The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations -- not necessarily the explicit geometry. This state-of-the-art report surveys the field of surface reconstruction, providing a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, this report provides a detailed characterization of the field, highlights similarities between diverse reconstruction techniques, and provides directions for future work in surface reconstruction.

https://hal.inria.fr/hal-01017700/document

State of the Art in Surface Reconstruction from Point Clouds

Reconstructing curves and surfaces from sets of points is a common activity in medical imaging, computer graphics, and engineering. Given a physical object, we often seek to build a digital representation of it from a set of discrete samples. This digital representation can then be visualized, analyzed and manipulated on the computer. To create this digital representation from samples collected from the physical object, we must employ algorithms to reconstruct the shape of the object. This text discusses algorithms for performing these reconstructions for both two-dimensional curves and three-dimensional surfaces. The text presents these algorithms in the context of the mathematical basis upon which they are derived and their properties proven. The mathematical content of the text is drawn from

Curve and surface reconstruction: algorithms with mathematical analysis by Tamal K. Dey Cambridge University Press

Surface reconstruction from point cloud is of great practical importance in computer graphics. Existing methods often realize reconstruction via a few phases with respective goals, whose integration may not give an optimal solution. In this paper, to avoid the inherent limitations of multi-phase processing in the prior art, we propose a unified framework that treats geometry and connectivity construction as one joint optimization problem. The framework is based on dictionary learning in which the dictionary consists of the vertices of the reconstructed triangular mesh and the sparse coding matrix encodes the connectivity of the mesh. The dictionary learning is formulated as a constrained e2,q-optimization (0

Robust surface reconstruction via dictionary learning

We present a method for reconstructing a 3D surface triangulation from an input point set The main component of the method is an algorithm that computes the restricted Voronoi diagram In our specific case, it corresponds to the intersection between the 3D Voronoi diagram of the input points and a set of disks centered at the points and orthogonal to the estimated normal directions The method does not require coherent normal orientations (just directions) Our algorithm is based on a property of the restricted Voronoi cells that leads to an embarrassingly parallel implementation We experimented our algorithm with scanned point sets with up to 100 million vertices that were processed within few minutes on a standard computer The complete implementation is provided

/pdf/surface-reconstruction-by-computing-restricted-voronoi-cells-3lgbxk4m0b.pdf

Surface reconstruction by computing restricted Voronoi cells in parallel

Quasi-interpolation for surface reconstruction from scattered data with radial basis function

Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of ‘singularities’ such as boundaries, sharp features, and non-manifolds. A few of the current research in reconstruction have addressed handling some of these singularities, but a unified approach to handle them all is missing. In this paper we allow the presence of various singularities by requiring that the sampled object is a collection of smooth surface patches with boundaries that can meet or intersect.

Our algorithm first identifies and reconstructs the features where singularities occur. Next, it reconstructs the surface patches containing these feature curves. The identification and reconstruction of feature curves are achieved by a novel combination of the Gaussian weighted graph Laplacian and the Reeb graphs. The global reconstruction is achieved by a method akin to the well known Cocone reconstruction, but with weighted Delaunay triangulation that allows protecting the feature samples with balls. We provide various experimental results to demonstrate the effectiveness of our feature-preserving singular surface reconstruction algorithm. © 2012 Wiley Periodicals, Inc.

Lei Wang

Papers

Feature-Preserving Reconstruction of Singular Surfaces

SMI 2013: Voronoi-based feature curves extraction for sampled singular surfaces

SMI 2011: Full Paper: Localized Cocone surface reconstruction

Automatic posing of a meshed human model using point clouds