  Surface registration is one of the most fundamental problems in geometry
processing. Many approaches have been developed to tackle this problem in cases
where the surfaces are nearly isometric. However, it is much more challenging
to compute correspondence between surfaces which are intrinsically less
similar. In this paper, we propose a variational model to align the
Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via
conformal deformations. This method enables us compute to geometric meaningful
point-to-point maps between non-isometric shapes. Our model is based on a novel
basis pursuit scheme whereby we simultaneously compute a conformal deformation
of a 'target shape' and its deformed LB eigensytem. We solve the model using an
proximal alternating minimization algorithm hybridized with the augmented
Lagrangian method which produces accurate correspondences given only a few
landmark points. We also propose a reinitialization scheme to overcome some of
the difficulties caused by the non-convexity of the variational problem.
Intensive numerical experiments illustrate the effectiveness and robustness of
the proposed method to handle non-isometric surfaces with large deformation
with respect to both noise on the underlying manifolds and errors within the
given landmarks.
