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   The retina is an ideal model for understanding the fundamental rules for how neural networks are constructed. The compact neural networks of the retina perform all of the initial processing of visual information before transmission to higher visual centers in the brain. The field of retinal connectomics uses high-resolution electron microscopy datasets to map the intricate organization of these networks and further our understanding of how these computations are performed by revealing the fundamental topologies and allowable networks behind retinal computations. In this article, we review some of the notable advances that retinal connectomics has provided in our understanding of the specific cells and the organization of their connectivities within the retina, as well as how these are shaped in development and break down in disease. Using these anatomical maps to inform modeling has been, and will continue to be, instrumental in understanding how the retina processes visual signals. 

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   Most current state-of-the-art connectome reconstruction pipelines have two major steps: initial pixel-based segmentation with affinity prediction and watershed transform, and refined segmentation by merging over-segmented regions. These methods rely only on local context and are typically agnostic to the underlying biology. Since a few merge errors can lead to several incorrectly merged neuronal processes, these algorithms are currently tuned towards over-segmentation producing an overburden of costly proofreading. We propose a third step for connectomics reconstruction pipelines to refine an over-segmentation using both local and global context with an emphasis on adhering to the underlying biology. We first extract a graph from an input segmentation where nodes correspond to segment labels and edges indicate potential split errors in the over-segmentation. In order to increase throughput and allow for large-scale reconstruction, we employ biologically inspired geometric constraints based on neuron morphology to reduce the number of nodes and edges. Next, two neural networks learn these neuronal shapes to further aid the graph construction process. Lastly, we reformulate the region merging problem as a graph partitioning one to leverage global context. We demonstrate the performance of our approach on four real-world connectomics datasets with an average variation of information improvement of 21.3%. 

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5. Network classification with applications to brain connectomics

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