Weakly well-composed cell complexes over nD pictures

In previous work we proposed a combinatorial algorithm to “locally repair” the cubical complex Q(I) that is canonically associated with a given 3D picture I. The algorithm constructs a 3D polyhedral complex P(I) which is homotopy equivalent to Q(I) and whose boundary surface is a 2D manifold. A polyhedral complex satisfying these properties is called well-composed. In the present paper we extend these results to higher dimensions. We prove that for a given n-dimensional picture the obtained cell complex is well-composed in a weaker sense but is still homotopy equivalent to the initial cubical complex.