  We introduce a new machine learning approach for image segmentation that uses
a neural network to model the conditional energy of a segmentation given an
image. Our approach, combinatorial energy learning for image segmentation
(CELIS) places a particular emphasis on modeling the inherent combinatorial
nature of dense image segmentation problems. We propose efficient algorithms
for learning deep neural networks to model the energy function, and for local
optimization of this energy in the space of supervoxel agglomerations. We
extensively evaluate our method on a publicly available 3-D microscopy dataset
with 25 billion voxels of ground truth data. On an 11 billion voxel test set,
we find that our method improves volumetric reconstruction accuracy by more
than 20% as compared to two state-of-the-art baseline methods: graph-based
segmentation of the output of a 3-D convolutional neural network trained to
predict boundaries, as well as a random forest classifier trained to
agglomerate supervoxels that were generated by a 3-D convolutional neural
network.
