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Connected networks are a fundamental structure of neurobiology. Understanding these networks will help us elucidate the neural mechanisms of computation. Mathematically speaking these networks are `graphs' - structures containing objects that are connected. In neuroscience, the objects could be regions of the brain, e.g. fMRI data, or be individual neurons, e.g. calcium imaging with fluorescence microscopy. The formal study of graphs, graph theory, can provide neuroscientists with a large bank of algorithms for exploring networks. Graph theory has already been applied in a variety of ways to fMRI data but, more recently, has begun to be applied at the scales of neurons, e.g. from functional calcium imaging. In this primer we explain the basics of graph theory and relate them to features of microscopic functional networks of neurons from calcium imaging - neuronal graphs. We explore recent examples of graph theory applied to calcium imaging and we highlight some areas where researchers new to the field could go awry., Comment: 28 pages, 11 figures, 1 table, 2 boxes

Accurate and reliable nuclei identification is an essential part of quantification in microscopy. A range of mathematical and machine learning approaches are used but all methods have limitations. Such limitations include sensitivity to user parameters or a need for pre-processing in classical approaches or the requirement for relatively large amounts of training data in deep learning approaches. Here we demonstrate a new approach for nuclei detection that combines mathematical morphology with the Hilbert transform to detect the centres, sizes and orientations of elliptical objects. We evaluate this approach on datasets from the Broad Bioimage Benchmark Collection and compare it to established algorithms and previously published results. We show this new approach to outperform established classical approaches and be comparable in performance to deep-learning approaches. We believe this approach to be a competitive algorithm for nuclei detection in microscopy., Comment: 11 pages, 5 figures, 1 table. Pre-review submission

A wide range of biomedical applications requires enhancement, detection, quantification and modelling of curvilinear structures in 2D and 3D images. Curvilinear structure enhancement is a crucial step for further analysis, but many of the enhancement approaches still suffer from contrast variations and noise. This can be addressed using a multiscale approach that produces a better quality enhancement for low contrast and noisy images compared with a single-scale approach in a wide range of biomedical images. Here, we propose the Multiscale Top-Hat Tensor (MTHT) approach, which combines multiscale morphological filtering with a local tensor representation of curvilinear structures in 2D and 3D images. The proposed approach is validated on synthetic and real data and is also compared to the state-of-the-art approaches. Our results show that the proposed approach achieves high-quality curvilinear structure enhancement in synthetic examples and in a wide range of 2D and 3D images.

How do you use imaging to analyse the development of the heart, which not only changes shape but also undergoes constant, high-speed, quasi-periodic changes? We have integrated ideas from prospective and retrospective optical gating to capture long-term, phase-locked developmental time-lapse videos. In this paper we demonstrate the success of this approach over a key developmental time period: heart looping, where large changes in heart shape prevent previous prospective gating approaches from capturing phase-locked videos. We use the comparison with other approaches to in vivo heart imaging to highlight the importance of collecting the most appropriate data for the biological question., Comment: Carl J. Nelson and Charlotte Buckley and John J. Mullins and Martin A. Denvir and Jonathan Taylor, "Imaging the Developing Heart: Synchronized Timelapse Microscopy During Developmental Changes", Proc. SPIE (10499), 10499-41 (2018). Copyright 2018 Society of Photo Optical Instrumentation Engineers (SPIE)

Enhancement and detection of 3D vessel-like structures has long been an open problem as most existing image processing methods fail in many aspects, including a lack of uniform enhancement between vessels of different radii and a lack of enhancement at the junctions. Here, we propose a method based on mathematical morphology to enhance 3D vessel-like structures in biomedical images. The proposed method, 3D bowler-hat transform, combines sphere and line structuring elements to enhance vessel-like structures. The proposed method is validated on synthetic and real data and compared with state-of-the-art methods. Our results show that the proposed method achieves a high-quality vessel-like structures enhancement in both synthetic and real biomedical images, and is able to cope with variations in vessels thickness throughout vascular networks while remaining robust at junctions.

Enhancement, followed by segmentation, quantification and modelling, of blood vessels in retinal images plays an essential role in computer-aid retinopathy diagnosis. In this paper, we introduce a new vessel enhancement method which is the bowler-hat transform based on mathematical morphology. The proposed method combines different structuring elements to detect innate features of vessel-like structures. We evaluate the proposed method qualitatively and quantitatively, and compare it with the existing, state-of-the-art methods using both synthetic and real datasets. Our results show that the proposed method achieves high-quality vessel-like structure enhancement in both synthetic examples and in clinically relevant retinal images, and is shown to be able to detect fine vessels while remaining robust at junctions.

We consider the problem of configuration formation in modular robot systems where a set of modules that are initially in different configurations and located at different locations are required to assume appropriate positions so that they can get into a new, user-specified, target configuration. We propose a novel algorithm based on graph isomorphism, where the modules select locations or spots in the target configuration using a utility-based framework, while retaining their original configuration to the greatest extent possible, to reduce the time and energy required by the modules to assume the target configuration. We have shown analytically that our proposed algorithm is complete and guarantees a Pareto-optimal allocation. Experimental simulations of our algorithm with different number of modules in different initial configurations and located initially at different locations, show that the planning time of our algorithm is nominal (order of msec. for 100 modules). We have also compared our algorithm against a market-based allocation algorithm and shown that our proposed algorithm performs better in terms of time and number of messages exchanged.