Automatic Nanoparticles Counting for <scp>TEM</scp> Images by Combination of Distance Transform, Watershed Segmentation and U‐Net Machine Learning

Accurate counting of nanoparticles in microscopy images such as SEM and TEM is critical for advancing materials science and nanotechnology. Though many conventional as well as novel methods exist to count particles in microscopy images, the presence of overlapping particles poses significant challenges. This study introduces a novel computational approach to count nanoparticles in microscopy images, addressing limitations in handling particle overlap. The proposed method integrates distance transform, watershed segmentation, and U-Net machine learning. Distance transform enhances finding center points of the particles; watershed segmentation effectively separates overlapping particles; and U-Net enables robust particle segmentation from complex image backgrounds. The methodology was first developed using computer-generated grayscale images with varying particle sizes and overlap percentages, then validated on a dataset of 17 TEM images (1022 × 668 pixels) of Fe₃O₄ and silica-coated Fe₃O₄ nanoparticles at 20 nm and 50 nm scales. Conventional convolution-based methods could accurately count non-overlapping particles but failed to give the accurate count when particles were overlapped. The accuracy of convolution-based methods also depended on kernel radius selection. Replacing convolution method with the distance transform and watershed method significantly improved the accuracy of particle counting in images with overlapping particles. The U-Net model, combined with a smooth blending algorithm, achieved a mean percentage error of 6.5% in particle counting on real TEM images. This approach demonstrates significant promise for applications in materials science, nanotechnology, and biology, where accurate particle quantification is essential. By addressing the limitations of conventional techniques, it offers a practical and efficient solution for automated nanoparticle analysis in microscopy images.