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.

We propose an approach for 3D reconstruction and tracking of dynamic surfaces using a single depth sensor, without any prior knowledge of the scene. It is robust to rapid inter-frame motions due to the probabilistic expectation-maximization non-rigid registration framework. Our pipeline subdivides each input depth image into non-rigidly connected surface patches, and deforms it towards the canonical pose by estimating a rigid transformation for each patch. The combination of a data term imposing similarity between model and data, and a regularizer enforcing as-rigid-as-possible motion of neighboring patches ensures that we can handle large deformations, while coping with sensor noise. We employ a surfel-based fusion technique, which lets us circumvent the repeated conversion between mesh and signed distance field representations which are used by related techniques. Furthermore, a robust keyframe-based scheme allows us to keep track of correspondences throughout the entire sequence. Through a variety of qualitative and quantitative experiments, we demonstrate resistance to larger motion and achieving lower reconstruction errors than related approaches.

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 L2inner 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.

We introduce a geometry-driven approach for real-time 3D reconstruction of deforming surfaces from a single RGB-D stream without any templates or shape priors. To this end, we tackle the problem of non-rigid registration by level set evolution without explicit correspondence search. Given a pair of signed distance fields (SDFs) representing the shapes of interest, we estimate a dense deformation field that aligns them. It is defined as a displacement vector field of the same resolution as the SDFs and is determined iteratively via variational minimization. To ensure it generates plausible shapes, we propose a novel regularizer that imposes local rigidity by requiring the deformation to be a smooth and approximately Killing vector field, i.e. generating nearly isometric motions. Moreover, we enforce that the level set property of unity gradient magnitude is preserved over iterations. As a result, KillingFusion reliably reconstructs objects that are undergoing topological changes and fast inter-frame motion. In addition to incrementally building a model from scratch, our system can also deform complete surfaces. We demonstrate these capabilities on several public datasets and introduce our own sequences that permit both qualitative and quantitative comparison to related approaches.