We describe a point-set registration algorithm based on a novel free point\ntransformer (FPT) network, designed for points extracted from multimodal\nbiomedical images for registration tasks, such as those frequently encountered\nin ultrasound-guided interventional procedures. FPT is constructed with a\nglobal feature extractor which accepts unordered source and target point-sets\nof variable size. The extracted features are conditioned by a shared multilayer\nperceptron point transformer module to predict a displacement vector for each\nsource point, transforming it into the target space. The point transformer\nmodule assumes no vicinity or smoothness in predicting spatial transformation\nand, together with the global feature extractor, is trained in a data-driven\nfashion with an unsupervised loss function. In a multimodal registration task\nusing prostate MR and sparsely acquired ultrasound images, FPT yields\ncomparable or improved results over other rigid and non-rigid registration\nmethods. This demonstrates the versatility of FPT to learn registration\ndirectly from real, clinical training data and to generalize to a challenging\ntask, such as the interventional application presented.\n