Motivation: Serial section microscopy is an established method for detailed anatomy reconstruction of biological specimen. During the last decade, high resolution electron microscopy (EM) of serial sections has become the de-facto standard for reconstruction of neural connectivity at ever increasing scales (EM connectomics). In serial section microscopy, the axial dimension of the volume is sampled by physically removing thin sections from the embedded specimen and subsequently imaging either the block-face or the section series. This process has limited precision leading to inhomogeneous non-planar sampling of the axial dimension of the volume which, in turn, results in distorted image volumes. This includes that section series may be collected and imaged in unknown order. Results: We developed methods to identify and correct these distortions through image-based signal analysis without any additional physical apparatus or measurements. We demonstrate the efficacy of our methods in proof of principle experiments and application to real world problems. Availability and Implementation: We made our work available as libraries for the ImageJ distribution Fiji and for deployment in a high performance parallel computing environment. Our sources are open and available at http://github.com/saalfeldlab/section-sort, http://github.com/saalfeldlab/z-spacing and http://github.com/saalfeldlab/z-spacing-spark. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: To gain fundamental insight into the development of embryos, biologists seek to understand the fate of each and every embryonic cell. For the generation of cell tracks in embryogenesis, so-called tracking-by-assignment methods are flexible approaches. However, as every two-stage approach, they suffer from irrevocable errors propagated from the first stage to the second stage, here from segmentation to tracking. It is therefore desirable to model segmentation and tracking in a joint holistic assignment framework allowing the two stages to maximally benefit from each other. RESULTS: We propose a probabilistic graphical model, which both automatically selects the best segments from a time series of oversegmented images/volumes and links them across time. This is realized by introducing intra-frame and inter-frame constraints between conflicting segmentation and tracking hypotheses while at the same time allowing for cell division. We show the efficiency of our algorithm on a challenging 3D+t cell tracking dataset from Drosophila embryogenesis and on a 2D+t dataset of proliferating cells in a dense population with frequent overlaps. On the latter, we achieve results significantly better than state-of-the-art tracking methods. AVAILABILITY AND IMPLEMENTATION: Source code and the 3D+t Drosophila dataset along with our manual annotations will be freely available on http://hci.iwr.uni-heidelberg.de/MIP/Research/tracking/

The quality of any tracking-by-assignment hinges on the accuracy of the foregoing target detection / segmentation step. In many kinds of images, errors in this first stage are unavoidable. These errors then propagate to, and corrupt, the tracking result. Our main contribution is the first probabilistic graphical model that can explicitly account for over- and under segmentation errors even when the number of tracking targets is unknown and when they may divide, as in cell cultures. The tracking model we present implements global consistency constraints for the number of targets comprised by each detection and is solved to global optimality on reasonably large 2D+t and 3D+t datasets. In addition, we empirically demonstrate the effectiveness of a post processing that allows to establish target identity even across occlusion / under segmentation. The usefulness and efficiency of this new tracking method is demonstrated on three different and challenging 2D+t and 3D+t datasets from developmental biology.