We consider an additive group structure in digital images and introduce the commutator in digital images. Then we calculate the hypercrossed complex pairings which generates a normal subgroup in dimension 2 and in dimension 3 by using 8-adjacency and 26-adjacency.
"Computing Hypercrossed Complex Pairings in Digital Images." Abstr. Appl. Anal. 2013 (SI12) 1 - 6, 2013. https://doi.org/10.1155/2013/675373