Subdivision-based Mesh Convolution Networks

Abstract

Convolutionalneural networks (CNNs) have made great breakthroughs in two-dimensional (2D) computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this article presents SubdivNet , an innovative and versatile CNN framework for three-dimensional (3D) triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g., variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers that uniformly merge four faces into one and an upsampling method that splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet’s effectiveness and efficiency.

Laplacian2Mesh: Laplacian-Based Mesh Understanding

“…Similar to the methods using the features from edges, face-based approaches focus on aggregating information between neighboring faces efficiently and effectively. SubdivNet [35] offers a more general and standard convolution directly defined on meshes and provides uniform downsampling inspired by loop subdivision operation.…”

“…Laplacian unpooling, the upper path of the Figure 7, is the reverse process of Laplacian pooling using inverse-Laplacian transform, which can restore the information of different spatial dimensions instead of obtaining high-dimensional information through interpolation approach like other algorithms (i.e. SubdivNet [35]). Thus, the Laplacian unpooling does not learnable parameters, and it also relies on the eigenvectors from the cotangent Laplacian.…”

“…9. Two evolutionary versions of the original dataset: the upper part is the data-meshcnn from [6], and the lower part is the data-subdivnet from [35].…”

“…For all tasks, there are currently two versions evolved from original datasets, data-meshcnn from MeshCNN [6] and data-subdivnet from SubdivNet [35]. The former simplified each mesh in the original dataset to roughly the same number of edges, and the latter performs remesh processing on the meshes in order to add the Loop subdivision sequence connectivity to the data.…”

“…For the training set, we apply random anisotropic scaling with a normal distribution mean µ = 1 and standard deviation δ = 0.1 on the vertex locations, following MeshCNN [6]. In order to increase the diversity of some datasets, we are inspired by SubdivNet [35] to randomly select three Euler angles (randomly sampled from 0, π/2, π, or 3π/2) to rotate the data.…”