  We show that by extending the Laplacian formalism, which was first introduced
in the Graphics community to regularize 3D meshes, we can turn the monocular 3D
shape reconstruction of a deformable surface given correspondences with a
reference image into a much better-posed problem. This allows us to quickly and
reliably eliminate outliers by simply solving a linear least squares problem.
This yields an initial 3D shape estimate, which is not necessarily accurate,
but whose 2D projections are. The initial shape is then refined by a
constrained optimization problem to output the final surface reconstruction.
  Our approach allows us to reduce the dimensionality of the surface
reconstruction problem without sacrificing accuracy, thus allowing for
real-time implementations.
