Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for high-performance and high-quality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for point-sampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new sub-sampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error tolerance #. Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a hole-free piecewise linear C continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.

We present a new scheme for the reconstruction of large geometric data. It is based on the well-known radial basis function model combined with an adaptive spatial and functional subdivision associated with a family of functions forming a partition of unity. This combination offers robust and efficient solution to a great variety of 2D and 3D reconstruction problems, such as the reconstruction of implicit curves or surfaces with attributes starting from unorganized point sets, image or mesh repairing, shape morphing or shape deformation, etc. After having presented the theoretical background, the paper mainly focuses on implementation details and issues, as well as on applications and experimental results.

In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key idea of this paper is to define both measurements and reconstructions as point clouds and describe all statistical assumptions in terms of this finite dimensional representation. This yields a discretization of the problem that can be solved using numerical optimization techniques. The resulting algorithm reconstructs both topology and geometry in form of a well-sampled point cloud with noise removed. In a final step, this representation is then converted into a triangle mesh. The proposed approach is conceptually simple and easy to extend. We apply the approach to reconstruct piecewise-smooth surfaces with sharp features and examine the performance of the algorithm on different synthetic and real-world data sets. Categories and Subject Descriptors (according to ACM CCS): I.5.1 [Models]: Statistical; I.3.5 [Computer Graphics]: Curve, surface, solid and object representations

We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and in particular interference between close-by surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlier-free and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a priority-driven normal propagation scheme based on a new priority measure and an orientation-aware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the close-by surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data. 1

This paper introduces a novel method for surface reconstruction using the depth discontinuity information captured by a multi-flash camera while the object moves along a known trajectory. Experimental results based on turntable sequences are presented. By observing the visual motion of depth discontinuities, surface points are accurately reconstructed – including many located deep inside concavities. The method extends well-established differential and global shape-from-silhouette surface reconstruction techniques by incorporating the significant additional information encoded in the depth discontinuities. The reconstruction method uses an implicit form of the epipolar parameterization and directly estimates point locations and corresponding surface normals on the surface of the object using a local temporal neighborhood of the depth discontinuities. Outliers, which correspond to the ill-conditioned cases of the reconstruction equations, are easily detected and removed by back-projection. Gaps resulting from curvaturedependent sampling and shallow concavities are filled by fitting an implicit surface to the oriented point cloud’s point locations and normal vectors. 1

Volumetric smooth particle data arise as atomic coordinates with electron density kernels for molecular structures, as well as fluid particle coordinates with a smoothing kernel in hydrodynamic flow simulations. In each case there is the need for efficiently computing approximations of relevant surfaces (molecular surfaces, material interfaces, shock waves, etc), along with surface and volume derivatives (normals, curvatures, etc.), from the irregularly spaced smooth particles. Additionally, molecular properties (charge density, polar potentials), as well as field variables from numerical simulations are often evaluated on these computed surfaces. In this paper we show how all the above problems can be reduced to a fast summation of irregularly spaced smooth kernel functions. For a scattered smooth particle system of M smooth kernels in R 3, where the Fourier coefficients have a decay of the type 1/ω 3, we present an O(M + n 3 log n + N) time, Fourier based algorithm to compute N approximate, irregular samples of a level set surface and its derivatives within a relative L2 error norm ǫ, where n is O(M 1/3 ǫ 1/3). Specifically, a truncated Gaussian of the form e −bx2 has the above decay, and n grows as √ b. In the case when the N output points are samples on a uniform grid, the back transform can be done exactly using a Fast Fourier transform algorithm, giving us an algorithm with O(M + n 3 log n + N log N) time complexity, where n is now approximately half its previously estimated value.

We describe a new method for surface reconstruction based on unorganized point clouds without normals. We also present a new algorithm for refining the initial triangulation. The output of the method is a refined triangular mesh with points on the moving least squares surface of the original point cloud.

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In this paper we present a high-fidelity surface approximation technique that aims at a faithful reconstruction of piecewise-smooth surfaces from a scattered point set. The presented method builds on the Moving Least-Squares (MLS) projection methodology, but introduces a fundamental modification: While the classical MLS uses a fixed approximation space, i.e., polynomials of a certain degree, the new method is data-dependent. For each projected point, it finds a proper local approximation space of piecewise polynomials (splines). The locally constructed spline encapsulates the local singularities which may exist in the data. The optional singularity for this local approximation space is modeled via a Singularity Indicator Field (SIF) which is computed over the input data points. We demonstrate the effectiveness of the method by reconstructing surfaces from real scanned 3D data, while being faithful to their most delicate features.

Point Set Surfaces define a (typically) manifold surface from a set of scattered points. The definition involves weighted centroids and a gradient field. The data points are interpolated if singular weight functions are used to define the centroids. While this way of deriving an interpolatory scheme appears natural we show that it has two deficiencies: convexity of the input is not preserved and the extension to Hermite data is numerically unstable. We present a generalization of the standard scheme that we call Hermite Point Set Surface. It allows interpolating given normal constraints in a stable way. In addition, it yields an intuitive parameter for shape control and preserves convexity in most situations.