Variational Level Set Evolution for Non-Rigid 3D Reconstruction From a Single Depth Camera

We present a framework for real-time 3D reconstruction of non-rigidly moving surfaces captured with a single RGB-D camera. Based on the variational level set method, it warps a given truncated signed distance field (TSDF) to a target TSDF via gradient flow without explicit correspondence search. We optimize an energy that contains a data term which steers towards voxel-wise alignment. To ensure geometrically consistent reconstructions, we develop and compare different strategies, namely an approximately Killing vector field regularizer, gradient flow in Sobolev space and newly devised accelerated optimization. The underlying TSDF evolution makes our approach capable of capturing rapid motions, topological changes and interacting agents, but entails loss of data association. To recover correspondences, we propose to utilize the lowest-frequency Laplacian eigenfunctions of the TSDFs, which encode inherent deformation patterns. For moderate motions we are able to obtain implicit associations via a term that imposes voxel-wise eigenfunction alignment. This is not sufficient for larger motions, so we explicitly estimate voxel correspondences via signature matching of lower-dimensional eigenfunction embeddings. We carry out qualitative and quantitative evaluation of our geometric reconstruction fidelity and voxel correspondence accuracy, demonstrating advantages over related techniques in handling topological changes and fast motions.