792 research outputs found
Principal component and Voronoi skeleton alternatives for curve reconstruction from noisy point sets
Surface reconstruction from noisy point samples must take into consideration the stochastic nature of the sample -- In other words, geometric algorithms reconstructing the surface or curve should not insist in following in a literal way each sampled point -- Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing through the best possible (in the statistical sense) geometric locus that represents the sample -- This work presents two new methods to find a Piecewise Linear approximation from a Nyquist-compliant stochastic sampling of a quasi-planar C1 curve C(u) : R → R3, whose velocity vector never vanishes -- One of the methods articulates in an entirely new way Principal Component Analysis (statistical) and Voronoi-Delaunay (deterministic) approaches -- It uses these two methods to calculate the best possible tape-shaped polygon covering the planarised point set, and then approximates the manifold by the medial axis of such a polygon -- The other method applies Principal Component Analysis to find a direct Piecewise Linear approximation of C(u) -- A complexity comparison of these two methods is presented along with a qualitative comparison with previously developed ones -- It turns out that the method solely based on Principal Component Analysis is simpler and more robust for non self-intersecting curves -- For self-intersecting curves the Voronoi-Delaunay based Medial Axis approach is more robust, at the price of higher computational complexity -- An application is presented in Integration of meshes originated in range images of an art piece -- Such an application reaches the point of complete reconstruction of a unified mes
Surface Reconstruction From 3D Point Clouds
The triangulation of a point cloud of a 3D object is a complex problem, since it
depends on the complexity of the shape of such object, as well as on the density
of points generated by a specific scanner.
In the literature, there are essentially two approaches to the reconstruction of
surfaces from point clouds: interpolation and approximation. In general, interpolation
approaches are associated with simplicial methods; that is, methods
that directly generate a triangle mesh from a point cloud. On the other hand,
approximation approaches generate a global implicit function — that represents
an implicit surface — from local shape functions, then generating a triangulation
of such implicit surface.
The simplicial methods are divided into two families: Delaunay and mesh growing.
Bearing in mind that the first of the methods presented in this dissertation
falls under the category of mesh growing methods, let us focus our attention
for now on these methods. One of the biggest problems with these methods is
that, in general, they are based on the establishment of dihedral angle bounds
between adjacent triangles, as needed to make the decision on which triangle
to add to the expansion mesh front. Typically, other bounds are also used for
the internal angles of each triangle. In the course of this dissertation, we will
see how this problem was solved.
The second algorithm introduced in this dissertation is also a simplicial method
but does not fit into any of the two families mentioned above, which makes
us think that we are in the presence of a new family: triangulation based on
the atlas of charts or triangle stars. This algorithm generates an atlas of the
surface that consists of overlapping stars of triangles, that is, one produces a
total surface coverage, thus solving one of the common problems of this family
of direct triangulation methods, which is the appearance of holes or incomplete
triangulation of the surface.
The third algorithm refers to an implicit method, but, unlike other implicit
methods, it uses an interpolation approach. That is, the local shape functions
interpolate the points of the cloud. It is, perhaps, one of a few implicit methods
that we can find in the literature that interpolates all points of the cloud.
Therefore, one of the biggest problems of the implicit methods is solved, which
has to do with the smoothing of the surface sharp features resulting from the blending of the local functions into the global function.
What is common to the three methods is the interpolation approach, either in
simple or implicit methods, that is, the linearization of the surface subject to
reconstruction. As will be seen, the linearization of the neighborhood of each
point allows us to solve several problems posed to the surface reconstruction
algorithms, namely: point sub‐sampling, non‐uniform sampling, as well as sharp
features.A triangulação de uma nuvem de pontos de um objeto 3D é um problema complexo,
uma vez que depende da complexidade da forma desse objeto, assim
como da densidade dos pontos extraídos desse objeto através de um scanner 3D
particular.
Na literatura, existem essencialmente duas abordagens na reconstrução de superfícies
a partir de nuvens de pontos: interpolação e aproximação. Em geral, as
abordagens de interpolação estão associadas aos métodos simpliciais, ou seja,
a métodos que geram diretamente uma malha de triângulos a partir de uma
nuvem de pontos. Por outro lado, as abordagens de aproximação estão habitualmente
associadas à geração de uma função implícita global —que representa
uma superfície implícita— a partir de funções locais de forma, para em seguida
gerar uma triangulação da dita superfície implícita.
Os métodos simpliciais dividem‐se em duas famílias: triangulação de Delaunay
e triangulação baseada em crescimento progressivo da triangulação (i.e., mesh
growing). Tendo em conta que o primeiro dos métodos apresentados nesta dissertação
se enquadra na categoria de métodos de crescimento progressivo, foquemos
a nossa atenção por ora nestes métodos. Um dos maiores problemas
destes métodos é que, em geral, se baseiam no estabelecimento de limites de
ângulos diédricos (i.e., dihedral angle bounds) entre triângulos adjacentes, para
assim tomar a decisão sobre qual triângulo acrescentar à frente de expansão da
malha. Tipicamente, também se usam limites para os ângulos internos de cada
triângulo. No decorrer desta dissertação veremos como é que este problema foi
resolvido.
O segundo algoritmo introduzido nesta dissertação também é um método simplicial,
mas não se enquadra em nenhuma das duas famílias acima referidas, o que
nos faz pensar que estaremos na presença de uma nova família: triangulação
baseada em atlas de vizinhanças sobrepostas (i.e., atlas of charts) ou estrelas
de triângulos (i.e., triangle star). Este algoritmo gera um atlas da superfície
que é constituído por estrelas sobrepostas de triângulos, ou seja, produz‐se a
cobertura total da superfície, resolvendo assim um dos problemas comuns desta
família de métodos de triangulação direta que é o do surgimento de furos ou de
triangulação incompleta da superfície.
O terceiro algoritmo refere‐se a um método implícito, mas, ao invés de grande parte dos métodos implícitos, utiliza uma abordagem de interpolação. Ou seja,
as funções locais de forma interpolam os pontos da nuvem. É, talvez, um dos
poucos métodos implícitos que podemos encontrar na literatura que interpola
todos os pontos da nuvem. Desta forma resolve‐se um dos maiores problemas dos
métodos implícitos que é o do arredondamento de forma resultante do blending
das funções locais que geram a função global, em particular ao longo dos vincos
da superfície (i.e., sharp features).
O que é comum aos três métodos é a abordagem de interpolação, quer em
métodos simpliciais quer em métodos implícitos, ou seja a linearização da superfície
sujeita a reconstrução. Como se verá, a linearização da vizinhança de
cada ponto permite‐nos resolver vários problemas colocados aos algoritmos de
reconstrução de superfícies, nomeadamente: sub‐amostragem de pontos (point
sub‐sampling), amostragem não uniforme (non‐uniform sampling), bem como
formas vincadas (sharp features)
Learning Delaunay Surface Elements for Mesh Reconstruction
We present a method for reconstructing triangle meshes from point clouds.
Existing learning-based methods for mesh reconstruction mostly generate
triangles individually, making it hard to create manifold meshes. We leverage
the properties of 2D Delaunay triangulations to construct a mesh from manifold
surface elements. Our method first estimates local geodesic neighborhoods
around each point. We then perform a 2D projection of these neighborhoods using
a learned logarithmic map. A Delaunay triangulation in this 2D domain is
guaranteed to produce a manifold patch, which we call a Delaunay surface
element. We synchronize the local 2D projections of neighboring elements to
maximize the manifoldness of the reconstructed mesh. Our results show that we
achieve better overall manifoldness of our reconstructed meshes than current
methods to reconstruct meshes with arbitrary topology
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
Optimized normal and distance matching for heterogeneous object modeling
This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper
Semi-Automated DIRSIG scene modeling from 3D lidar and passive imagery
The Digital Imaging and Remote Sensing Image Generation (DIRSIG) model is an established, first-principles based scene simulation tool that produces synthetic multispectral and hyperspectral images from the visible to long wave infrared (0.4 to 20 microns). Over the last few years, significant enhancements such as spectral polarimetric and active Light Detection and Ranging (lidar) models have also been incorporated into the software, providing an extremely powerful tool for multi-sensor algorithm testing and sensor evaluation. However, the extensive time required to create large-scale scenes has limited DIRSIG’s ability to generate scenes ”on demand.” To date, scene generation has been a laborious, time-intensive process, as the terrain model, CAD objects and background maps have to be created and attributed manually. To shorten the time required for this process, this research developed an approach to reduce the man-in-the-loop requirements for several aspects of synthetic scene construction. Through a fusion of 3D lidar data with passive imagery, we were able to semi-automate several of the required tasks in the DIRSIG scene creation process. Additionally, many of the remaining tasks realized a shortened implementation time through this application of multi-modal imagery. Lidar data is exploited to identify ground and object features as well as to define initial tree location and building parameter estimates. These estimates are then refined by analyzing high-resolution frame array imagery using the concepts of projective geometry in lieu of the more common Euclidean approach found in most traditional photogrammetric references. Spectral imagery is also used to assign material characteristics to the modeled geometric objects. This is achieved through a modified atmospheric compensation applied to raw hyperspectral imagery. These techniques have been successfully applied to imagery collected over the RIT campus and the greater Rochester area. The data used include multiple-return point information provided by an Optech lidar linescanning sensor, multispectral frame array imagery from the Wildfire Airborne Sensor Program (WASP) and WASP-lite sensors, and hyperspectral data from the Modular Imaging Spectrometer Instrument (MISI) and the COMPact Airborne Spectral Sensor (COMPASS). Information from these image sources was fused and processed using the semi-automated approach to provide the DIRSIG input files used to define a synthetic scene. When compared to the standard manual process for creating these files, we achieved approximately a tenfold increase in speed, as well as a significant increase in geometric accuracy
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