In this paper, we present a novel error measure to compare a computer-generated segmentation of images or volumes against ground truth. This measure, which we call Tolerant Edit Distance (TED), is motivated by two observations that we usually encounter in biomedical image processing: (1) Some errors, like small boundary shifts, are tolerable in practice. Which errors are tolerable is application dependent and should be explicitly expressible in the measure. (2) Non-tolerable errors have to be corrected manually. The effort needed to do so should be reflected by the error measure. Our measure is the minimal weighted sum of split and merge operations to apply to one segmentation such that it resembles another segmentation within specified tolerance bounds. This is in contrast to other commonly used measures like Rand index or variation of information, which integrate small, but tolerable, differences. Additionally, the TED provides intuitive numbers and allows the localization and classification of errors in images or volumes. We demonstrate the applicability of the TED on 3D segmentations of neurons in electron microscopy images where topological correctness is arguable more important than exact boundary locations. Furthermore, we show that the TED is not just limited to evaluation tasks. We use it as the loss function in a max-margin learning framework to find parameters of an automatic neuron segmentation algorithm. We show that training to minimize the TED, i.e., to minimize crucial errors, leads to higher segmentation accuracy compared to other learning methods.

Structured learning provides a powerful framework for empirical risk minimization on the predictions of structured models. It allows end-to-end learning of model parameters to minimize an application specific loss function. This framework is particularly well suited for discrete optimization models that are used for neuron reconstruction from anisotropic electron microscopy (EM) volumes. However, current methods are still learning unary potentials by training a classifier that is agnostic about the model it is used in. We believe the reason for that lies in the difficulties of (1) finding a representative training sample, and (2) designing an application specific loss function that captures the quality of a proposed solution. In this paper, we show how to find a representative training sample from human generated ground truth, and propose a loss function that is suitable to minimize topological errors in the reconstruction. We compare different training methods on two challenging EM-datasets. Our structured learning approach shows consistently higher reconstruction accuracy than other current learning methods.

Automated reconstruction of neural connectivity graphs from electron microscopy image stacks is an essential step towards large-scale neural circuit mapping. While significant progress has recently been made in automated segmentation of neurons and detection of synapses, the problem of synaptic partner assignment for polyadic (one-to-many) synapses, prevalent in the Drosophila brain, remains unsolved. In this contribution, we propose a method which automatically assigns pre- and postsynaptic roles to neurites adjacent to a synaptic site. The method constructs a probabilistic graphical model over potential synaptic partner pairs which includes factors to account for a high rate of one-to-many connections, as well as the possibility of the same neuron to be pre-synaptic in one synapse and post-synaptic in another. The algorithm has been validated on a publicly available stack of ssTEM images of Drosophila neural tissue and has been shown to reconstruct most of the synaptic relations correctly.