A Proximal Bregman Projection Approach to Continuous Max-Flow Problems Using Entropic Distances

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.