Bijectivity conjecture for the polar curve and polar discriminant

Let $(X,x)$ be the germ under consideration, let $f$ be the defining function, and let $\ell$ be a linear form general enough. Write $\phi_\ell=(\ell,f):(X,x)\to(\mathbb{C}^2,0)$ for the induced map-germ, and let $\Gamma$ and $\Delta$ denote respectively the polar curve and polar discriminant of $f$ relative to $\ell$ at $0$. Bijectivity conjecture. The map-germ $\phi_\ell$ induces a bijective morphism between $\Gamma$ and $\Delta$. This assertion is used to simplify the construction of the vanishing polyhedron; the supplied text does not indicate whether it has been proved or disproved.