A greedy region growing algorithm for anisotropic stretch adaptive triangulation of geometry images

The geometry image representation is a remeshing of an irregular triangle surface mesh onto a rectangular grid of points and facilitates the processing of surface geometry. Its connectivity is commonly generated by splitting each rectangular quad of grid points along the shorter diagonal. However, this simple approach typically yields skinny triangles on the surface when the underlying local surface metric tensor eigenvalues differ significantly. Sequences of such triangles can appear like jaggedness. This paper presents a greedy, region growing algorithm for anisotropic triangulation of geometry images obtained by geometric stretch parametrization. The algorithm compensates for the local stretch anisotropy and variations in the principal directions of the metric tensor by minimizing the total length of the new edges of triangles added to the grown region. The surface reconstructed is more faithful to the original surface than the ones reconstructed by quad-splitting connectivity and recognized triangulation approaches for point clouds.