The work presented in this thesis addresses the problem of the automatic
extraction of the wiring diagram of a nervous system from anisotropic electron
microscopy volumes with high x- and y-resolution but low z-resolution, as
obtained by serial section electron microscopy imaging procedures.
A necessary step towards this goal is the segmentation of neural tissue to
separate neuron cell interior from membrane and extracellular space, and thus
reveal the 3D shape of each neuron, a process called

*neuron
reconstruction*.

The core of this thesis is a novel method for the reconstruction of neurons from
serial section electron microscopy images. Due to the anisotropy of serial
section imaging methods, we treat the data as a stack of 2D images, rather then
a continuous 3D volume.
However, the detection of neuron slices (i.e., cross-sections of neural
processes) in 2D images is difficult due to ambiguities in the data. Therefore,
we propose to enumerate several diverse and possibly contradictory candidate
neuron slices by identifying separating membranes with varying thresholds for
each image individually. Between candidates of adjacent images in the stack, we
enumerate assignments that reflect possible ways to follow a neural process from
one image to another. We assign costs to each candidate and assignment and
formulate constraints that ensure consistency between the assignments. We show
how a globally cost-minimal segmentation of neuron slices and assignments
between images can be found jointly and efficiently. Furthermore, we derive a
structured learning formulation to learn the assignment costs from annotated
ground truth and show its effectiveness compared to other methods.

Since the candidate selection is a crucial step in our model, we also introduce
an alternative candidate generation method that samples candidates from a
conditional random field (CRF) based on convolutional neural network
predictions. The CRF is designed and trained to capture the statistics of 2D
electron microscopy images of neural tissue. We show that sampling from this
model produces plausible neuron slice candidates that are well suited for our
reconstruction method, while additionally providing labels for synapse, glia
cells, and mitochondria.

For the application to very large datasets, inference has to be distributed.
However, since our model performs a global optimization, this is not trivial. We
tackle this problem by presenting a distribution scheme for our model that is
based on dual decomposition and guarantees global optimality. For that, the
original problem is decomposed into several regions that communicate with each
other to find an agreement. If such an agreement can be found, the collected
answers from all regions is provably optimal. We introduce a messaging strategy
that ensures that such an agreement can always be found under suitable
assumptions.

Finally, we review error measures used for neuron reconstruction algorithms and
discuss their properties. We introduce a new measure that reflects the edit
distance between a reconstruction and a ground truth within certain tolerated
variations and compare it to existing measures.

Given the extremely high accuracy requirements for biological use cases and the
challenging ambiguities encountered in EM images, the complete automatic
reconstruction of neurons is still out of reach. Nevertheless, we believe that
the methods introduced in this thesis made a significant contribution towards
this goal and can already be used to assist the tedious manual reconstruction.

[thesis]