We consider in $\mathbb{R}^2$ all curvature equation $\frac{\partial u}{\partial t}=|Du|G({\rm curv}(u))$ where G is a nondecreasing function and curv(u) is the curvature of the level line passing by x. These equations are invariant with respect to any contrast change u → g(u), with g nondecreasing. Consider the contrast invariant operator $T_t: u_o\to u(t)$. A Matheron theorem asserts that all contrast invariant operator T can be put in a form $(Tu)({\bf x}) = \inf_{B\in {\cal B}}\sup_{{\bf y}\in B} u({\bf x}+{\bf y})$. We show the asymptotic equivalence of both formulations. More precisely, we show that all curvature equations can be obtained as the iteration of Matheron operators $T_h^n$ where h → 0 and n → ∞ with nh=t.