Why the simplest “Hueckel” edge detector is a Roberts operator

The simplest nontrivial case of edge detection dealing with a 2 × 2 neighborhood is studied. In more complicated cases, namely larger neighborhoods, Hueckel's algorithm provides an approximate solution to an optimization problem. In this simple 2 × 2 case it is shown here that Hueckel's solution is exactly optimal. This allows us to interpret why Hueckel's operator turns out to be equivalent to the Roberts operator.