Abstract
An $n$-D pure regular cell complex $K$ is weakly well-composed (wWC) if, for each vertex $v$ of $K$, the set of $n$-cells incident to $v$ is face-connected. In previous work we proved that if an $n$-D picture $I$ is digitally well composed (DWC) then the cubical complex $Q(I)$ associated to $I$ is wWC. If $I$ is not DWC, we proposed a combinatorial algorithm to locally repair $Q(I)$ obtaining an $n$-D pure simplicial complex $P_S(I)$ homotopy equivalent to $Q(I)$ which is always wWC. In this paper we give a combinatorial procedure to compute a simplicial complex $P_S(\bar{I})$ which decomposes the complement space of $|P_S(I)|$ and prove that $P_S(\bar{I})$ is also wWC. This paper means one more step on the way to our ultimate goal: to prove that the $n$-D repaired complex is continuously well-composed (CWC), that is, the boundary of its continuous analog is an $(n-1)$-manifold.