FoR$^2$M: Recognition and Repair of Foldings in Mesh Surfaces. Application to 3D Object Degradation

Abstract: Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the self-intersections that may be present in mesh surfaces that have been created by a scanning procedure or by a deformation transformation, such as off-setting. Mesh foldings comprise a special case of mesh surface self-intersections, where the faces of the 3D model intersect and become reversed, with respect to the unfolded part of the mesh surface. A novel method for the recognition and repair of mesh surface foldings is presented, which exploits the structural characteristics of the foldings in order to efficiently detect the folded regions. Following detection, the foldings are removed and any gaps so created are filled based on the geometry of the 3D model. The proposed method is directly applicable to simple mesh surface representations while it does not perform any embedding of the 3D mesh (i.e. voxelization, projection). Target of the proposed method is to facilitate mesh degradation procedures in a fashion that retains the original structure, given the operator, in the most efficient manner.