| BOISSONNAT J. D.: Geometric structures for three-dimensional shape representation. ACM Trans. Graph. 3, 4 (1984), 266--286. |
....28155 GALIA) Researchers from the computational geometry community based their algorithms on the Delaunay complex of the sample points. In three dimensions the Delaunay complex is a tetrahedralization of the point set. It is well studied and has found many applications over the years. Boissonnat [8] gave the first Delaunay based reconstruction algorithm that removes tetrahedra and triangles violating certain conditions from the Delaunay complex. Unfortunately, it applies only to surfaces of genus zero. complex is a subcomplex of the Delaunay complex and usually it is computed via the ....
J.-D. Boissonnat. Geometric structures for three-dimensional shape representation. ACM Transactions on Graphics, 3(4):266--286, 1984.
....category. The differences in their methods lie in the cell selection strategy. The volume based scheme decomposes the space into cells, removes those cells that are not in the volume bounded by the sampled surface and creates the surface from the selected cells. Most algorithms in this category [Boi84, Vel95, ABK98] are based on Delaunay triangulation of the input points. The distance function of a surface gives the shortest distance from any point to the surface. The surface passes through the zeroes of this distance function. This approach leads to approximating instead of interpolatory ....
....[CL96, HDD 92] The basic idea behind incremental surface reconstruction is to build up the surface using surface oriented properties of the input data points. The approach of Mencl and Muller [MM98] use graph based techniques to complete the surface. Boissonnat s surface contouring algorithm [Boi84] starts with an edge and iteratively attaches further triangles at boundary edges of the emerging surface using a projection based approach to generate manifolds without boundaries. The Spiraling Edge triangulation technique proposed by Crossno and Angel [CA97] is similar to our algorithm. ....
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J. D. Boissonnat. Geometric structures for three-dimensional shape representation. ACM Trans. on Graphics, 3(4):266--286, 1984.
....of a surface while implicit surfaces represent a surface as a particular isocontour of a scalar function. Popular explicit representations include parametric surfaces using NURBS e.g. PT97, Rog00] and triangulated surfaces using Voronoi diagrams and Delaunay triangulations e.g. ABE98, ABK98, Boi84, Ede98, EM94] Tracking of large deformations and topological changes can be a problem using explicit surfaces. Recently, implicit surfaces or volumetric representations have attracted a lot of attention. The traditional approach [BBB 97, Mur91, TO99] uses a combination of smooth basis ....
J.D. Boissonnat. Geometric structures for three dimensional shape reconstruction. ACM Trans. Graphics 3, pages 266-286, 1984.
....of computing a piecewise linear surface that approximates the original surface from which only a set of discrete sample points are given as input. Because of its widespread application, this problem has been studied intensely in recent years. A very early paper on the problem was by Boissonnat [6] who proposed a sculpting of the Delaunay triangulation for reconstruction. A more refined sculpting strategy was designed by Edelsbrunner and Mucke [14] in their # shape algorithm. Bajaj, Bernardini and Xu [4] used # shapes for reconstructing scalar fields and three dimensional CAD models. The # ....
J. D. Boissonnat. Geometric structures for three dimensional shape representation, ACM Transact. on Graphics 3(4), (1984) 266--286.
....a tangent plane at each sample point using its k nearest neighbors and use the distance to the plane of the nearest sample as an estimative of the signed distance function to the surface. The zero set of this distance function is extracted using the marching cubes algorithm [11] Other algorithms [8, 9, 13] use a greedy approach. The ball pivoting algorithm [9] rolls a ball over the sample points; it requires the normal to the surface at each sample point, but it can create artifacts. Boissonnat [8] starts by finding an initial edge pq in the triangulated reconstruction; he then computes a tangent ....
....this distance function is extracted using the marching cubes algorithm [11] Other algorithms [8, 9, 13] use a greedy approach. The ball pivoting algorithm [9] rolls a ball over the sample points; it requires the normal to the surface at each sample point, but it can create artifacts. Boissonnat [8] starts by finding an initial edge pq in the triangulated reconstruction; he then computes a tangent plane around the edge, projects the k nearest neighbors of both vertices onto this plane and determines the point r that maximizes the angle # p r q (where the bar represents projected points ....
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J. D. Boissonnat. Geometric structures for three-dimensional shape reconstruction. ACM Transactions on Graphics 3(4):266--289, 1984.
....and our previous algorithm. 1. Introduction A triangulation for a given set of points is a well known topic of computational geometry [1, 2] and has many applications such as finite element analysis, solid modeling, shape representation, terrain modeling, volume rendering and computer vision [3, 4, 5]. Delaunay triangulation (DT) has been most attractive for triangulation due to its special feature that the circumscribed circle of a triangle must not constain other points than points of the triangle. There have been much research in DT. The time complexity of constructing Delaunay triangles ....
J. D. Boissonnat, Geometric Structures for Three Dimensional Shape Representation, ACM Transactions on Graphics 3 (1984) 266-286.
....that cross each other at the actual 3 D cursor position, which is shown as crosshair on each of the planes. In this fashion, one can always select a plane for position determination, that is far from being parallel to the target surface s local tangent plane. The Delaunay tetrahedralization [8] of the selected anchor points is then computed and sculpted by successive deletion of Delaunay tetrahedra from the convex hull, until all selected points lay on the surface shown in Figure 5c) In the current implementation, the user is required to guide the sculpturing interactively. However, ....
J.-D. Boissonnat. Geometric structures for threedimensional shape representation. ACM Transactions on Graphics, 3:266--286, October 1984.
....only. Figure 10 shows a cut out of the original data set. The ventricle appears as a gray crescent above the left eye. We segment the ventricle by using a Velcro Surface. After the anchor points are selected, the convex hull of the point cloud is computed. The Delaunay tetrahedralization [18] of the Figure 10: Clipped data set. The cuboid contains now mainly the left part of the patient s brain. The patient is facing towards us. On the front plane a part of his left eye is visible. The gray crescent above the eye is the left lateral ventricle which is clearly visible. convex hull ....
J.-D. Boissonnat. Geometric structures for three-dimensional shape representation. ACM Transactions on Graphics, 3:266--286, October 1984.
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BOISSONNAT J. D.: Geometric structures for three-dimensional shape representation. ACM Trans. Graph. 3, 4 (1984), 266--286.
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Boissonnat. Geometric structures for threedimensional shape representatio. ACM Transactions on Graphics, 1984.
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BOISSONNAT, J.-D. Geometric structures for three-dimensional shape representation. ACM Transactions on Graphics 3, 4 (Oct. 1984), 266--286.
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J.-D. Boissonnat. Geometric structures for three-dimensional shape representation. ACM Trans. Graph., 3(4), 1984.
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J-D. Boissonnat. Geometric structures for three-dimensional shape reconstruction. ACM Trans. Graphics 3 (1984) 266--286.
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J-D. Boissonnat. Geometric structures for three-dimensional shape reconstruction, ACM Trans. Graphics 3 (1984) 266-- 286.
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J. D. Boissonnat. Geometric structures for three dimensional shape representation. ACM Trans. Graphics, 3:266-286, 1984.
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J. D. Boissonnat. Geometric structures for three-dimensional shape reconstruction. ACM Transactions on Graphics 3(4):266--289, 1984.
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Boissonnat J.-D.: Geometric structures for three-dimensional shape reconstruction. ACM Transactions on Graphics 3(4):266--289, 1984. 1, 3
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J. D. Boissonnat. Geometric structures for three-dimensional shape representation. ACM Trans. on Graphics, 3(4):266--286, 1984.
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J. D. Boissonnat. Geometric structures for three-dimensional shape reconstruction. ACM Transactions on Graphics 3(4):266--289, 1984.
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J. D. Boissonnat. Geometric structures for three dimensional shape representation, ACM Transact. on Graphics 3(4), (1984) 266--286.
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J.-D. Boissonnat. Geometric structures for three-dimensional shape representation. ACM Trans. Graphics, 3:266-286, 1984.
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J.-D. Boissonnat, Geometric structures for three-dimensional shape reconstruction, ACM Transactions on Graphics 3 (4) (1984) 266--286.
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J-D. Boissonnat. Geometric structures for three-dimensional shape reconstruction. ACM Trans. Graphics 3 (1984) 266--286.
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J.-D. Boissonnat, "Geometric structures for threedimensional shape representation", ACM Transactions on Graphics, 3(4):266-286, October 1984.
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J.-D. Boissonnat. Geometric structures for three-dimensional shape representation. tCM Trans. aph., 3(4), 1984.
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