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An extended registration model is presented to register medical image triples acquired for brain dopamine receptor scintigraphies. The model operates with rigid and nonlinear transformations in parallel, where all transformation parameters are optimized by one optimization method. The concept of the transformation-sampling-similarity measurement minimizes the memory usage of a real implementation. A partial-fine sampling method is proposed to decrease the processing time of the registration. Real medical data was collected to compare our method with well-known prior ones. The first tests show that the model outperforms the classic registration methods in both speed and accuracy.