Julie Digne

Scale Space Meshing of Raw Data Point Sets

This paper develops a scale space strategy for orienting and meshing exactly and completely a raw point set. The scale space is based on the intrinsic heat equation, also called mean curvature motion (MCM). A simple iterative scheme implementing MCM directly on the raw point set is described, and a mathematical proof of its consistency with MCM is given. Points evolved by this MCM implementation can be trivially backtracked to their initial raw position. Therefore, both the orientation and mesh of the data point set obtained at a smooth scale can be transported back on the original. The gain in visual accuracy is demonstrated on archaeological objects by comparison with several state of the art meshing methods.

Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets

We introduce a robust and feature-capturing surface reconstruction and simplification method that turns an input point set into a low triangle-count simplicial complex. Our approach starts with a (possibly non-manifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex—both seen as mass distributions. Our approach is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries. Our new feature-sensitive metric between point sets and triangle meshes can also be used as a post-processing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.

Self-similarity for accurate compression of point sampled surfaces

Most surfaces, be it from a fine‐art artifact or a mechanical object, are characterized by a strong self‐similarity. This property finds its source in the natural structures of objects but also in the fabrication processes: regularity of the sculpting technique, or machine tool. In this paper, we propose to exploit the self‐similarity of the underlying shapes for compressing point cloud surfaces which can contain millions of points at a very high precision. Our approach locally resamples the point cloud in order to highlight the self‐similarity of the shape, while remaining consistent with the original shape and the scanner precision. It then uses this self‐similarity to create an ad hoc dictionary on which the local neighborhoods will be sparsely represented, thus allowing for a light‐weight representation of the total surface. We demonstrate the validity of our approach on several point clouds from fine‐arts and mechanical objects, as well as a urban scene. In addition, we show that our approach also achieves a filtering of noise whose magnitude is smaller than the scanner precision.

Similarity based filtering of point clouds

Denoising surfaces is a a crucial step in the surface processing pipeline. This is even more challenging when no underlying structure of the surface is known, id est when the surface is represented as a set of unorganized points. In this paper, a denoising method based on local similarities is introduced. The contributions are threefold: first, we do not denoise directly the point positions but use a low/high frequency decomposition and denoise only the high frequency. Second, we introduce a local surface parameterization which is proved stable. Finally, this method works directly on point clouds, thus avoiding building a mesh of a noisy surface which is a difficult problem. Our approach is based on denoising a height vector field by comparing the neighborhood of the point with neighborhoods of other points on the surface. It falls into the non-local denoising framework that has been extensively used in image processing, but extends it to unorganized point clouds.

Farman Institute 3D Point Sets - High Precision 3D Data Sets

This article is dedicated to describe a new type of data: high precision raw data coming from the acquisition of objects by a 3D laser scanner. Supplementary Material The datasets described in this article can be downloaded from the associated IPOL web page1.

An Analysis and Implementation of a Parallel Ball Pivoting Algorithm

The problem of surface reconstruction from a set of 3D points given by their coordinates and oriented normals is a difficult problem, which has been tackled with many different approaches. In 1999, Bernardini and colleagues introduced a very elegant and efficient r method that uses a ball pivoting around triangle edges and adds new triangles if the ball is incident to three points and contains no other points. This paper details an implementation and parallelization of this algorithm. Source Code The ANSI C++ source code permitting to reproduce results from the on-line demo is available at the IPOL web page of this article 1 . The Ball Pivoting Algorithm is linked with patent US6968299B1, it is made available for the exclusive aim of serving as a scientific tool to verify the soundness and completeness of the algorithm description.

High Fidelity Scan Merging

For each scanned object 3D triangulation laser scanners deliver multiple sweeps corresponding to multiple laser motions and orientations. The problem of aligning these scans has been well solved by using rigid and, more recently, non‐rigid transformations. Nevertheless, there are always residual local offsets between scans which forbid a direct merging of the scans, and force to some preliminary smoothing. Indeed, the tiling and aliasing effects due to the tiniest normal displacements of the scans can be dramatic. This paper proposes a general method to tackle this problem. The algorithm decomposes each scan into its high and low frequency components and fuses the low frequencies while keeping intact the high frequency content. It produces a mesh with the highest attainable resolution, having for vertices all raw data points of all scans. This exhaustive fusion of scans maintains the finest texture details. The method is illustrated on several high resolution scans of archeological objects.

Sparse representation of terrains for procedural modeling

In this paper, we present a simple and efficient method to represent terrains as elevation functions built from linear combinations of landform features (atoms). These features can be extracted either from real world data‐sets or procedural primitives, or from any combination of multiple terrain models. Our approach consists in representing the elevation function as a sparse combination of primitives, a concept which we call Sparse Construction Tree, which blends the different landform features stored in a dictionary. The sparse representation allows us to represent complex terrains using combinations of atoms from a small dictionary, yielding a powerful and compact terrain representation and synthesis tool. Moreover, we present a method for automatically learning the dictionary and generating the Sparse Construction Tree model. We demonstrate the efficiency of our method in several applications: inverse procedural modeling of terrains, terrain amplification and synthesis from a coarse sketch.

Numerical analysis of differential operators on raw point clouds

Abstract3D acquisition devices acquire object surfaces with growing accuracy by obtaining 3D point samples of the surface. This sampling depends on the geometry of the device and of the scanned object and is therefore very irregular. Many numerical schemes have been proposed for applying PDEs to regularly meshed 3D data. Nevertheless, for high precision applications it remains necessary to compute differential operators on raw point clouds prior to any meshing. Indeed differential operators such as the mean curvature or the principal curvatures provide crucial information for the orientation and meshing process itself. This paper reviews a half dozen local schemes which have been proposed to compute discrete curvature-like shape indicators on raw point clouds. All of them will be analyzed mathematically in a unified framework by computing their asymptotic form when the size of the neighborhood tends to zero. They are given in terms of the principal curvatures or of higher order intrinsic differential operators which, in return, characterize the discrete operators. All considered local schemes are of two kinds: either they perform a polynomial local regression, or they compute directly local moments. But the polynomial regression of order 1 is demonstrated to play a special role, because its iterations yield a scale space. This analysis is completed with numerical experiments comparing the accuracies of these schemes. We demonstrate that this accuracy is enhanced for all operators by applying previously the scale space.

Mesh segmentation and model extraction

High precision laser scanners deliver virtual surfaces of industrial objects whose accuracy must be evaluated. But this requires the automatic detection of reliable components such as facets, cylindric and spherical parts, etc. The method described here finds automatically parts in the surface to which geometric primitives can be fitted. Knowing certain properties of the input object, this primitive fitting helps quantifying the precision of an acquisition process and of the scanned mires. The method combines mesh segmentation with model fitting. The mesh segmentation method is based on the level set tree of a scalar function defined on the mesh. The method is applied with the simplest available intrinsic scalar function on the mesh, the mean curvature. In a first stage a fast algorithm extracts the level sets of the scalar function. Adapting to meshes a well known method for extracting Maximally Stable Extremal Regions from the level set tree on digital images, the method segments automatically the mesh into smooth parts separated by high curvature regions (the edges). This segmentation is followed by a model selection on each part permitting to fit planes, cylinders and spheres and to quantify the overall accuracy of the acquisition process.