  The sparse representation of signals defined on Euclidean domains has been
successfully applied in signal processing. Bringing the power of sparse
representations to non-regular domains is still a challenge, but promising
approaches have started emerging recently. In this paper, we investigate the
problem of sparsely representing discrete surfaces and propose a new
representation that is capable of providing tools for solving different
geometry processing problems. The sparse discrete surface representation is
obtained by combining innovative approaches into an integrated method. First,
to deal with irregular mesh domains, we devised a new way to subdivide discrete
meshes into a set of patches using a feature-aware seed sampling. Second, we
achieve good surface approximation with over-fitting control by combining the
power of a continuous global dictionary representation with a modified
Orthogonal Marching Pursuit. The discrete surface approximation results
produced were able to preserve the shape features while being robust to
over-fitting. Our results show that the method is quite promising for
applications like surface re-sampling and mesh compression.
