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