  This paper addresses the problem of computing dense correspondence between 3D
shapes in the form of point clouds, which is a challenging and fundamental
problem in computer vision and digital geometry processing. Conventional
approaches often solve the problem in a supervised manner, requiring massive
annotated data, which is difficult and/or expensive to obtain. Motivated by the
intuition that one can transform two aligned point clouds to each other more
easily and meaningfully than a misaligned pair, we propose CorrNet3D -- the
first unsupervised and end-to-end deep learning-based framework -- to drive the
learning of dense correspondence by means of deformation-like reconstruction to
overcome the need for annotated data. Specifically, CorrNet3D consists of a
deep feature embedding module and two novel modules called correspondence
indicator and symmetric deformation. Feeding a pair of raw point clouds, our
model first learns the pointwise features and passes them into the indicator to
generate a learnable correspondence matrix used to permute the input pair. The
symmetric deformer, with an additional regularized loss, transforms the two
permuted point clouds to each other to drive the unsupervised learning of the
correspondence. The extensive experiments on both synthetic and real-world
datasets of rigid and non-rigid 3D shapes show our CorrNet3D outperforms
state-of-the-art methods to a large extent, including those taking meshes as
input. CorrNet3D is a flexible framework in that it can be easily adapted to
supervised learning if annotated data are available.
