Self-Validated Learning for Particle Separation: A Correctness-Based Self-Training Framework Without Human Labels

Non-destructive 3D imaging of large multi-particulate samples is essential for quantifying particle-level properties, such as size, shape, and spatial distribution, across applications in mining, materials science, and geology. However, accurate instance segmentation of particles in tomographic data remains challenging due to high morphological variability and frequent particle contact, which limit the effectiveness of classical methods like watershed algorithms. While supervised deep learning approaches offer improved performance, they rely on extensive annotated datasets that are labor-intensive, error-prone, and difficult to scale. In this work, we propose self-validated learning, a novel self-training framework for particle instance segmentation that eliminates the need for manual annotations. Our method leverages implicit boundary detection and iteratively refines the training set by identifying particles that can be consistently matched across reshuffled scans of the same sample. This self-validation mechanism mitigates the impact of noisy pseudo-labels, enabling robust learning from unlabeled data. After just three iterations, our approach accurately segments over 97% of the total particle volume and identifies more than 54,000 individual particles in tomographic scans of quartz fragments. Importantly, the framework also enables fully autonomous model evaluation without the need for ground truth annotations, as confirmed through comparisons with state-of-the-art instance segmentation techniques. The method is integrated into the Biomedisa image analysis platform (https://github.com/biomedisa/biomedisa/).