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.Comment: 10 page

A Continuous Max-Flow Approach to Cyclic Field Reconstruction

Reconstruction of an image from noisy data using Markov Random Field theory has been explored by both the graph-cuts and continuous max-flow community in the form of the Potts and Ishikawa models. However, neither model takes into account the particular cyclic topology of specific intensity types such as the hue in natural colour images, or the phase in complex valued MRI. This paper presents \textit{cyclic continuous max-flow} image reconstruction which models the intensity being reconstructed as having a fundamentally cyclic topology. This model complements the Ishikawa model in that it is designed with image reconstruction in mind, having the topology of the intensity space inherent in the model while being readily extendable to an arbitrary intensity resolution.Comment: 8 pages, 1 figur

Shape Complexes in Continuous Max-Flow Hierarchical Multi-Labeling Problems

Although topological considerations amongst multiple labels have been previously investigated in the context of continuous max-flow image segmentation, similar investigations have yet to be made about shape considerations in a general and extendable manner. This paper presents shape complexes for segmentation, which capture more complex shapes by combining multiple labels and super-labels constrained by geodesic star convexity. Shape complexes combine geodesic star convexity constraints with hierarchical label organization, which together allow for more complex shapes to be represented. This framework avoids the use of co-ordinate system warping techniques to convert shape constraints into topological constraints, which may be ambiguous or ill-defined for certain segmentation problems.Comment: 9 pages, 1 figur