  Three dimensional (3D) interest point detection plays a fundamental role in
3D computer vision and graphics. In this paper, we introduce a new method for
detecting mesh interest points based on geometric measures and sparse
refinement (GMSR). The key point of our approach is to calculate the 3D
interest point response function using two intuitive and effective geometric
properties of the local surface on a 3D mesh model, namely Euclidean distances
between the neighborhood vertices to the tangent plane of a vertex and the
angles of normal vectors of them. The response function is defined in
multi-scale space and can be utilized to effectively distinguish 3D interest
points from edges and flat areas. Those points with local maximal 3D interest
point response value are selected as the candidates of 3D interest points.
Finally, we utilize an $\ell_0$ norm based optimization method to refine the
candidates of 3D interest points by constraining its quality and quantity.
Numerical experiments demonstrate that our proposed GMSR based 3D interest
point detector outperforms current several state-of-the-art methods for
different kinds of 3D mesh models.
