Neural marching cubes

We introduce Neural Marching Cubes, a data-driven approach for extracting a triangle mesh from a discretized implicit field. We base our meshing approach on Marching Cubes (MC), due to the simplicity of its input, namely a uniform grid of signed distances or occupancies, which frequently arise in surface reconstruction and from neural implicit models. However, classical MC is defined by coarse tessellation templates isolated to individual cubes. While more refined tessellations have been proposed by several MC variants, they all make heuristic assumptions, such as trilinearity, when determining the vertex positions and local mesh topologies in each cube. In principle, none of these approaches can reconstruct geometric features that reveal coherence or dependencies between nearby cubes (e.g., a sharp edge), as such information is unaccounted for, resulting in poor estimates of the true underlying implicit field. To tackle these challenges, we re-cast MC from a deep learning perspective, by designing tessellation templates more apt at preserving geometric features, and learning the vertex positions and mesh topologies from training meshes, to account for contextual information from nearby cubes. We develop a compact per-cube parameterization to represent the output triangle mesh, while being compatible with neural processing, so that a simple 3D convolutional network can be employed for the training. We show that all topological cases in each cube that are applicable to our design can be easily derived using our representation, and the resulting tessellations can also be obtained naturally and efficiently by following a few design guidelines. In addition, our network learns local features with limited receptive fields, hence it generalizes well to new shapes and new datasets. We evaluate our neural MC approach by quantitative and qualitative comparisons to all well-known MC variants. In particular, we demonstrate the ability of our network to recover sharp features such as edges and corners, a long-standing issue of MC and its variants. Our network also reconstructs local mesh topologies more accurately than previous approaches. Code and data are available at https://github.com/czq142857/NMC.