NASM: Neural Anisotropic Surface Meshing

TL;DR

A graph neural network is proposed to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve curvature-based anisotropic metric by using a dot product loss between high-d edge vectors to dramatically reduce the computational time and increase the scalability.

Abstract

This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve curvature-based anisotropic metric by using a dot product loss between high-d edge vectors. This can dramatically reduce the computational time and increase the scalability. Then, we propose a novel feature-sensitive remeshing on the generated high-d embedding to automatically capture sharp geometric features. We define a high-d normal metric, and then derive an automatic differentiation on a high-d centroidal Voronoi tessellation (CVT) optimization with the normal metric to simultaneously preserve geometric features and curvature anisotropy that exhibit in the original 3D shapes. To our knowledge, this is the first time that a deep learning framework and a large dataset are proposed to construct a high-d Euclidean embedding space for 3D anisotropic surface meshing. Experimental results are evaluated and compared with the state-of-the-art in anisotropic surface meshing on a large number of surface models from Thingi10K dataset as well as tested on extensive unseen 3D shapes from Multi-Garment Network dataset and FAUST human dataset.

Figures (19)

• Figure 1: The overview pipeline of the proposed neural anisotropic surface meshing (NASM) approach. Our method includes two main components: neural high-d Euclidean embedding and high-d normal metric CVT for feature-sensitive anisotropic meshing. The training data for neural high-d Euclidean embedding is generated based on $\text{SIFHDE}^2$Embedding2018. More details are given in Section A of Supplemental Document.
• Figure 2: The architecture of the proposed high-d Euclidean embedding network. Each residual block combines two graph convolution layers with skip-connection. Each convolution layer is followed by a normalization layer and an activation layer except the output layer. The numbers represent the feature dimensions of each network layer. The graph convolution computation and neighboring feature aggregation are illustrated in detail.
• Figure 3: Our anisotropic surface meshing results on smooth surfaces (top three rows) and surfaces with sharp or weak features (bottom four rows). (left to right: curvature tensors with corresponding stretching ratios denoted in colors, anisotropic meshing, and a zoom-in illustration). The files' IDs are provided from Thingi10k dataset. Left column: $133077,76778,46461,741525,81589,87688,51015$; Right column: $72870,68380,61258,39086,40992,107910,75989$.
• Figure 4: Comparison between our method and $\text{SIFHDE}^2$Embedding2018 on models from Thingi10k dataset with the same number of vertices.
• Figure 5: Comparison between our method and LCT method fu2014anisotropic on Rocker Arm and Fertility models with the same number of vertices.