  The eigenfunctions of the Laplace-Beltrami operator have widespread
applications in a number of disciplines of engineering, computer
vision/graphics, machine learning, etc. These eigenfunctions or manifold
harmonics, provide the means to smoothly interpolate data on a manifold. They
are highly effective, specifically as it relates to geometry representation and
editing; manifold harmonics form a natural basis for multi-resolution
representation (and editing) of complex surfaces and functioned defined
therein. In this paper, we seek to develop the framework to exploit the
benefits of manifold harmonics for shape reconstruction. To this end, we
develop a highly compressible, multi-resolution shape reconstruction scheme
using manifold harmonics. The method relies on subdivision basis sets to
construct both boundary element isogeometric methods for analysis and surface
finite elements to construct manifold harmonics. We pair this technique with
the volumetric source reconstruction method to determine an initial starting
point. Examples presented highlight efficacy of the approach in the presence of
noisy data, including significant reduction in the number of degrees of freedom
for complex objects, the accuracy of reconstruction, and multi-resolution
capabilities.
