A binary three-dimensional (3D) image I is well-composed if the boundary
surface of its continuous analog is a 2D manifold. Since 3D images are not
often well-composed, there are several voxel-based methods ("repairing"
algorithms) for turning them into well-composed ones but these methods either
do not guarantee the topological equivalence between the original image and its
corresponding well-composed one or involve sub-sampling the whole image.
In this paper, we present a method to locally "repair" the cubical complex
Q(I) (embedded in R3) associated to I to obtain a polyhedral
complex P(I) homotopy equivalent to Q(I) such that the boundary of every
connected component of P(I) is a 2D manifold. The reparation is performed via
a new codification system for P(I) under the form of a 3D grayscale image
that allows an efficient access to cells and their faces