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This paper presents a unified image analysis approach for automated detection, segmentation, and classification of breast cancer nuclei using a neural network, which learns to cluster shapes and to classify nuclei. The proposed neural network is incrementally grown by creating a new cluster whenever a previously unseen shape is presented. Each hidden node represents a cluster used as a template to provide faster and more accurate nuclei detection and segmentation. Online learning gives the system improved performance with continued use. The effectiveness of the resulting system is demonstrated on a task of cytological image analysis, with classification of individual nuclei used to diagnose the sample. This demonstrates the potential effectiveness of such a system on diagnostic tasks that require the classification of individual cells.