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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

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.

This article outlines a procedure for speeding up segmentation of images using active mesh systems. Active meshes and other deformable models are very popular in image segmentation due to their ability to capture weak or missing boundary information; however, where strong edges exist, computations are still done after mesh nodes have settled on the boundary. This can lead to extra computational time whilst the system continues to deform completed regions of the mesh. We propose a local termination procedure, reducing these unnecessary computations and speeding up segmentation time with minimal loss of quality.