  As point clouds are 3D signals with permutation invariance, most existing
works train their reconstruction networks by measuring shape differences with
the average point-to-point distance between point clouds matched with
predefined rules. However, the static matching rules may deviate from actual
shape differences. Although some works propose dynamically-updated learnable
structures to replace matching rules, they need more iterations to converge
well. In this work, we propose a simple but effective reconstruction loss,
named Learnable Chamfer Distance (LCD) by dynamically paying attention to
matching distances with different weight distributions controlled with a group
of learnable networks. By training with adversarial strategy, LCD learns to
search defects in reconstructed results and overcomes the weaknesses of static
matching rules, while the performances at low iterations can also be guaranteed
by the basic matching algorithm. Experiments on multiple reconstruction
networks confirm that LCD can help achieve better reconstruction performances
and extract more representative representations with faster convergence and
comparable training efficiency. The source codes are provided in
https://github.com/Tianxinhuang/LCDNet.git.
