  We present a method for segmenting neuron membranes in 2D electron microscopy
imagery. This segmentation task has been a bottleneck to reconstruction efforts
of the brain's synaptic circuits. One common problem is the misclassification
of blurry membrane fragments as cell interior, which leads to merging of two
adjacent neuron sections into one via the blurry membrane region. Human
annotators can easily avoid such errors by implicitly performing gap
completion, taking into account the continuity of membranes.
  Drawing inspiration from these human strategies, we formulate the
segmentation task as an edge labeling problem on a graph with local topological
constraints. We derive an integer linear program (ILP) that enforces membrane
continuity, i.e. the absence of gaps. The cost function of the ILP is the
pixel-wise deviation of the segmentation from a priori membrane probabilities
derived from the data.
  Based on membrane probability maps obtained using random forest classifiers
and convolutional neural networks, our method improves the neuron boundary
segmentation accuracy compared to a variety of standard segmentation
approaches. Our method successfully performs gap completion and leads to fewer
topological errors. The method could potentially also be incorporated into
other image segmentation pipelines with known topological constraints.
