A novel approach in modeling the empirical mode decomposition (EMD) is proposed here, allowing a perfect image recovery and, for instance, a straightforward extension for multidimensional $\mathbb{R}^{n}$ signals. In fact, thanks to a new sifting process modeling, where the two-dimensional (2-D) local mean envelope is formulated with the morphological median operator, we prove its consistency with a mean curvature motion-like partial differential equation. We provide both theoretical contributions and noticeable improvements in terms of quality of decomposition modes and computation times; our approach is illustrated on synthetic and real images, and compared to state of art 2-D EMD algorithms.