# Combining Mathematical Morphology and the Hilbert Transform for Fully Automatic Nuclei Detection in Fluorescence Microscopy

## TL;DR

This paper introduces a novel nuclei detection method combining mathematical morphology and the Hilbert transform, which outperforms classical methods and rivals deep learning in accuracy, offering a parameter-insensitive and efficient solution for microscopy analysis.

## Contribution

The paper presents a new nuclei detection technique that integrates mathematical morphology with the Hilbert transform, reducing reliance on training data and parameter tuning.

## Key findings

- Outperforms classical nuclei detection algorithms.
- Comparable in performance to deep learning methods.
- Effective on diverse microscopy datasets.

## Abstract

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.