetry due to fundamental physical processes. Making use of this symmetry constraint, we present a technique to automatically recover the axisymmetric structure of bipolar planetary nebulae from two-dimensional images. With GPU-based volume rendering driving a nonlinear optimization, we estimate the nebula's local emission density as a function of its radial and axial coordinates, and we recover the orientation of the nebula relative to Earth. The optimization refines the nebula model and its orientation by minimizing the differences between the rendered image and the original astronomical image. The resulting model enables realistic 3D visualizations of planetary nebulae, e.g. for educational purposes in planetarium shows. In addition, the recovered spatial distribution of the emissive gas allows validating computer simulation results of the astrophysical formation processes of planetary nebulae.