How can we tell complex point clouds with different small scale characteristics apart, while disregarding global features? Can we find a suitable transformation of such data in a way that allows to discriminate between differences in this sense with statistical guarantees? In this paper, we consider the analysis and classification of complex point clouds as they are obtained, e.g., via single molecule localization microscopy. We focus on the task of identifying differences between noisy point clouds based on small scale characteristics, while disregarding large scale information such as overall size. We propose an approach based on a transformation of the data via the so-called Distance-to-Measure (DTM) function, a transformation which is based on the average of nearest neighbor distances. For each data set, we estimate the probability density of average local distances of all data points and use the estimated densities for classification. While the applicability is immediate and the practical performance of the proposed methodology is very good, the theoretical study of the density estimators is quite challenging, as they are based on non-i.i.d. observations that have been obtained via a complicated transformation. In fact, the transformed data are stochastically dependent in a non-local way that is not captured by commonly considered dependence measures. Nonetheless, we show that the asymptotic behaviour of the density estimator is driven by a kernel density estimator of certain i.i.d. random variables by using theoretical properties of $U$-statistics, which allows to handle the dependencies via a Hoeffding decomposition. We show via a numerical study and in an application to simulated single molecule localization microscopy data of chromatin fibers that unsupervised classification tasks based on estimated DTM-densities achieve excellent separation results.

MOTIVATIONS: De novo sequencing of genomes is followed by annotation analyses aiming at identifying functional genomic features such as genes, non-coding RNAs or regulatory sequences, taking advantage of diverse datasets. These steps sometimes fail at detecting non-coding functional sequences: for example, origins of replication, centromeres and rDNA positions have proven difficult to annotate with high confidence. Here, we demonstrate an unconventional application of Chromosome Conformation Capture (3C) technique, which typically aims at deciphering the average 3D organization of genomes, by showing how functional information about the sequence can be extracted solely from the chromosome contact map. RESULTS: Specifically, we describe a combined experimental and bioinformatic procedure that determines the genomic positions of centromeres and ribosomal DNA clusters in yeasts, including species where classical computational approaches fail. For instance, we determined the centromere positions in Naumovozyma castellii, where these coordinates could not be obtained previously. Although computed centromere positions were characterized by conserved synteny with neighboring species, no consensus sequences could be found, suggesting that centromeric binding proteins or mechanisms have significantly diverged. We also used our approach to refine centromere positions in Kuraishia capsulata and to identify rDNA positions in Debaryomyces hansenii. Our study demonstrates how 3C data can be used to complete the functional annotation of eukaryotic genomes. AVAILABILITY AND IMPLEMENTATION: The source code is provided in the Supplementary Material. This includes a zipped file with the Python code and a contact matrix of Saccharomyces cerevisiae. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Automatic segmentation and tracking of biological objects from dynamic microscopy data is of great interest for quantitative biology. A successful framework for this task are active contours, curves that iteratively minimize a cost function, which contains both data-attachment terms and regularization constraints reflecting prior knowledge on the contour geometry. However the choice of these latter terms and of their weights is largely arbitrary, thus requiring time-consuming empirical parameter tuning and leading to sub-optimal results. Here, we report on a first attempt to use regularization terms based on known biophysical properties of cellular membranes. The present study is restricted to 2D images and cells with a simple to skeletal cortex underlying the membrane. We describe our new active contour model and its implementation, and show a first application to real biological images. The obtained segmentation is slightly better than standard active contours, however the main advantage lies in the self-consistent and automated determination of the weights of regularization terms. This encouraging result will lead us to extend the approach to 3D and more complex cells.

We propose an extension of parametric active contours designed to track nonoccluding objects transiently touching each other, a task where both parametric and single level set-based methods usually fail. Our technique minimizes a cost functional that depends on all contours simultaneously and includes a penalty for contour overlaps. This scheme allows us to take advantage of known constraints on object topology, namely, that objects cannot merge. The coupled contours preserve the identity of previously isolated objects during and after a contact event, thus allowing segmentation and tracking to proceed as desired.

Cell migrations and deformations play essential roles in biological processes, such as parasite invasion, immune response, embryonic development, and cancer. We describe a fully automatic segmentation and tracking method designed to enable quantitative analyses of cellular shape and motion from dynamic three-dimensional microscopy data. The method uses multiple active surfaces with or without edges, coupled by a penalty for overlaps, and a volume conservation constraint that improves outlining of cell/cell boundaries. Its main advantages are robustness to low signal-to-noise ratios and the ability to handle multiple cells that may touch, divide, enter, or leave the observation volume. We give quantitative validation results based on synthetic images and show two examples of applications to real biological data.

This paper presents a segmentation and tracking method for quantitative analysis of cell dynamics from in vitro videomicroscopy data. The method is based on parametric active contours and includes several adaptations that address important difficulties of cellular imaging, particularly the presence of low-contrast boundary deformations known as pseudopods, and the occurence of multiple contacts between cells. First, we use an edge map based on the average intensity dispersion that takes advantage of relative background homogeneity to facilitate the detection of both pseudopods and interfaces between adjacent cells. Second, we introduce a repulsive interaction between contours that allows correct segmentation of objects in contact and overcomes the shortcomings of previously reported techniques to enforce contour separation. Our tracking technique was validated on a realistic data set by comparison with a manually defined ground-truth and was successfully applied to study the motility of amoebae in a biological research project.