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.