Hyperplane patch mixing-and-folding decoder and weighted chamfer distance loss for 3D point set reconstruction.

3D point set reconstruction is an important and challenging 3D shape analysis task. Current state-of-the-art algorithms for 3D point set reconstruction employ a deep neural network (DNN) having an encoder–decoder architecture. Recently, the decoder DNNs that transform multiple 2D planar patches to reconstruct a 3D shape have seen some success. These "patch-folding" decoders are adept at approximating smooth surfaces in 3D objects. However, 3D point sets generated by these decoders often lack local geometrical details, as 2D planar patches tend to overly constrain the patch folding process. In this paper, we propose a novel decoder DNN for 3D point sets called Hyperplane Mixing and Folding Net (HMF-Net). HMF-Net uses less constrained hyperplane, not 2D plane, patches as its input to the folding process. HMF-Net has, as its core building block, a stack of token-mixing layers to effectively learn global consistency among the hyperplane patches. In addition to HMF-Net, we also propose a novel loss for 3D point set reconstruction called Weighted Chamfer Distance (WCD). WCD tries to weight, or amplify, loss from parts of shape that are highly variable across training samples by emphasizing higher point-pair distance values between a generated point set and a groundtruth point set. This helps the decoder DNN learn shape details better. We comprehensively evaluate our algorithm under three 3D point set reconstruction scenarios, that are, shape completion, shape upsampling, and shape reconstruction from 2D images. Experimental results demonstrate that our algorithm yields accuracies higher than the existing algorithms for 3D point set reconstruction. [ABSTRACT FROM AUTHOR]