PMBP: PatchMatch Belief Propagation for Correspondence Field Estimation – Supplementary Material

where M̂t→s(ut ) := Bt (ut ) − Ms→t (ut ) is called the pre-message from t to s. Note that the pre-message is a function of ut . In our implementation, we pull messages from nodes, rather than pushing them, which means that the message Mt→s(us) is pulled and calculated when the algorithm is updating node s, for all neighbours t. Consequently, since the pre-message M̂t→s(ut ) is a function of ut only, and thus independent from the states of s, we can cache all the pre-messages coming out of a certain node after having iterated over it. Since during one iteration, at each node, incoming messages need to be calculated every time a new particle is sampled, we gain in computational efficiency by using this caching mechanism.