Lineage tracing, the joint segmentation and tracking of living cells as they move and divide in a sequence of light microscopy images, is a challenging task. Jug et al. [21] have proposed a mathematical abstraction of this task, the moral lineage tracing problem (MLTP), whose feasible solutions define both a segmentation of every image and a lineage forest of cells. Their branch-and-cut algorithm, however, is prone to many cuts and slow convergence for large instances. To address this problem, we make three contributions: (i) we devise the first efficient primal feasible local search algorithms for the MLTP, (ii) we improve the branch-and-cut algorithm by separating tighter cutting planes and by incorporating our primal algorithms, (iii) we show in experiments that our algorithms find accurate solutions on the problem instances of Jug et al. and scale to larger instances, leveraging moral lineage tracing to practical significance.

MOTIVATION: A significant focus of biological research is to understand the development, organization and function of tissues. A particularly productive area of study is on single layer epithelial tissues in which the adherence junctions of cells form a 2D manifold that is fluorescently labeled. Given the size of the tissue, a microscope must collect a mosaic of overlapping 3D stacks encompassing the stained surface. Downstream interpretation is greatly simplified by preprocessing such a dataset as follows: (i) extracting and mapping the stained manifold in each stack into a single 2D projection plane, (ii) correcting uneven illumination artifacts, (iii) stitching the mosaic planes into a single, large 2D image and (iv) adjusting the contrast. RESULTS: We have developed PreMosa, an efficient, fully automatic pipeline to perform the four preprocessing tasks above resulting in a single 2D image of the stained manifold across which contrast is optimized and illumination is even. Notable features are as follows. First, the 2D projection step employs a specially developed algorithm that actually finds the manifold in the stack based on maximizing contrast, intensity and smoothness. Second, the projection step comes first, implying all subsequent tasks are more rapidly solved in 2D. And last, the mosaic melding employs an algorithm that globally adjusts contrasts amongst the 2D tiles so as to produce a seamless, high-contrast image. We conclude with an evaluation using ground-truth datasets and present results on datasets from Drosophila melanogaster wings and Schmidtae mediterranea ciliary components. AVAILABILITY AND IMPLEMENTATION: PreMosa is available under https://cblasse.github.io/premosa. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Lineage tracing, the tracking of living cells as they move and divide, is a central problem in biological image analysis. Solutions, called lineage forests, are key to understanding how the structure of multicellular organisms emerges. We propose an integer linear program (ILP) whose feasible solutions define, for every image in a sequence, a decomposition into cells (segmentation) and, across images, a lineage forest of cells (tracing). In this ILP, path-cut inequalities enforce the morality of lineages, i.e., the constraint that cells do not merge. To find feasible solutions of this NP-hard problem, with certified bounds to the global optimum, we define efficient separation procedures and apply these as part of a branch-and-cut algorithm. To show the effectiveness of this approach, we analyze feasible solutions for real microscopy data in terms of bounds and run-time, and by their weighted edit distance to lineage forests traced by humans.