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 a set of edges between voxels is constructed from the dense voxel embeddings generated by a convolutional network. Partitioning the metric graph with long-range edges as repulsive constraints yields an initial segmentation with high precision, with substantial accuracy gain for very thin objects. The convolutional embedding net is reused without any modification to agglomerate the systematic splits caused by complex "self-contact" motifs. 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.

We define and study error detection and correction tasks that are useful for 3D reconstruction of neurons from electron microscopic imagery, and for image segmentation more generally. Both tasks take as input the raw image and a binary mask representing a candidate object. For the error detection task, the desired output is a map of split and merge errors in the object. For the error correction task, the desired output is the true object. We call this object mask pruning, because the candidate object mask is assumed to be a superset of the true object. We train multiscale 3D convolutional networks to perform both tasks. We find that the error-detecting net can achieve high accuracy. The accuracy of the error-correcting net is enhanced if its input object mask is ``advice'' (union of erroneous objects) from the error-detecting net.

Convolutional networks (ConvNets) have become a popular approach to computer vision. It is important to accelerate ConvNet training, which is computationally costly. We propose a novel parallel algorithm based on decomposition into a set of tasks, most of which are convolutions or FFTs. Applying Brent's theorem to the task dependency graph implies that linear speedup with the number of processors is attainable within the PRAM model of parallel computation, for wide network architectures. To attain such performance on real shared-memory machines, our algorithm computes convolutions converging on the same node of the network with temporal locality to reduce cache misses, and sums the convergent convolution outputs via an almost wait-free concurrent method to reduce time spent in critical sections. We implement the algorithm with a publicly available software package called ZNN. Benchmarking with multi-core CPUs shows that ZNN can attain speedup roughly equal to the number of physical cores. We also show that ZNN can attain over 90× speedup on a many-core CPU (Xeon Phi™ Knights Corner). These speedups are achieved for network architectures with widths that are in common use. The task parallelism of the ZNN algorithm is suited to CPUs, while the SIMD parallelism of previous algorithms is compatible with GPUs. Through examples, we show that ZNN can be either faster or slower than certain GPU implementations depending on specifics of the network architecture, kernel sizes, and density and size of the output patch. ZNN may be less costly to develop and maintain, due to the relative ease of general-purpose CPU programming.

Sliding window convolutional networks (ConvNets) have become a popular approach to computer vision problems such as image segmentation and object detection and localization. Here we consider the parallelization of inference, i.e., the application of a previously trained ConvNet, with emphasis on 3D images. Our goal is to maximize throughput, defined as the number of output voxels computed per unit time. We propose CPU and GPU primitives for convolutional and pooling layers, which are combined to create CPU, GPU, and CPU-GPU inference algorithms. The primitives include convolution based on highly efficient padded and pruned FFTs. Our theoretical analyses and empirical tests reveal a number of interesting findings. For example, adding host RAM can be a more efficient way of increasing throughput than adding another GPU or more CPUs. Furthermore, our CPU-GPU algorithm can achieve greater throughput than the sum of CPU-only and GPU-only throughputs.

Efforts to automate the reconstruction of neural circuits from 3D electron microscopic (EM) brain images are critical for the field of connectomics. An important computation for reconstruction is the detection of neuronal boundaries. Images acquired by serial section EM, a leading 3D EM technique, are highly anisotropic, with inferior quality along the third dimension. For such images, the 2D max-pooling convolutional network has set the standard for performance at boundary detection. Here we achieve a substantial gain in accuracy through three innovations. Following the trend towards deeper networks for object recognition, we use a much deeper network than previously employed for boundary detection. Second, we incorporate 3D as well as 2D filters, to enable computations that use 3D context. Finally, we adopt a recursively trained architecture in which a first network generates a preliminary boundary map that is provided as input along with the original image to a second network that generates a final boundary map. Backpropagation training is accelerated by ZNN, a new implementation of 3D convolutional networks that uses multicore CPU parallelism for speed. Our hybrid 2D-3D architecture could be more generally applicable to other types of anisotropic 3D images, including video, and our recursive framework for any image labeling problem.