Understanding the structure of coronal mass ejections (CMEs) is one of the primary challenges in solar astrophysics. White-light coronagraphs make images of line-of-sight projections of the CME electron density (Ne ). The combination of the coronagraphs on the STEREO and SOHO spacecraft provides three simultaneous viewpoints that vary in angle with time, according to the spacecraft orbits. Three viewpoints are not enough to permit tomographic reconstruction via classical methods, but we argue here that recent advances in image processing methods that take into account prior information about the CME geometry may allow one to determine the CME density structure with only three viewpoints. The prior information considered here is that the CME is separated from a known (or simple) background by a closed surface, which may be described by a level set. We propose an alternating iterative procedure in which the surface is evolved via geometric partial differential equations in one step and the interior (and exterior) Ne values are determined in the next step.