This stores all the data like a mesh, and even more storage than meshes; so you can calculate each sample based on this, why is it an implicit rather than explicit approach?
Does aliasing with level set methods cause problems in practice, like with interpreting medical data stored in this format? If so, how do we prevent misinterpreting results due to the effects of aliasing?
If this were in 3d, wouldn't we have to store a 3d grid of interpolated values? That seems really expensive because it takes O(n^3) memory where n is the side length.