Performance comparison of adapted delaunay triangulation method over nurbs for surface optimization problems

Traditionally NURBS (Non-Uniform Rational Basis Spline) are used as the basis for defining free-form surfaces as they can define non-regular surfaces with minimal control points. However, they require parameters such as knot vectors and weights to configure a surface. Similarly, DT (Delaunay Triangulation) is proven and used widely for meshing, rendering and surface reconstruction applications, but its capability in freeform surface design for optimization is untested. Thus, this paper proposes Adapted Delaunay Triangulation (ADT) method which can generate a surface from scattered data points without any parameters. The paper presents a comparison of the performance of ADT method and NURBS fitting method for surface generation from scattered 3D coordinate points. This method was suggested so that the generated surface could be used in Stochastic Optimization Algorithm (SOA) methods and computational fluid dynamics applications (CFD) simultaneously. Data points that other 3D point clouds fitting methods would ignore as outliers are included in ADT method. Small change in each data point during optimization cycle should show a distinctive change in its output as SOA approaches depend on such differences for its optimal performance. Special consideration has been made for fast processing and rendering of the surface with minimum complexity (removing parameters such as knots and weights) and storage requirements as SOA methods demand generation of numerous surfaces to solve any problem

Reconstruction of freeform surfaces for metrology

The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.EMR

Técnicas de creación y manipulación de imágenes de estructuras orgánicas tridimensionales. Nuevos entornos de aplicación didáctica

The development of computer-generated images opens new perspectives in the field of teaching. These techniques permit geometric modelling of three-dimensional structures, allowing the production and manipulation of real images and the numerical and graphic characterization of two-three-dimensional contours. The procedure proposed is based on the manipulation, by geometric (turns, traslations) and algebraic (addition, intersection) operations, of an initially finite set of surfaces (elipsoids, paraboloids, cylinders and planes), defined by their parameters, for teaching purposes

Estimation incrémentale de surface à partir d'un nuage de point épars reconstruit à partir d'images omnidirectionnelles

National audienceCet article introduit une méthode incrémentale de reconstruction de surface (une 2-variété). Elle prend en entrée un nuage de points 3D épars reconstruit à partir d'une séquence d'images, par opposition aux algorithmes habituels denses. De plus, notre méthode est incrémentale : la surface est mise à jour à chaque nouvelle pose de caméra donnée en entrée, et la mise à jour a lieu dans un voisinage restreint de la nouvelle pose. Comparée aux autres méthodes de reconstruction de surface, notre méthode a l'avantage de cumuler toutes ces propriétés (nuage épars en entrée, 2-variété en sortie, calcul incrémental et local). La qualité et le temps d'exécution sont évalués sur une séquence d'images omnidirectionnelles (longue de 2.5 km) prise en environnement urbain, et la méthode est quantitativement évaluée sur une séquence urbaine synthétique

Graph matching with a dual-step EM algorithm

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data

Point cloud representation

Reconstructing a surface out of a three-dimensional set of points, which is obtained by sampling an object\u27s boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object\u27s surface only by the point cloud. We discuss how such a point cloud representation can be visualized and present processing steps like coarsifying and smoothing, which are important for dealing with the objects. Further we apply a multiresolution method to point cloud representations and use this technique as well as others for modelling purposes

Three-dimensional alpha shapes

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in \Real^3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter \alpha \in \Real controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.Comment: 32 page

Modèles 3d à partir d'un nuage épars de points et une caméra catadioptrique

Session "Articles"National audienceLa majorité des méthodes automatiques de modélisation 3d à partir d'images reconstruisent un ensemble dense de points. Nous proposons ici de reconstruire une surface directement à partir de l'ensemble épars de points reconstruits en estimant la géométrie. Deux méthodes voisines sont présentées, l'une est progressive (la surface est progressivement complétée au fur et à mesure que les images sont lues) et l'autre pas. Il s'agit aussi d'obtenir une variété topologique de dimension 2, pas une simple soupe de triangles mals connectés les uns aux autres. Malgrés le faible nombre de points reconstruits, l'expérience montre que l'on peut obtenir des résultats intéressants pour des environnements extérieurs avec une caméra catadioptrique

Virtual simulation of the postsurgical cosmetic outcome in patients with pectus excavatum

Pectus excavatum is the most common congenital deformity of the anterior chest wall, in which several ribs and the sternum grow abnormally. Nowadays, the surgical correction is carried out in children and adults through Nuss technic. This technic has been shown to be safe with major drivers as cosmesis and the prevention of psychological problems and social stress. Nowadays, no application is known to predict the cosmetic outcome of the pectus excavatum surgical correction. Such tool could be used to help the surgeon and the patient in the moment of deciding the need for surgery correction. This work is a first step to predict postsurgical outcome in pectus excavatum surgery correction. Facing this goal, it was firstly determined a point cloud of the skin surface along the thoracic wall using Computed Tomography (before surgical correction) and the Polhemus FastSCAN (after the surgical correction). Then, a surface mesh was reconstructed from the two point clouds using a Radial Basis Function algorithm for further affine registration between the meshes. After registration, one studied the surgical correction influence area (SCIA) of the thoracic wall. This SCIA was used to train, test and validate artificial neural networks in order to predict the surgical outcome of pectus excavatum correction and to determine the degree of convergence of SCIA in different patients. Often, ANN did not converge to a satisfactory solution (each patient had its own deformity characteristics), thus invalidating the creation of a mathematical model capable of estimating, with satisfactory results, the postsurgical outcome.Fundação para a Ciência e a Tecnologia, Portugal (FCT) through the Postdoc grant referenced SFRH/BPD/46851/2008 and R&D project referenced PTDC/SAU-BEB/103368/2008