  Random fields have remained a topic of great interest over past decades for
the purpose of structured inference, especially for problems such as image
segmentation. The local nodal interactions commonly used in such models often
suffer the short-boundary bias problem, which are tackled primarily through the
incorporation of long-range nodal interactions. However, the issue of
computational tractability becomes a significant issue when incorporating such
long-range nodal interactions, particularly when a large number of long-range
nodal interactions (e.g., fully-connected random fields) are modeled.
  In this work, we introduce a generalized random field framework based around
the concept of stochastic cliques, which addresses the issue of computational
tractability when using fully-connected random fields by stochastically forming
a sparse representation of the random field. The proposed framework allows for
efficient structured inference using fully-connected random fields without any
restrictions on the potential functions that can be utilized. Several
realizations of the proposed framework using graph cuts are presented and
evaluated, and experimental results demonstrate that the proposed framework can
provide competitive performance for the purpose of image segmentation when
compared to existing fully-connected and principled deep random field
frameworks.
