Stochastic surface mesh reconstruction

This research was funded by TUBITAK – The Scientific and Technological Research Council of Turkey (Project ID: 115Y239) and by the Scientific Research Projects of Bülent Ecevit University (Project ID: 2015-47912266-01)A generic and practical methodology is presented for 3D surface mesh reconstruction from the terrestrial laser scanner (TLS) derived point clouds. It has two main steps. The first step deals with developing an anisotropic point error model, which is capable of computing the theoretical precisions of 3D coordinates of each individual point in the point cloud. The magnitude and direction of the errors are represented in the form of error ellipsoids. The following second step is focused on the stochastic surface mesh reconstruction. It exploits the previously determined error ellipsoids by computing a point-wise quality measure, which takes into account the semi-diagonal axis length of the error ellipsoid. The points only with the least errors are used in the surface triangulation. The remaining ones are automatically discarded.Publisher's Versio

Indoor rigid sphere recognition based on 3D point cloud data

This paper presents a method for recognising spherical shapes in 3D point cloud XYZ coordinate data obtained by scanning an indoor environment using a LIDAR scanner. Firstly, bilateral smoothing is performed to smooth the surfaces consisting of points. Then, the surface curvature and surface roughness of each point in the scan are extracted by analysing the point cloud data. Finally, a three layer multilayer perceptron neural network trained by the Levenberg-Marquardt algorithm is used to automatically distinguish points belonging to spheres from all the other points making use of extracted features. A novel feedback technique is applied in which the neural network is used several times on the recognised data. This method can be applied to automate 3D scan alignment

A quasi-Monte Carlo method for computing areas of point-sampled surfaces

A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy–Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.postprin

Thin shell analysis from scattered points with maximum-entropy approximants

We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of any genus. It combines three ingredients: (1) the automatic detection of the local geometric structure of the manifold by statistical learning methods; (2) the local parameterization of the surface using smooth meshfree (here maximum-entropy) approximants; and (3) patching together the local representations by means of a partition of unity. Mesh-based methods can deal with surfaces of complex topology, since they rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, whereas previous meshfree methods for thin shells consider a global parametric domain, which seriously limits the kinds of surfaces that can be treated. We present the implementation of the method in the context of Kirchhoff–Love shells, but it is applicable to other calculations on manifolds in any dimension. With the smooth approximants, this fourth-order partial differential equation is treated directly. We show the good performance of the method on the basis of the classical obstacle course. Additional calculations exemplify the flexibility of the proposed approach in treating surfaces of complex topology and geometry

Point-based multiscale surface representation

In this article we present a new multiscale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of point-based surface approximations at successively higher levels of smoothness, that is, coarser scales of detail, using geometric low-pass filtering. These point clouds are then encoded relative to each other by expressing each level as a scalar displacement of its predecessor. Low-pass filtering and encoding are combined in an efficient multilevel projection operator using local weighted least squares fitting. Our representation is motivated by the need for higher-level editing semantics which allow surface modifications at different scales. The user would be able to edit the surface at different approximation levels to perform coarse-scale edits on the whole model as well as very localized modifications on the surface detail. Additionally, the multiscale representation provides a separation in geometric scale which can be understood as a spectral decomposition of the surface geometry. Based on this observation, advanced geometric filtering methods can be implemented that mimic the effects of Fourier filters to achieve effects such as smoothing, enhancement, or band-bass filtering. © 2006 ACM

Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations

In many applications, one would like to perform calculations on smooth manifolds of dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. In this thesis, we approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients: (1) partitioning of the point set into subregions of trivial topology, (2) the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques, (3) the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and (4) patching together the local representations by means of a partition of unity. In this thesis we show the generality, flexibility, and accuracy of the method in four different problems. First, we exercise it in the context of Kirchhoff-Love thin shells, (d=2, D=3). We test our methodology against classical linear and non linear benchmarks in thin-shell analysis, and highlight its ability to handle point-set surfaces of complex topology and geometry. We then tackle problems of much higher dimensionality. We perform reduced order modeling in the context of finite deformation elastodynamics, considering a nonlinear reduced configuration space, in contrast with classical linear approaches based on Principal Component Analysis (d=2, D=10000's). We further quantitatively unveil the geometric structure of the motility strategy of a family of micro-organisms called Euglenids from experimental videos (d=1, D~30000's). Finally, in the context of enhanced sampling in molecular dynamics, we automatically construct collective variables for the molecular conformational dynamics (d=1...6, D~30,1000's)

Reconstructing plant architecture from 3D laser scanner data

En infographie, les modèles virtuels de plantes sont de plus en plus réalistes visuellement. Cependant, dans le contexte de la biologie et l'agronomie, l'acquisition de modèles précis de plantes réelles reste un problème majeur pour la construction de modèles quantitatifs du développement des plantes. Récemment, des scanners laser 3D permettent d'acquérir des images 3D avec pour chaque pixel une profondeur correspondant à la distance entre le scanner et la surface de l'objet visé. Cependant, une plante est généralement un ensemble important de petites surfaces sur lesquelles les méthodes classiques de reconstruction échouent. Dans cette thèse, nous présentons une méthode pour reconstruire des modèles virtuels de plantes à partir de scans laser. Mesurer des plantes avec un scanner laser produit des données avec différents niveaux de précision. Les scans sont généralement denses sur la surface des branches principales mais recouvrent avec peu de points les branches fines. Le cur de notre méthode est de créer itérativement un squelette de la structure de la plante en fonction de la densité locale de points. Pour cela, une méthode localement adaptative a été développée qui combine une phase de contraction et un algorithme de suivi de points. Nous présentons également une procédure d'évaluation quantitative pour comparer nos reconstructions avec des structures reconstruites par des experts de plantes réelles. Pour cela, nous explorons d'abord l'utilisation d'une distance d'édition entre arborescence. Finalement, nous formalisons la comparaison sous forme d'un problème d'assignation pour trouver le meilleur appariement entre deux structures et quantifier leurs différences. (Résumé d'auteur