Figure 1.

(a) Paraboloidal grey levels: I(x,y)=x²+5y². (b) The paraboloidal grey levels of (a), presented as a two-dimensional surface in three-dimensional space. (c) Gradient argument of (a). Discontinuity ray at the negative x-axis. (d) Y_arg of (a) (=(∂/∂y) of (c)). (e) Rotation of (a) (90° c.c.w.), calculation of gradient argument and inverse rotation. (f) Rotation of (a) (90° c.c.w.), calculation of Y_arg and inverse rotation. (g) Response of D_arg, the isotropic operator. (h) D_arg² (the square of (g)).