+encodes the foreground,
-the background, and
*the resulting crack edges.
sign of difference image insert cracks resulting CrackEdgeImage + . - . - . * . . . + - - . . . . . . * * * . + + - => + . + . - => . . . * . + + + . . . . . . . . * * + . + . + . . . . .
Starting from the original binary image (left), we insert crack pixels to get to the double-sized image (center). Finally, we mark all crack pixels whose non-crack neighbors have different signs as crack edge points, while all other pixels (crack and non-crack) become region pixels.
Requirements on a Crack Edge Image:
The last two requirements ensure that both edges and regions are 4-connected. Thus, 4-connectivity and 8-connectivity yield identical connected components in a Crack Edge Image (so called well-composedness). This ensures that Crack Edge Images have nice topological properties (cf. L. J. Latecki: "Well-Composed Sets", Academic Press, 2000).