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We introduce a non-parametric hierarchical Bayesian approach for open-ended 3D object categorization, named the Local Hierarchical Dirichlet Process (Local-HDP). This method allows an agent to learn independent topics for each category incrementally and to adapt to the environment in time. Hierarchical Bayesian approaches like Latent Dirichlet Allocation (LDA) can transform low-level features to high-level conceptual topics for 3D object categorization. However, the efficiency and accuracy of LDA-based approaches depend on the number of topics that is chosen manually. Moreover, fixing the number of topics for all categories can lead to overfitting or underfitting of the model. In contrast, the proposed Local-HDP can autonomously determine the number of topics for each category. Furthermore, the online variational inference method has been adapted for fast posterior approximation in the Local-HDP model. Experiments show that the proposed Local-HDP method outperforms other state-of-the-art approaches in terms of accuracy, scalability, and memory efficiency by a large margin. Moreover, two robotic experiments have been conducted to show the applicability of the proposed approach in real-time applications.