Splat-based surface reconstruction from defect-laden point sets☆
Graphical abstract
Introduction
The growing variety of scanning devices and technologies nowadays provides measurements of objects in the form of point sets. Despite the advances in scanning technologies, achieving a perfect scan is very unlikely and, in general, these point sets contain two main types of defects: noise and outliers. Noise refers to the inaccuracy of the resulting measurements, and is related to the lack of precision and repeatability of the scanning process used, while outliers are wrong measurements that are produced by errors during the scanning (e.g., reflections on the surface when using laser scanners).
Having the object represented as a point set complicates the interpretation of the data since the notion of visibility of the shape from a given viewpoint is lost. For this reason, surface reconstruction methods are required. We aim at obtaining the surface in the form of a surface triangle mesh, which allows further processing such as remeshing or simplification. In this paper, we present a surface reconstruction method that is able to provide a smooth approximation of the sampled shape while dealing with noise and a large number of outliers. Moreover, the method is able, to some extent, to reconstruct surfaces with boundaries.
Section snippets
Related work
Surface reconstruction methods are broadly divided according to their ability to interpolate or approximate the measured points.
Interpolation-based methods have been proposed mainly by the computational geometry community. They commonly rely on extracting the surface from a space partitioning such as the Delaunay triangulation and its dual, the Voronoi diagram. Well-known methods in this area include the Cocone method [1], and the Power Crust method [2]. They use a principled way to separate
Overview and contributions
Our method is based on computing a global surface approximation using local surfaces. Instead of producing a consistent global representation of the surface through a memory-intensive global solver (such as solving for a signed distance or indicator function) and then using an isosurface meshing approach, our approach performs the merging of the different local surfaces at the meshing step.
We denote as splats these local surfaces, which may not be just planar but higher-degree approximations
Creating the splats
Given the input point set P, we compute a splat-based representation in which each splat is a local approximation of the surface. In its simplest form, a splat is a disk tangent to the surface and with a radius adapted to the local density of the point set. However, our method allows higher-degree approximations through so-called jet surfaces. We next explain how these jet surfaces are computed and how we combine them with RANSAC in order to achieve robustness to outliers.
Meshing
We have generated one splat for each input point where RANSAC was successful, and because of the redundancy between them, the same area may be covered by more than one splat. In order to obtain the final surface triangle mesh from the splats, we use a coarse-to-fine meshing algorithm based on the concept of Restricted Delaunay Triangulation (RDT) and Delaunay refinement [27]. Given a set of points E on or near a surface, the RDT is a subcomplex of the 3D Delaunay triangulation of E formed by
Results
We implemented our method using components from the CGAL library [34]. Our current implementation is sequential. Table 1 lists all the parameters used by the two steps of our algorithm. Note that some parameters are not critical and thus have been set once for all experiments shown. The data-dependent parameters are k (nearest neighbors) and those driving the splat-RANSAC procedure. There are 3 additional parameters required for meshing. All the parameters used to generate the results are
Conclusions and future work
We have presented a surface reconstruction method that is able to recover smooth representations of a surface under a large quantity of outliers and noise. The separation of the splat creation and the surface meshing steps makes the method modular, and provides re-usability of the results obtained at each intermediate step. Our method works without any other information than the raw point set, and the local nature of the individual splats makes the method recover, to some extent, the boundaries
Acknowledgments
The authors thank the Stanford 3D Scanning Repository (Stanford University Computer Graphics Laboratory), Michael Kazhdan (Johns Hopkins University), the AIM@SHAPE consortium (the ISTI-CNR Visual Computing Laboratory and Inria), Renaud Keriven and Jean-Philippe Pons for providing the models used in this paper. This work was partially funded through MINECO under Grant CTM2010-15216, the EU under Grant FP7-ICT-2011-7-288704 and the European Research Council (ERC Starting Grant “Robust Geometry
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This paper has been recommended for acceptance by Tamal Dey and Peter Lindstrom.