A 3D binary image I can be naturally represented
by a combinatorial-algebraic structure called cubical complex
and denoted by Q(I ), whose basic building blocks are
vertices, edges, square faces and cubes. In Gonzalez-Diaz
et al. (Discret Appl Math 183:59–77, 2015), we presented a
method to “locally repair” Q(I ) to obtain a polyhedral complex
P(I ) (whose basic building blocks are vertices, edges,
specific polygons and polyhedra), homotopy equivalent to
Q(I ), satisfying that its boundary surface is a 2D manifold.
P(I ) is called a well-composed polyhedral complex over the
picture I . Besides, we developed a new codification system
for P(I ), encoding geometric information of the cells
of P(I ) under the form of a 3D grayscale image, and the
boundary face relations of the cells of P(I ) under the form
of a set of structuring elements. In this paper, we build upon
(Gonzalez-Diaz et al. 2015) and prove that, to retrieve topological
and geometric information of P(I ), it is enough to
store just one 3D point per polyhedron and hence neither
grayscale image nor set of structuring elements are needed.
From this “minimal” codification of P(I ), we finally present
a method to compute the 2-cells in the boundary surface of
P(I ).Ministerio de Economía y Competitividad MTM2015-67072-
