MeshCNN

Abstract

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly captureboth shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN , a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of MeshCNN on various learning tasks applied to 3D meshes.

Deep Community Detection Method for Social Networks

“…15Set the weight of node vi in the next iteration plus the value of temp. (16) end for (17) end for (18) end while (19) Return the ID of the node with a highest weight.…”

“…The gradient descent method is adopted for the optimization of auto-encoder based on convolutional neural network. The weights in the neural network are updated by Equations (16), (17), (18), (19), (20) and (21). When the training process is complete, the reconstructed adjacency matrix will be inputted into the trained neural network to retrieve the values of neurons (i.e.,  …”

Deep geometric texture synthesis

“…The most related work is MeshCNN [Hanocka et al 2019], a neural network with operators that delete and un-collapse edges from a mesh for discriminative tasks like segmentation. However, unlike Hanocka et al [2019], in this work, we propose a generative network for synthesizing new mesh geometries. Since we learn from local geometric patches, our framework is oblivious to genus, and can transfer textures between arbitrary genus shapes (Figures 2 and 8).…”

“…Yet, common 3D modeling representations are irregular and unordered, which challenges the straightforward adaptation from image-based techniques. Recent advances enable applying convolutional neural networks (CNNs) on irregular structures, like point clouds and meshes [Li et al 2018a;Hanocka et al 2019]. So far, these CNN-based methods have demonstrated promising success for discriminative tasks like classification and segmentation.…”

“…In this work, we calculate deep features directly on the mesh triangles and exploit a unique property of triangular meshes. Every triangle in manifold triangular mesh is adjacent to exactly three faces (Figure 3), which defines a fixed-sized convolutional neighborhood, similar in spirit to MeshCNN [Hanocka et al 2019]. Our network generates mesh vertex displacements to synthesize local geometries, which are indistinguishable from the local statistics of the reference texture.…”