One More Step Towards Well-Composedness Of Cell Complexes Over Nd Pictures

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 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((I) over bar) which decomposes the complement space of vertical bar P-S(I)vertical bar and prove that P-S((I) over bar) 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.