633 research outputs found
Weighted simplicial complex reconstruction from mobile laser scanning using sensor topology
We propose a new method for the reconstruction of simplicial complexes
(combining points, edges and triangles) from 3D point clouds from Mobile Laser
Scanning (MLS). Our method uses the inherent topology of the MLS sensor to
define a spatial adjacency relationship between points. We then investigate
each possible connexion between adjacent points, weighted according to its
distance to the sensor, and filter them by searching collinear structures in
the scene, or structures perpendicular to the laser beams. Next, we create and
filter triangles for each triplet of self-connected edges and according to
their local planarity. We compare our results to an unweighted simplicial
complex reconstruction.Comment: 8 pages, 11 figures, CFPT 2018. arXiv admin note: substantial text
overlap with arXiv:1802.0748
Cone fields and topological sampling in manifolds with bounded curvature
Often noisy point clouds are given as an approximation of a particular
compact set of interest. A finite point cloud is a compact set. This paper
proves a reconstruction theorem which gives a sufficient condition, as a bound
on the Hausdorff distance between two compact sets, for when certain offsets of
these two sets are homotopic in terms of the absence of {\mu}-critical points
in an annular region. Since an offset of a set deformation retracts to the set
itself provided that there are no critical points of the distance function
nearby, we can use this theorem to show when the offset of a point cloud is
homotopy equivalent to the set it is sampled from. The ambient space can be any
Riemannian manifold but we focus on ambient manifolds which have nowhere
negative curvature. In the process, we prove stability theorems for
{\mu}-critical points when the ambient space is a manifold.Comment: 20 pages, 3 figure
Computational Geometry Column 38
Recent results on curve reconstruction are described.Comment: 3 pages, 1 figure, 18 ref
Approximating Local Homology from Samples
Recently, multi-scale notions of local homology (a variant of persistent
homology) have been used to study the local structure of spaces around a given
point from a point cloud sample. Current reconstruction guarantees rely on
constructing embedded complexes which become difficult in high dimensions. We
show that the persistence diagrams used for estimating local homology, can be
approximated using families of Vietoris-Rips complexes, whose simple
constructions are robust in any dimension. To the best of our knowledge, our
results, for the first time, make applications based on local homology, such as
stratification learning, feasible in high dimensions.Comment: 23 pages, 14 figure
Feature preserving smoothing of 3D surface scans
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2004.Includes bibliographical references (p. 63-70).With the increasing use of geometry scanners to create 3D models, there is a rising need for effective denoising of data captured with these devices. This thesis presents new methods for smoothing scanned data, based on extensions of the bilateral filter to 3D. The bilateral filter is a non-linear, edge-preserving image filter; its extension to 3D leads to an efficient, feature preserving filter for a wide class of surface representations, including points and "polygon soups."by Thouis Raymond Jones.S.M
Reconstruction d'ensembles compacts 3D
Reconstruire un modèle à partir d'échantillons est un problème central se posant en médecine numérique, en ingénierie inverse, en sciences naturelles, etc. Ces applications ont motivé une recherche substantielle pour la reconstruction de surfaces, la question de la reconstruction de modèles plus généraux n'ayant pas été examinée. Ce travail présente an algorithme visant à changer le paradigme de reconstruction en 3D comme suit. Premièrement, l'algorithme reconstruit des formes générales--des ensembles compacts et non plus des surfaces. Sous des hypothèses appropriées, nous montrons que la reconstruction a le type d'homotopie de l'objet de départ. Deuxièmement, l'algorithme ne génère pas une seule reconstruction, mais un ensemble de reconstructions plausibles. Troisièmement, l'algorithme peut être couplé à la persistance topologique, afin de sélectionner les traits les plus stables du modèle reconstruit. Enfin, en cas d'échec de la reconstruction, la méthode permet une identification aisée des régions sous-echantillonnées, afin éventuellement de les enrichir. Ces points clefs sont illustrés sur des modèles difficiles, et devraient permettre de mieux tirer parti de leurs caractéristiques dans les application sus-citées
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