  We present Free Point Transformer (FPT) - a deep neural network architecture
for non-rigid point-set registration. Consisting of two modules, a global
feature extraction module and a point transformation module, FPT does not
assume explicit constraints based on point vicinity, thereby overcoming a
common requirement of previous learning-based point-set registration methods.
FPT is designed to accept unordered and unstructured point-sets with a variable
number of points and uses a "model-free" approach without heuristic
constraints. Training FPT is flexible and involves minimizing an intuitive
unsupervised loss function, but supervised, semi-supervised, and partially- or
weakly-supervised training are also supported. This flexibility makes FPT
amenable to multimodal image registration problems where the ground-truth
deformations are difficult or impossible to measure. In this paper, we
demonstrate the application of FPT to non-rigid registration of prostate
magnetic resonance (MR) imaging and sparsely-sampled transrectal ultrasound
(TRUS) images. The registration errors were 4.71 mm and 4.81 mm for complete
TRUS imaging and sparsely-sampled TRUS imaging, respectively. The results
indicate superior accuracy to the alternative rigid and non-rigid registration
algorithms tested and substantially lower computation time. The rapid inference
possible with FPT makes it particularly suitable for applications where
real-time registration is beneficial.
