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Free Point Transformer (FPT) has been proposed as a data-driven, non-rigid point set registration approach using deep neural networks. As FPT does not assume constraints based on point vicinity or correspondence, it may be trained simply and in a flexible manner by minimizing an unsupervised loss based on the Chamfer Distance. This makes FPT amenable to real-world medical imaging applications where ground-truth deformations may be infeasible to obtain, or in scenarios where only a varying degree of completeness in the point sets to be aligned is available. To test the limit of the correspondence finding ability of FPT and its dependency on training data sets, this work explores the generalizability of the FPT from well-curated non-medical data sets to medical imaging data sets. First, we train FPT on the ModelNet40 dataset to demonstrate its effectiveness and the superior registration performance of FPT over iterative and learning-based point set registration methods. Second, we demonstrate superior performance in rigid and non-rigid registration and robustness to missing data. Last, we highlight the interesting generalizability of the ModelNet-trained FPT by registering reconstructed freehand ultrasound scans of the spine and generic spine models without additional training, whereby the average difference to the ground truth curvatures is 1.3 degrees, across 13 patients.