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This paper addresses the problem of jointly clustering two segmentations of closely correlated images. We focus in particular on the application of reconstructing neuronal structures in over-segmented electron microscopy images. We formulate the problem of co-clustering as a quadratic semi-assignment problem and investigate convex relaxations using semidefinite and linear programming. We further introduce a linear programming method with manageable number of constraints and present an approach for learning the cost function. Our method increases computational efficiency by orders of magnitude while maintaining accuracy, automatically finds the optimal number of clusters, and empirically tends to produce binary assignment solutions. We illustrate our approach in simulations and in experiments with real EM data.

Future progress in neuroscience hinges on reconstruction of neuronal circuits to the level of individual synapses. Because of the specifics of neuronal architecture, imaging must be done with very high resolution and throughput. While Electron Microscopy (EM) achieves the required resolution in the transverse directions, its depth resolution is a severe limitation. Computed tomography (CT) may be used in conjunction with electron microscopy to improve the depth resolution, but this severely limits the throughput since several tens or hundreds of EM images need to be acquired. Here, we exploit recent advances in signal processing to obtain high depth resolution EM images computationally. First, we show that the brain tissue can be represented as sparse linear combination of local basis functions that are thin membrane-like structures oriented in various directions. We then develop reconstruction techniques inspired by compressive sensing that can reconstruct the brain tissue from very few (typically 5) tomographic views of each section. This enables tracing of neuronal connections across layers and, hence, high throughput reconstruction of neural circuits to the level of individual synapses.