The isotropicity definition clearly states uniform response on all orientation; hence, on images, the brightness magnitude should not be different for different dimensions. However, it is not clear for me how to test a given edge-detector-function for isotropicity.
For example, I'd like to test the following edge detector for isotropicity:
(Ex^2-Ey^2)ExEy-Exy(Exx-Eyy); (E being the intensity function (E(x,y)), while the Ex and Ey denote corresponding derivatives; as well as Exx and Eyy denoting second derivatives.)