
Except for that normalization which converts the gradient vector to a surface normal.Once we build in that normalization, we have G, the geometry tensor. G tells you everything you might want to know about implicit surface curvature, so it is G that we measure for our curvature-based transfer functions.
[Note: This was sneaky. The normalization which converts the gradient vector to the surface normal includes a minus sign, but that is NOT implied by my diagrams, because they would be too confusing otherwise. I figured that those in the audience who caught this sloppiness would sympathize, and those who didn't would be none the wiser....]