Technical note on the paper :

In Section 3.1 of [1] a methodology is presented to compute the salient points of a 3D mesh based on the computation of its protrusion function, see Equation (1) in [1]. Explicitly each point υ of the Mesh is examined as a potential salient point. Specifically a geodesic neighborhood is constructed for each point of the mesh and it is considered as a salient point if it is the local maximum of the protrusion function constrained to the points of the neighborhood. This methodology, although technically sound, has a high complexity, i.e. O(N Nmax log(Nmax)), where N is the number of vertices in the mesh and Nmax is the maximum number of points of the mesh that can be contained in the geodesic neighborhood of one of its vertices. This complexity has a significant impact on meshes containing more than 50k points and a methodology will be presented in order to reduce it. The discrete form of the protrusion function is given by Equation (2) in [1], where the mesh is tessellated into M compact regions { i V }, i.e. it is defined for each