Increasing Accuracy of Optimal Surfaces Using Min-Marginal Energies

Optimal surface methods are a class of graph cut methods posing surface estimation as an n-ary ordered labeling problem. They are used in medical imaging to find interacting and layered surfaces optimally and in low order polynomial time. Representing continuous surfaces with discrete sets of labels, however, leads to discretization errors and, if graph representations are made dense, excessive memory usage. Limiting memory usage and computation time of graph cut methods are important and graphs that locally adapt to the problem has been proposed as a solution. Min-marginal energies computed using dynamic graph cuts offer a way to estimate solution uncertainty and these uncertainties have been used to decide where graphs should be adapted. Adaptive graphs, however, introduce extra parameters, complexity, and heuristics. We propose a way to use min-marginal energies to estimate continuous solution labels that does not introduce extra parameters and show empirically on synthetic and medical imaging datasets that it leads to improved accuracy. The increase in accuracy was consistent and in many cases comparable with accuracy otherwise obtained with graphs up to eight times denser, but with proportionally less memory usage and improvements in computation time.