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Image registration is an indispensable process in the detection of brain structural and anatomical abnormities. Inverse-consistency, topology preserving and real time application are essential to provide accurate deformation fields for statistical analysis of brain variability. Unfortunately, the previous algorithms lacked of these features. We present a registration method by adapting the optimization procedure on a Lie pseudo-group so that the generated deformations are smooth with low energy of the deformation. In order to speed up the performance of registration method, we have implemented it on Nvidia 8800GTX GPU with Computer Unified Device Architecture (CUDA) platform. Experimental results indicate that large deformation compatible and topology preserving demonstrated through experiments on synthetic data and real brain CT images. Additionally, a faster runtime among the available GPU-based registration implementations against straight forward CPU version was achieved.