Representation of enclosing surfaces from simple voxelized objects by means of a chain code

• A new method for representing the enclosing surface of simple voxelized solids is described.
• We propose a new 3D chain code composed of nine elements for the representation of any voxelized surface.
• We suggest the use of Hamiltonian cycles tracking the enclosing surface of 3D solids as a method for representing 3D objects.
• A number of definitions and properties for this unidimensional descriptor are developed to give the basis for the analysis and manipulation of 3D objects directly from their chain.
• We derive from our method a sort of applications such as data compression and morphological transformation.

A chain code for representing three-dimensional (3D) simple objects is defined. Once digitalized, any solid composed of voxels and homeomorphic to the sphere can be described by means of a codified sequence of faces in the enclosing surface. This sequence is obtained from a Hamiltonian cycle in the face adjacency graph of such a surface. For the proposed code each chain element takes one of nine possible values and the length of a chain is determined by the number of faces in the surface. Since this code only considers relative changes of direction, the descriptor is invariant under rotation and translation. We also show some simple operations over the chain to make this descriptor invariant under mirroring and complement transformations. Finally, we present some results of this code applied to large objects and demonstrate its convenience over other codes. Part of the relevance of this work is the lossless compact representation of 3D objects by using a single chain regardless of its position and orientation.