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We introduce a labeled point set registration algorithm based on a family of novel information-theoretic measures derived as a generalization of the well-known Shannon entropy. This generalization, known as the Havrda-Charvat-Tsallis entropy, permits a fine-tuning between solution types of varying degrees of robustness of the divergence measure between multiple point sets. A variant of the traditional free-form deformation approach, known as directly manipulated free-form deformation, is used to model the transformation of the registration solution. We provide an overview of its open source implementation based on the Insight Toolkit of the National Institutes of Health. Characterization of the proposed framework includes comparison with other state of the art kernel-based methods and demonstration of its utility for lung registration via labeled point set representation of lung anatomy.