Efficient Surface Reconstruction for Piecewise Smooth Objects

In this report we present a new surface reconstruction technique from unstructured point clouds for piecewise smooth objects, such as scans of architectural and other man-made artifacts. The new technique operates in three conceptual steps: First, a set of basis functions is computed and a topology is established among these functions that respect sharp features using a RANSAC technique. Second, a linearized, statistically motivated optimization problem is solved employing this discretization. Lastly, an implicit function based meshing technique is employed to determine a clean, manifold mesh representation. The main benefit of our new proposal in comparison to previous work is its robustness and efficiency, which we examine by applying the algorithm to a set of synthetic and real-world benchmark data sets

A Singularity-Avoiding Moving Least Squares Scheme for Two Dimensional Unstructured Meshes

Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has addressed this issue specifically. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which singularities occur are identified. The theory is then applied in the form of a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner, while attempting to maintain stencil symmetry as closely as possible. Finally, the scheme is used in a convection-diffusion equation solver, and the results of a number of simulations are presented

Feature Preserving Point Set Surfaces based on Non-Linear Kernel Regression

International audienceMoving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [SOS04,Kol05] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non-robust approaches

Feature Preserving Mesh Generation from 3D Point Clouds

Special issue for EUROGRAPHICS Symposium on Geometry Processing, Lyon 2010International audienceWe address the problem of generating quality surface triangle meshes from 3D point clouds sampled on piecewise smooth surfaces. Using a feature detection process based on the covariance matrices of Voronoi cells, we first ex- tract from the point cloud a set of sharp features. Our algorithm also runs on the input point cloud a reconstruction process, such as Poisson reconstruction, providing an implicit surface. A feature preserving variant of a Delaunay refinement process is then used to generate a mesh approximating the implicit surface and containing a faithful representation of the extracted sharp edges. Such a mesh provides an enhanced trade-off between accuracy and mesh complexity. The whole process is robust to noise and made versatile through a small set of parameters which govern the mesh sizing, approximation error and shape of the elements. We demonstrate the effectiveness of our method on a variety of models including laser scanned datasets ranging from indoor to outdoor scenes

Voronoi-Based Curvature and Feature Estimation from Point Clouds

International audienceWe present an efficient and robust method for extracting curvature information, sharp features, and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show that these matrices contain information related to curvature in the smooth parts of the surface, and information about the directions and angles of sharp edges around the features of a piecewise-smooth surface. Our method is applicable in both two and three dimensions, and can be easily parallelized, making it possible to process arbitrarily large point clouds, which was a challenge for Voronoi-based methods. In addition, we describe a Monte-Carlo version of our method, which is applicable in any dimension. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models. As a sample application, we use our feature detection method to segment point cloud samplings of piecewise-smooth surfaces

A Survey of Surface Reconstruction from Point Clouds

International audienceThe 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. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques, and provide directions for future work in surface reconstruction