We show dense voxel embeddings learned via deep metric learning can be employed to produce a highly accurate segmentation of neurons from 3D electron microscopy images. A metric graph on an arbitrary set of short and long-range edges can be constructed from the dense embeddings generated by a convolutional network. Partitioning the metric graph with long-range affinities as repulsive constraints can produce an initial segmentation with high precision, with substantial improvements on very thin objects. The convolutional embedding net is reused without any modification to agglomerate the systematic splits caused by complex "self-touching"' objects. Our proposed method achieves state-of-the-art accuracy on the challenging problem of 3D neuron reconstruction from the brain images acquired by serial section electron microscopy. Our alternative, object-centered representation could be more generally useful for other computational tasks in automated neural circuit reconstruction.