Signed Distance Fields for Rigid and Deformable 3D Reconstruction

Capturing three-dimensional environments is a key task in the growing fields of virtual and augmented reality. Methods have to work at sensor frame rates and be extremely accurate to ensure a credible reconstruction. Moreover, they have to be able to not only recover the geometry of a fixed scene, but also capture it when people are moving and interacting with objects in it. This thesis addresses the task of 3D reconstruction of both static and dynamic objects and scenes scanned with a single hand-held RGB-D camera, without any markers or prior knowledge. Reconstructing rigid environments requires estimating the six degrees-offreedom camera pose at every time instance, and subsequently fusing the acquired data into a geometrically consistent computer model. The task of reconstructing deformable objects is more challenging, as additionally the nonrigid motion that occurred in every frame has to be determined and factored out. Solutions are typically based on variants of the iterative closest points (ICP) algorithm, which iteratively establishes correspondences and minimizes the distance between two point sets. While this approach is general and versatile, it is dependent on a good initialization and a low amount of noise. Recently, point-to-implicit approaches have shown higher robustness than ICP for rigid registration. They align a point cloud with the zero level set of a signed distance field (SDF). The SDF is an implicit surface representation, stored as a voxel grid in which outside areas have positive values and inside areas have negative ones, leaving the surface as the zero-valued interface. It permits registration to be done as a direct minimization without correspondence search. Inspired by this, we propose to tackle both the rigid and deformable reconstruction problems via implicit-to-implicit alignment of SDF pairs. In the static case, we obtain more accurate pose estimates with a framework that permits straightforward incorporation of various additional constraints, such as surface colour and orientation. We start with the reconstruction of smallto medium-scale household objects and demonstrate how to extend the approach to larger spaces such as rooms. To this end, we develop a limited-extent volume strategy that restricts registration to the most geometrically distinctive regions of a scene, leading to significantly improved rotational motion estimation. Finally, we adapt our approach to dynamic scenes by modifying our implicitto-implicit approach so that new data is incremented appropriately. For this purpose we evolve an initial SDF to a target SDF by imposing rigidity constraints that require the underlying deformation field to be approximately Killing, i.e. volume-preserving and generating locally isometric motions. Alternatively, we employ gradient flow in the smooth Sobolev space, which favours global deformations over finer-scale details. These strategies also circumvent explicit correspondence search and thus avoid the repeated conversion between SDF and mesh representations that other techniques entail. Nevertheless, we ensure that correspondence information can be recovered by proposing two strategies based on Laplacian eigenfunctions, which are known to encode natural deformation patterns. Thanks to the used SDF representation, our non-rigid reconstruction approach is able to handle topological changes and fast motion, which are major obstacles for existing approaches.