Given new pairs of source and target point sets, standard point set registration methods often repeatedly
conduct the independent iterative search of desired geometric transformation to align the source point set
with the target one. This limits their use in applications to handle the real-time point set registration
with large volume dataset. This paper presents a novel method, named coherent point drift networks (CPD-Net),
for the unsupervised learning of geometric transformation towards real-time non-rigid point set registration.
In contrast to previous efforts (e.g. coherent point drift), CPD-Net can learn displacement field function
to estimate geometric transformation from a training dataset, consequently, to predict the desired
geometric transformation for the alignment of previously unseen pairs without any additional iterative
optimization process. Furthermore, CPD-Net leverages the power of deep neural networks to fit an arbitrary
function, that adaptively accommodates different levels of complexity of the desired geometric
transformation. Particularly, CPD-Net is proved with a theoretical guarantee to learn a continuous
displacement vector function that could further avoid imposing additional parametric smoothness constraint
as in previous works. Our experiments verify the impressive performance of CPD-Net for non-rigid point set
registration on various 2D/3D datasets, even in the presence of significant displacement noise, outliers,
and missing points. Our code will be available at this https URL.
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