An nD 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 nD 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 nD pure simplicial complex PS(I)
homotopy equivalent to Q(I) which is always wWC. In this paper we give
a combinatorial procedure to compute a simplicial complex PS(¯I) which
decomposes the complement space of |PS(I)| and prove that PS(¯I) is also
wWC. This paper means one more step on the way to our ultimate goal:
to prove that the nD repaired complex is continuously well-composed
(CWC), that is, the boundary of its continuous analog is an (n − 1)-
manifold.Ministerio de Economía y Competitividad MTM2015-67072-