 The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian, restricted most computations to a thin band of active voxels immediately surrounding the interface, thus reducing the time complexity in three dimensions to formula_4 for most operations.Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an formula_5 operation in which voxels over the entire volume were accessed.The storage complexity for this narrowband scheme was still formula_6 Differential constructions over the narrow band domain edge require careful interpolation and domain alteration schemes to stabilise the solution.