Partitioning a polygonal mesh into meaningful parts can be challenging. Many
applications require decomposing such structures for further processing in
computer graphics. In the last decade, several methods were proposed to tackle
this problem, at the cost of intensive computational times. Recently, machine
learning has proven to be effective for the segmentation task on 3D structures.
Nevertheless, these state-of-the-art methods are often hardly generalizable and
require dividing the learned model into several specific classes of objects to
avoid overfitting. We present a data-driven approach leveraging deep learning
to encode a mapping function prior to mesh segmentation for multiple
applications. Our network reproduces a neighborhood map using our knowledge of
the \textsl{Shape Diameter Function} (SDF) method using similarities among
vertex neighborhoods. Our approach is resolution-agnostic as we downsample the
input meshes and query the full-resolution structure solely for neighborhood
contributions. Using our predicted SDF values, we can inject the resulting
structure into a graph-cut algorithm to generate an efficient and robust mesh
segmentation while considerably reducing the required computation times.

该论文提出了一种数据驱动的方法，利用深度学习编码映射函数进行网格分割，该方法利用顶点邻域之间的相似性重建邻域映射，并将预测的 SDF 值注入到图割算法中，从而大幅度降低计算时间。

用于高效网格分割的神经形状直径函数

Neural Shape Diameter Function for Efficient Mesh Segmentation

This study presents a self-prior-based mesh inpainting framework that
requires only an incomplete mesh as input, without the need for any training
datasets. Additionally, our method maintains the polygonal mesh format
throughout the inpainting process without converting the shape format to an
intermediate, such as a voxel grid, a point cloud, or an implicit function,
which are typically considered easier for deep neural networks to process. To
achieve this goal, we introduce two graph convolutional networks (GCNs):
single-resolution GCN (SGCN) and multi-resolution GCN (MGCN), both trained in a
self-supervised manner. Our approach refines a watertight mesh obtained from
the initial hole filling to generate a completed output mesh. Specifically, we
train the GCNs to deform an oversmoothed version of the input mesh into the
expected completed shape. To supervise the GCNs for accurate vertex
displacements, despite the unknown correct displacements at real holes, we
utilize multiple sets of meshes with several connected regions marked as fake
holes. The correct displacements are known for vertices in these fake holes,
enabling network training with loss functions that assess the accuracy of
displacement vectors estimated by the GCNs. We demonstrate that our method
outperforms traditional dataset-independent approaches and exhibits greater
robustness compared to other deep-learning-based methods for shapes that less
frequently appear in shape datasets.

本研究提出一种自我先验的网格修补框架，通过引入两个自监督图卷积网络训练来实现，从而在不需要任何训练数据集的情况下只需一个不完整的网格作为输入，并在修补过程中保持原始多边形网格格式，最终可以生成一个修补好的多边形网格。