  One issue limiting the adaption of large-scale multi-region segmentation is
the sometimes prohibitive memory requirements. This is especially troubling
considering advances in massively parallel computing and commercial graphics
processing units because of their already limited memory compared to the
current random access memory used in more traditional computation. To address
this issue in the field of continuous max-flow segmentation, we have developed
a \textit{pseudo-flow} framework using the theory of Bregman proximal
projections and entropic distances which implicitly represents flow variables
between labels and designated source and sink nodes. This reduces the memory
requirements for max-flow segmentation by approximately 20\% for Potts models
and approximately 30\% for hierarchical max-flow (HMF) and directed acyclic
graph max-flow (DAGMF) models. This represents a great improvement in the
state-of-the-art in max-flow segmentation, allowing for much larger problems to
be addressed and accelerated using commercially available graphics processing
hardware.
