“Geometry-Topology” Iterative Optimization for Mesh Inpainting

In this paper, a "geometry-topology" iterative optimization algorithm is proposed for feature preserved mesh inpainting. For a given incomplete triangular mesh model, the hole boundaries are first identified and dynamic programming algorithm is adapted to initialize the hole areas and construct the topology connectivity for the holes. Then, a pair of feature points on the boundary of each hole is identified and roughly fit the feature curve based on the feature points and their normals. The local connectivity of mesh hole is adjusted under the guidance of the feature curve. This is what we named the topology adjustment. For the geometry optimization, a local variational energy function is built based on the hole and its N ring neighborhood based on total variation, and solves this energy function iteratively to get the optimal vertex positions. Finally, local topology adjustment and geometry optimization are alternately repeated until there is no topology adjustment occurs. Parts of the existing complete meshes are manually removed to get the incomplete models with holes. Compared with other algorithms, proposed algorithm can effectively restore the salient features of the hole areas, and has obvious advantages in repair time and error statistics.