Accurate classification of white blood cells in peripheral blood is essential for diagnosing hematological diseases. Due to constantly evolving clinical settings, data sources, and disease classifications, it is necessary to update machine learning classification models regularly for practical real-world use. Such models significantly benefit from sequentially learning from incoming data streams without forgetting previously acquired knowledge. However, models can suffer from catastrophic forgetting, causing a drop in performance on previous tasks when fine-tuned on new data. Here, we propose a rehearsal-based continual learning approach for class incremental and domain incremental scenarios in white blood cell classification. To choose representative samples from previous tasks, we employ exemplar set selection based on the model's predictions. This involves selecting the most confident samples and the most challenging samples identified through uncertainty estimation of the model. We thoroughly evaluated our proposed approach on three white blood cell classification datasets that differ in color, resolution, and class composition, including scenarios where new domains or new classes are introduced to the model with every task. We also test a long class incremental experiment with both new domains and new classes. Our results demonstrate that our approach outperforms established baselines in continual learning, including existing iCaRL and EWC methods for classifying white blood cells in cross-domain environments.

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