The analysis of deforming 3D surface meshes is accelerated by autoencoders since the low-dimensional embeddings can be used to visualize underlying dynamics. But, state-of-the-art mesh convolutional autoencoders require a fixed connectivity of all input meshes handled by the autoencoder. This is due to either the use of spectral convolutional layers or mesh dependent pooling operations. Therefore, the types of datasets that one can study are limited and the learned knowledge cannot be transferred to other datasets that exhibit similar behavior. To address this, we transform the discretization of the surfaces to semi-regular meshes that have a locally regular connectivity and whose meshing is hierarchical. This allows us to apply the same spatial convolutional filters to the local neighborhoods and to define a pooling operator that can be applied to every semi-regular mesh. We apply the same mesh autoencoder to different datasets and our reconstruction error is more than 50% lower than the error from state-of-the-art models, which have to be trained for every mesh separately. Additionally, we visualize the underlying dynamics of unseen mesh sequences with an autoencoder trained on different classes of meshes.

本文介绍了一种新方法，将表面网格的离散化转换为半正则网格，使其具有局部正则性连接和分层网格的性质，并使用空间卷积过滤器和池化算子来处理所有半正则网格，该方法的重构误差比当前最先进的模型低50％以上。

用于不同大小半正则网格的网格卷积自编码器