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Extended Differentiable Marching Cubes by Manifold-Preserving Shape Inflation

This paper introduces an extended differentiable marching cubes (DMC) method for end-to-end learning of precise 3D surface geometries using a neural network. The original DMC method extracts the isosurface using a fixed-size voxel grid, similar to the traditional marching cubes. Therefore, the original method involves a trade-off between output resolution and memory consumption. In contrast, there remains room to increase the output resolution without increasing the number of voxels because an output surface often exists over a limited number of voxels. According to this observation, our method deforms an input point cloud to occupy the voxel grid as widely as possible, thereby refining small parts of the target shape. To obtain such deformation, we apply normalizing flow (NF), typically used to transform probability density functions. Its invertibility allows us to reproduce a mesh for the input point cloud by cancelling the deformation of the mesh obtained for the deformed point cloud using DMC. To obtain appropriate deformation, NF is conditioned by a global shape feature and is trained by several loss functions to inflate the input shape while preserving its manifold structure. We tested the proposed method with two shape datasets and showed that our extended DMC achieves higher performance than the original DMC, even used with a simple deformation.