Total variation denoising in l1l^1 anisotropy

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of finding the solution is reduced to a finite algorithm. We discuss some implications of this result, for instance we use it to prove that continuity is preserved by both considered problems.Comment: 34 pages, 9 figure

Polar space based shape averaging for star-shaped biological objects

In this paper, we propose an averaging method for expert segmentation proposals of microbial organisms, resulting in a smooth, naturally looking segmentation ground truth. The approach exploits a geometrical property of the majority of the organisms - star-shapedness - and is based on contour averaging in polar space. It is robust and computationally efficient, where robustness is due to the absence of tuneable parameters. Moreover, the algorithm preserves the uncertainty (in terms of the standard deviation) of the experts' opinion, which allows to introduce an uncertainty-aware metric for estimation of the segmentation quality. This metric emphasizes the influence of ground truth regions with low variance. We study the performance of the proposed averaging method on time-lapse microscopy data of Corynebacterium glutamicum and the uncertainty-aware metric on synthetic data

Automated Characterization of Catalytically Active Inclusion Body Production in Biotechnological Screening Systems

We here propose an automated pipeline for the microscopy image-based characterization of catalytically active inclusion bodies (CatIBs), which includes a fully automatic experimental high-throughput workflow combined with a hybrid approach for multi-object microbial cell segmentation. For automated microscopy, a CatIB producer strain was cultivated in a microbioreactor from which samples were injected into a flow chamber. The flow chamber was fixed under a microscope and an integrated camera took a series of images per sample. To explore heterogeneity of CatIB development during the cultivation and track the size and quantity of CatIBs over time, a hybrid image processing pipeline approach was developed, which combines an ML-based detection of in-focus cells with model-based segmentation. The experimental setup in combination with an automated image analysis unlocks high-throughput screening of CatIB production, saving time and resources. Biotechnological relevance - CatIBs have wide application in synthetic chemistry and biocatalysis, but also could have future biomedical applications such as therapeutics. The proposed hybrid automatic image processing pipeline can be adjusted to treat comparable biological microorganisms, where fully data-driven ML-based segmentation approaches are not feasible due to the lack of training data. Our work is the first step towards image-based bioprocess control