The field of quaternion-based systems and medical imaging analysis is witnessing significant developments, with a focus on innovative applications and methodological advancements. Researchers are exploring the potential of quaternions in representing rotations and postures, leading to improved designs for observer systems and neural networks. Additionally, quaternion-valued neural networks are being proposed for supervised learning tasks, offering advantages in terms of convergence and reliability. In the domain of medical imaging analysis, novel frameworks are being introduced for automated white blood cell classification and segmentation, as well as for analyzing circulating blood cell clusters. These frameworks leverage deep learning techniques, such as saliency-guided feature fusion and multi-channel flow cytometry imaging, to achieve high accuracy and interpretability. Noteworthy papers in this area include the development of a quaternion-valued supervised learning Hopfield-structured neural network, which achieves high accuracy and fast convergence, and the introduction of a saliency-guided cross-layer deep feature fusion framework for white blood cell analysis, which offers a practical and explainable path toward more reliable automated analysis. Furthermore, the application of deep learning techniques to malaria detection from blood cell images has shown promising results, with certain networks achieving average accuracy of over 97%. Overall, these advancements are contributing to the growth of quaternion-based systems and medical imaging analysis, with potential applications in various fields, including robotics, control systems, and clinical workflows.