Definition (Voronoi regions)

Let $Q$ be a NNVQ and let $\tilde{R}_{i}$ be the quantizer cells for $i=1,\dots,N$. We showed that $\tilde{R}_{1},\dots,\tilde{R}_{N}$ are Convex Polytopes and we call them the Voronoi Regions corresponding to reproduction points $\mathbf{c}_{1},\dots,\mathbf{c}_{N}$.