In the cerebral cortex, local circuits consist of tens of thousands of neurons, each of which makes thousands of synaptic connections. Perhaps the biggest impediment to understanding these networks is that we have no wiring diagrams of their interconnections. Even if we had a partial or complete wiring diagram, however, understanding the network would also require information about each neuron’s function. Here we show that the relationship between structure and function can be studied in the cortex with a combination of in vivo physiology and network anatomy. We used two-photon calcium imaging to characterize a functional property–the preferred stimulus orientation–of a group of neurons in the mouse primary visual cortex. Large-scale electron microscopy of serial thin sections was then used to trace a portion of these neurons’ local network. Consistent with a prediction from recent physiological experiments, inhibitory interneurons received convergent anatomical input from nearby excitatory neurons with a broad range of preferred orientations, although weak biases could not be rejected.

We introduce an efficient search strategy to substantially accelerate feature based registration. Previous feature based registration algorithms often use truncated search strategies in order to achieve small computation times. Our new accelerated search strategy is based on the realization that the search for corresponding features can be dramatically accelerated by utilizing Johnson-Lindenstrauss dimension reduction. Order of magnitude calculations for the search strategy we propose here indicate that the algorithm proposed is more than a million times faster than previously utilized naive search strategies, and this advantage in speed is directly translated into an advantage in accuracy as the fast speed enables more comparisons to be made in the same amount of time. We describe the accelerated scheme together with a full complexity analysis. The registration algorithm was applied to large transmission electron microscopy (TEM) images of neural ultrastructure. Our experiments demonstrate that our algorithm enables alignment of TEM images with increased accuracy and efficiency compared to previous algorithms.

3D reconstruction from serial 2D microscopy images depends on non-linear alignment of serial sections. For some structures, such as the neuronal circuitry of the brain, very large images at very high resolution are necessary to permit reconstruction. These very large images prevent the direct use of classical registration methods. We propose in this work a method to deal with the non-linear alignment of arbitrarily large 2D images using the finite support properties of cubic B-splines. After initial affine alignment, each large image is split into a grid of smaller overlapping sub-images, which are individually registered using cubic B-splines transformations. Inside the overlapping regions between neighboring sub-images, the coefficients of the knots controlling the B-splines deformations are blended, to create a virtual large grid of knots for the whole image. The sub-images are resampled individually, using the new coefficients, and assembled together into a final large aligned image. We evaluated the method on a series of large transmission electron microscopy images and our results indicate significant improvements compared to both manual and affine alignment.