Previouswork onneural 3Dreconstruction demonstrated benefits, butalso limitations, ofpoint cloud, voxel, surface mesh, and implicit function representations. Unlike existing volumetric approaches,DEFTET optimizes for both vertex placement and occupancy, and is differentiable with respect to standard 3D reconstruction lossfunctions.

Previous work on neural 3D reconstruction demonstrated benefits, but also limitations, of point cloud, voxel, surface mesh, and implicit function representations. We introduce \emph{Deformable Tetrahedral Meshes} (DefTet) as a particular parameterization that utilizes volumetric tetrahedral meshes for the reconstruction problem. Unlike existing volumetric approaches, DefTet optimizes for both vertex placement and occupancy, and is differentiable with respect to standard 3D reconstruction loss functions. It is thus simultaneously high-precision, volumetric, and amenable to learning-based neural architectures. We show that it can represent arbitrary, complex topology, is both memory and computationally efficient, and can produce high-fidelity reconstructions with a significantly smaller grid size than alternative volumetric approaches. The predicted surfaces are also inherently defined as tetrahedral meshes, thus do not require post-processing. We demonstrate that DefTetmatches or exceeds both the quality of the previous best approaches and the performance of the fastest ones. Our approach obtains high-quality tetrahedral meshes computed directly from noisy point clouds, and is the first to showcase high-quality 3D results using only a single image as input.

Previous work on neural 3D reconstruction demonstrated benefits, but also limitations, of point cloud, voxel, surface mesh, and implicit function representations. We introduce \emph{Deformable Tetrahedral Meshes} (DefTet) as a particular parameterization that utilizes volumetric tetrahedral meshes for the reconstruction problem. Unlike existing volumetric approaches, DefTet optimizes for both vertex placement and occupancy, and is differentiable with respect to standard 3D reconstruction loss functions. It is thus simultaneously high-precision, volumetric, and amenable to learning-based neural architectures. We show that it can represent arbitrary, complex topology, is both memory and computationally efficient, and can produce high-fidelity reconstructions with a significantly smaller grid size than alternative volumetric approaches. The predicted surfaces are also inherently defined as tetrahedral meshes, thus do not require post-processing.

High-quality observations of the real world are crucial for a variety of applications, including producing 3D printed replicas of small-scale scenes and conducting inspections of large-scale infrastructure. These 3D observations are commonly obtained by combining multiple sensor measurements from different views. Guiding the selection of suitable views is known as the NBV planning problem. Most NBV approaches reason about measurements using rigid data structures (e.g., surface meshes or voxel grids). This simplifies next best view selection but can be computationally expensive, reduces real-world fidelity, and couples the selection of a next best view with the final data processing. This paper presents the Surface Edge Explorer, a NBV approach that selects new observations directly from previous sensor measurements without requiring rigid data structures. SEE uses measurement density to propose next best views that increase coverage of insufficiently observed surfaces while avoiding potential occlusions. Statistical results from simulated experiments show that SEE can attain similar or better surface coverage with less observation time and travel distance than evaluated volumetric approaches on both small- and large-scale scenes. Real-world experiments demonstrate SEE autonomously observing a deer statue using a 3D sensor affixed to a robotic arm.