Total 8-connectivity on the square raster

In order to avoid logical inconsistencies on the regular square raster, the foreground and the background in a binary image have to be treated differently during, for example, labelling or thinning operations. If the foreground is considered 8-connected, then the background has to be 4-connected, or vice versa. It is demonstrated that after certain topographic and possibly topological changes to a binary image, its foreground and background can both be considered 8-connected and the inconsistencies are eliminated. In particular, the foreground and background can be thinned using 8-connectivity. The erosion and dilatation problems that arise as a result of the changes can be overcome by constrained erosions and dilations which do not create possibilities of penetration or blocking of passages. After logical operations it is best to check the resultant image for penetration numbers