  We propose a novel Deformed Implicit Field (DIF) representation for modeling
3D shapes of a category and generating dense correspondences among shapes. With
DIF, a 3D shape is represented by a template implicit field shared across the
category, together with a 3D deformation field and a correction field dedicated
for each shape instance. Shape correspondences can be easily established using
their deformation fields. Our neural network, dubbed DIF-Net, jointly learns a
shape latent space and these fields for 3D objects belonging to a category
without using any correspondence or part label. The learned DIF-Net can also
provides reliable correspondence uncertainty measurement reflecting shape
structure discrepancy. Experiments show that DIF-Net not only produces
high-fidelity 3D shapes but also builds high-quality dense correspondences
across different shapes. We also demonstrate several applications such as
texture transfer and shape editing, where our method achieves compelling
results that cannot be achieved by previous methods.
