Neighbourhood message passing computation on a lattice with cP systems

Abstract

We propose neighbourhood message passing (NMP), an abstract framework for loopy belief propagation (BP), as used in stereo matching (SM). We focus here on generic inter-processing-element messaging over a two-dimensional square grid, but our results apply to lattices of any shape through minimal modification. Specifically, this paper investigates three cP Systems (a type of P systems) models for loopy BP: One based on the classical globally synchronous BP, and two novel variants, (totally) asynchronous and locally synchronous. To model the classic globally synchronous NMP, we extend cP systems messaging rules with antiport features, similar to those used in other P systems. Next, we propose a novel version of NMP by extending it to the asynchronous case. We then derive a locally synchronous NMP variant, which arises naturally as a middle ground between our asynchronous and the classical globally synchronous variants. To clarify the operation of the asynchronous NMP system, we supply a short worked example. Following this, we analyse the proposed asynchronous system and prove that it uses precisely the same number of messages as the globally synchronous variant. We further put forward some runtime and correctness conjectures. Furthermore, we experimentally investigate the asynchronous system’s run-time characteristics. Messages spread from a given location on the lattice similarly in both the asynchronous and synchronous versions, even in the face of slow channels. We also conduct computer experiments and find that, in practice, the locally synchronous system is usually faster than the traditional globally synchronous approach (about 5–13%), and the asynchronous system is typically quicker still (often by approximately another 10%). We thus believe that it is a promising novel approach for faithful implementations of NMP and should be preferred.