SobolevFusion: 3D Reconstruction of Scenes Undergoing Free Non-rigid Motion

We present a system that builds 3D models of non-rigidly moving surfaces from scratch in real time using a single RGB-D stream. Our solution is based on the variational level set method, thus it copes with arbitrary geometry, including topological changes. It warps a given truncated signed distance field (TSDF) to a target TSDF via gradient flow. Unlike previous approaches that define the gradient using an L ² inner product, our method relies on gradient flow in Sobolev space. Its favourable regularity properties allow for a more straightforward energy formulation that is faster to compute and that achieves higher geometric detail, mitigating the over-smoothing effects introduced by other regularization schemes. In addition, the coarse-to-fine evolution behaviour of the flow is able to handle larger motions, making few frames sufficient for a high-fidelity reconstruction. Last but not least, our pipeline determines voxel correspondences between partial shapes by matching signatures in a low-dimensional embedding of their Laplacian eigenfunctions, and is thus able to reliably colour the output model. A variety of quantitative and qualitative evaluations demonstrate the advantages of our technique.