An efficient region expansion algorithm for regular triangulated meshes

Region expansion-the growth of regions to include all points within a certain distance of their perimeters-is a basic, widely applicable operation, but is expensive to perform exactly. It has been shown that, if the solution is approximated by relaxing the distance metric to the L_∞-norm, efficiency can be greatly improved using properties of quadtrees. The method as described, however, requires the quadtrees to be square, both for the metric and the particular details of the algorithm. In some cases, such as spherical surface approximation, it is desirable for the quadtree nodes to be triangular instead. In this work, we thus describe an adaptation of the L_∞-norm metric and the previously described algorithm to allow efficient approximation of region expansion in images represented as regular triangulated meshes. Like the original method for square quadtrees, our algorithm achieves sublinear time with respect to expansion radius.