We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.

Poisson surface reconstruction

Computer graphics, 3D computer vision and robotics communities have produced multiple approaches to representing 3D geometry for rendering and reconstruction. These provide trade-offs across fidelity, efficiency and compression capabilities. In this work, we introduce DeepSDF, a learned continuous Signed Distance Function (SDF) representation of a class of shapes that enables high quality shape representation, interpolation and completion from partial and noisy 3D input data. DeepSDF, like its classical counterpart, represents a shape's surface by a continuous volumetric field: the magnitude of a point in the field represents the distance to the surface boundary and the sign indicates whether the region is inside (-) or outside (+) of the shape, hence our representation implicitly encodes a shape's boundary as the zero-level-set of the learned function while explicitly representing the classification of space as being part of the shapes interior or not. While classical SDF's both in analytical or discretized voxel form typically represent the surface of a single shape, DeepSDF can represent an entire class of shapes. Furthermore, we show state-of-the-art performance for learned 3D shape representation and completion while reducing the model size by an order of magnitude compared with previous work.

/pdf/deepsdf-learning-continuous-signed-distance-functions-for-43v0fu25wz.pdf

DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation

Simultaneous localization and mapping (SLAM) consists in the concurrent construction of a model of the environment (the map ), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications and witnessing a steady transition of this technology to industry. We survey the current state of SLAM and consider future directions. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors’ take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved?

/pdf/past-present-and-future-of-simultaneous-localization-and-27i1pn9khc.pdf

Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved?

/pdf/past-present-and-future-of-simultaneous-localization-and-dhljw0akg5.pdf

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Poisson surface reconstruction creates watertight surfaces from oriented point sets. In this work we extend the technique to explicitly incorporate the points as interpolation constraints. The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poisson equation. In contrast to other image and geometry processing techniques, the screening term is defined over a sparse set of points rather than over the full domain. We show that these sparse constraints can nonetheless be integrated efficiently. Because the modified linear system retains the same finite-element discretization, the sparsity structure is unchanged, and the system can still be solved using a multigrid approach. Moreover we present several algorithmic improvements that together reduce the time complexity of the solver to linear in the number of points, thereby enabling faster, higher-quality surface reconstructions.

/pdf/screened-poisson-surface-reconstruction-1qtztseo1f.pdf

Screened poisson surface reconstruction

We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from point-cloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs allow us to model large data sets, consisting of millions of surface points, by a single RBF — previously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages. The energy-minimisation characterisation of polyharmonic splines result in a “smoothest” interpolant. This scale-independent characterisation is well-suited to reconstructing surfaces from non-uniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a non-interpolating approximation when the data is noisy. The functional representation is in effect a solid model, which means that gradients and surface normals can be determined analytically. This helps generate uniform meshes and we show that the RBF representation has advantages for mesh simplification and remeshing applications. Results are presented for real-world rangefinder data.

/pdf/reconstruction-and-representation-of-3d-objects-with-radial-1col9c83sl.pdf

Reconstruction and representation of 3D objects with radial basis functions

This paper shows that scattered range data can be smoothed at low cost by fitting a Radial Basis Function (RBF) to the data and convolving with a smoothing kernel (low pass filtering). The RBF exactly describes the range data and interpolates across holes and gaps. The data is smoothed during evaluation of the RBF by simply changing the basic function. The amount of smoothing can be varied as required without having to fit a new RBF to the data. The key feature of our approach is that it avoids resampling the RBF on a fine grid or performing a numerical convolution. Furthermore, the computation required is independent of the extent of the smoothing kernel, i.e., the amount of smoothing. We show that particular smoothing kernels result in the applicability of fast numerical methods. We also discuss an alternative approach in which a discrete approximation to the smoothing kernel achieves similar results by adding new centres to the original RBF during evaluation. This approach allows arbitrary filter kernels, including anisotropic and spatially varying filters, to be applied while also using established fast evaluation methods. We illustrate both techniques with LIDAR laser scan data and noisy synthetic data.

Smooth surface reconstruction from noisy range data

/pdf/author-correction-hypervirulent-pneumococcal-serotype-1-bxep52pq.pdf

Author Correction: Hypervirulent pneumococcal serotype 1 harbours two pneumolysin variants with differential haemolytic activity

Streptococcus pneumoniae (the pneumococcus) is a major human pathogen causing invasive disease, including community-acquired bacteraemia, and remains a leading cause of global mortality. Understanding the role of phagocytes in killing bacteria is still limited, especially in vivo. In this study, we established a zebrafish model to study the interaction between intravenously administered pneumococci and professional phagocytes such as macrophages and neutrophils, to unravel bacterial killing mechanisms employed by these immune cells. Our model confirmed the key role of polysaccharide capsule in promoting pneumococcal virulence through inhibition of phagocytosis. Conversely, we show pneumococci lacking a capsule are rapidly internalised by macrophages. Low doses of encapsulated S. pneumoniae cause near 100% mortality within 48 hours postinfection (hpi), while 50 times higher doses of unencapsulated pneumococci are easily cleared. Time course analysis of in vivo bacterial numbers reveals that while encapsulated pneumococcus proliferates to levels exceeding 105 CFU at the time of host death, unencapsulated bacteria are unable to grow and are cleared within 20 hpi. Using genetically induced macrophage depletion, we confirmed an essential role for macrophages in bacterial clearance. Additionally, we show that upon phagocytosis by macrophages, phagosomes undergo rapid acidification. Genetic and chemical inhibition of vacuolar ATPase (v-ATPase) prevents intracellular bacterial killing and induces host death indicating a key role of phagosomal acidification in immunity to invading pneumococci. We also show that our model can be used to study the efficacy of antimicrobials against pneumococci in vivo. Collectively, our data confirm that larval zebrafish can be used to dissect killing mechanisms during pneumococcal infection in vivo and highlight key roles for phagosomal acidification in macrophages for pathogen clearance.

T. J. Mitchell

Papers

Reconstruction and representation of 3D objects with radial basis functions

Smooth surface reconstruction from noisy range data

Author Correction: Hypervirulent pneumococcal serotype 1 harbours two pneumolysin variants with differential haemolytic activity

Phagosomal Acidification Is Required to Kill Streptococcus pneumoniae in a Zebrafish Model