Although homology describes the topology of 3D objects in terms of connected components, tunnels and cavities, it fails to resolve all matching and pattern recognition problems that arise in computer imaging. To enrich the topological tools available to us, we define two maps Delta_2 and Delta_3 on homology. The map Delta_2 is homologically dual to the cup product, and Delta_3 is the coassociator when the object is simply-connected. But whether or not Delta_3 is the coassociator in the non-simply connected setting is an open question. We exhibit experimental results for some simple 3D digital images.