Constrained Inverse Volume Rendering for Planetary Nebulae

	He2-437 movie	M1-92 movie	Mz-3 movie

M. Magnor, G. Kindlmann, C. Hansen, N. Duric, "Reconstruction and Visualization of Planetary Nebulae," IEEE Trans. on Visualization and Computer Graphics, vol.11, no.5, pp.485-496, September 2005

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 the physics of the interacting gas flows), and because the glowing photo-ionized gas comprising the nebula exhibits negligible absorption. %self-occlusion. Making use of these properties, we present a technique to automatically recover the three-dimensional structure of bipolar planetary nebulae from conventional two-dimensional images. With GPU-based volume rendering driving a non-linear 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 three-dimensional nebula model is useful for astrophysics research, as well as offering novel viewpoints for educational displays, as in planetarium shows.

Our constrained inverse volume rendering (CIVR) approach is based on three physical and observational properties:

• The axisymmetry of bipolar PNe simplifies the reconstruction by reducing the 3D nebula volume to a 2D local emission density function of cylindrical coordinates.
• Scattering and absorption is negligible at visible wavelengths (at which our astronomical images are acquired).
• Planetary nebula span only a few arc minutes in the sky (less than a tenth of a degree), so their projected appearance is essentially orthographic.

Visualization Results Views from outer space: The planetary nebulae He2-437, M1-92, and Mz-3 (top to bottom) as they would look at inclination angles of 85 deg, 35 deg, and 10 deg (left to right). The strong variations in appearance has long prevented the discovery of the common nature of planetary nebulae.