  Although 3D point cloud data has received widespread attentions as a general
form of 3D signal expression, applying point clouds to the task of dense
correspondence estimation between 3D shapes has not been investigated widely.
Furthermore, even in the few existing 3D point cloud-based methods, an
important and widely acknowledged principle, i.e . one-to-one matching, is
usually ignored. In response, this paper presents a novel end-to-end
learning-based method to estimate the dense correspondence of 3D point clouds,
in which the problem of point matching is formulated as a zero-one assignment
problem to achieve a permutation matching matrix to implement the one-to-one
principle fundamentally. Note that the classical solutions of this assignment
problem are always non-differentiable, which is fatal for deep learning
frameworks. Thus we design a special matching module, which solves a doubly
stochastic matrix at first and then projects this obtained approximate solution
to the desired permutation matrix. Moreover, to guarantee end-to-end learning
and the accuracy of the calculated loss, we calculate the loss from the learned
permutation matrix but propagate the gradient to the doubly stochastic matrix
directly which bypasses the permutation matrix during the backward propagation.
Our method can be applied to both non-rigid and rigid 3D point cloud data and
extensive experiments show that our method achieves state-of-the-art
performance for dense correspondence learning.
