FUCHS H., KEDEM Z., USELTON S., "Optimal surface reconstruction from planar contours", Communications of the ACM, vol. 20, num. 10, 1977, p. 693-702.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....approximation; the design of transfer functions for mapping data elements onto visual attributes; and lastly image synthesis. 2. 2 Data Acquisition and Representation The original incentive for developing volume visualisation was to create an effective method for displaying digital medical data [FKU77, HL79, Art79] Today, digitisation techniques are frequently used to create volume data in a number of different fields, although the medical field perhaps remains Rendering Indirect Surface Volume Estimation Gradient Transfer Opacity Reconstruct Rendering Volume Segment Acquisition ....

....a closed contour. Finally, the closed contours in adjacent slices throughout the whole volume are connected with triangles to form a piecewise planar approximation to the original iso surface. Keppel [Kep75] presents a contour tracking approach which maximises the enclosed object. Fuchs et al. FKU77] describe a similar method but use a heuristic for minimising the total surface area occupied by the triangles. Christiansen and Sederberg [CS78] use yet another heuristic which attempts to minimise the average polygon size. Unfortunately, all of these methods exhibit ambiguities either when ....

H. Fuchs, Z.M. Kedem, and S. Uselton. Optimal surface reconstruction from planar contours. Communications of the ACM, 20(10):693--702, October 1977.

....The parametric methods try to find corresponding pairs of points between the boundaries of two 2D shapes. Afterwards the intermediate samples are interpolated from these pairs of points. An early application of this approach was a contour interpolation technique published by Fuchs et al. [4]. The idea was to find a minimal area triangulation connecting two corresponding contours. Further improvements were also published like defining quality measures for the correspondence between contours and optimizing the basic method [5, 6] The major drawback of the parametric methods is the ....

H. Fuchs, Z. M. Kedem, S. P. Uselton, Optimal Surface Reconstruction from Planar Contours, Communications of the ACM, 20(10), pages 693-702, October, 1977.

....contours. Using the MC algorithm in this setting suffers from the already discussed problems: staircase artifacts (due to the undersampling and 1 bit quantization especially bothersome) and very large surface models. A large number of publications treat the problem of connecting contours, see [14, 8, 4, 17, 3, 20, 1, 23] and [19, 21, 27] for overviews. All these algorithms have to decide which vertices in the neighboring contour must be connected with a given vertex to form triangles. Unfortunately, this correspondence problem cannot be answered uniquely and suffers from the same problem of missing information ....

H. Fuchs, Z.M. Kedem, and S.P. Uselton. Optimal surface re-construction from planar contours. Comm. of the ACM, 20:693--702, 1977.

....that can be advantageously exploited for distance calculations during a subsequent simplification step. Keywords: distance field, reconstruction from contours, mesh simplification. 1 Introduction and previous work A large number of publications treat the problem of connecting contours, see [14, 7, 3, 17, 2, 19, 1, 22] and [18, 21, 25] for overviews. All these algorithms have to decide which vertices in the neighboring contour must be connected with a given vertex to form triangles (cor respondence problem) Unfortunately, this problem cannot be answered uniquely (especially in cases with large differences ....

H. Fuchs, Z. Kedem, and S. Uselton. Optimal surface reconstruction from planar contours. Comm. of the ACM, 20:693--702, 1977.

....process. After obtaining d s , and in order to get the coordinates of p we applied : x s = x s d s n x y s = y s d s n y z s = z s d s n z In this way we obtain p , and it is a point of the surface of the face that guarantees that the surface is acceptable according to [Fuc77] since only they have modified the x, y, z coordinates, and didn t get hold of their normal vectors and their connections in the mesh of triangles T so we can obtain T . RESULTS Using a computerized tool to model the skull [Pla96] based on the mathematical model that we describe in this ....

....craneometrical points: Bregma, Metopio and Estefanio. 4.CONCLUTIONS We have presented a mathematical model for landmark based 3D mesh warping for skull based face reconstruction. We have postulated the model based on the methodology [Leb93] accomplishing the conditions of acceptability stated by [Fuc77]. The model is applicable to warp any type of surface that fulfill the following conditions: 1. The starting surface is defined by a mesh of triangles and it s acceptable according to [Fuc77] 2. The behavior of the resulting surface in a number of characteristic points (that is to say the ....

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Fuchs H., Kedem Z. M. Uselton S.P. "Optimal surface reconstruction from planar contours" . Graphics and Image Processing. Oct, Vol 20, Not 10, pp 693-702. 1977.

....that the morph is self intersection free when the given polygons have genus greater that zero. In this paper we present such an algorithm. A related intriguing problem that has been studied in the literature is the reconstruction of a solid object from a series of parallel planar cross sections [1 4,6]. It has important applications in medical imaging, topography and solid modeling. A common approach for solving this problem is to subdivide it into subproblems of surface reconstruction between pairs of successive slices. The latter problem is defined as follows: Given a pair of parallel planar ....

H. Fuchs, Z. Kedem, and S. Uselton, Optimal surface reconstruction from planar contours, Comm. of the ACM, 20 (1977), pp. 693--702.

....1 : P 1 4 as shown. De#ne the knot vectors of these two B splines to be simply k 0 = #k 0 1 ; k 0 n0 # = #1; 3; 5; 7; 8# and k 1 = #k 1 1 ; k 1 n1 # = #1; 2; 3; 5#. Shape Blending of Curves 3 P 1 1 P 1 2 P 1 3 P 1 4 P 0 1 P 0 2 P 0 3 P 0 4 P 0 5 k = [1, 2, 3, 5] k = 1, 3, 5, 7, 8] P 1 1 P 1 2 =P 1 3 P 1 4 P 1 5 P 0 1 P 0 2 P 0 3 P 0 4 P 0 5 k = 1, 2, 2, 3, 5] k = 1, 3, 5, 7, 8] k = 1, 2.5, 3.5, 5, 6.5] Fig. 2. Polygons as linear B splines, before and after shape blend. Then, each B spline curve is piecewise linear ....

....De#ne the knot vectors of these two B splines to be simply k 0 = #k 0 1 ; k 0 n0 # = #1; 3; 5; 7; 8# and k 1 = #k 1 1 ; k 1 n1 # = #1; 2; 3; 5#. Shape Blending of Curves 3 P 1 1 P 1 2 P 1 3 P 1 4 P 0 1 P 0 2 P 0 3 P 0 4 P 0 5 k = 1, 2, 3, 5] k = [1, 3, 5, 7, 8] P 1 1 P 1 2 =P 1 3 P 1 4 P 1 5 P 0 1 P 0 2 P 0 3 P 0 4 P 0 5 k = 1, 2, 2, 3, 5] k = 1, 3, 5, 7, 8] k = 1, 2.5, 3.5, 5, 6.5] Fig. 2. Polygons as linear B splines, before and after shape blend. Then, each B spline curve is piecewise linear given by P j #t#= ....

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Fuchs, H., Z. M. Kedem, and S. P. Uselton, Optimal surface reconstruction from planar contours, Comm. ACM 20 #1977#, 693#702.

....surfaces from contours. Rather, what matters more is that the surfacing algorithm produces a correct result. The traditional method for building triangulated surfaces from planar contours consists of solving three subproblems for each structure in the volume: correspondence, tiling, and branching [4, 6, 15, 21]. However, because these methods process the structures serially, rather than processing them simultaneously, they do not necessarily produce correct results for volumes in which surfaces abut. Full volumetric models, such as torso models, cranial models, or pelvic models are often comprised ....

....corresponding contours from consecutive slices There has been much research targeted at solving this problem efficiently. The problem was reformulated by Keppel [11] as finding a path through a toroidal graph. Formalization of this method and efficiency improvements were subsequently introduced [3, 6, 21]. These methods vary in the heuristics used for optimizing the tiling, as well as in the complexity of their search. The simplest method is a greedy algorithm that marches through pairs of contours. For each step, it chooses whether to advance along the top contour or the bottom contour by picking ....

H. Fuchs, Z. M. Kedem, and S. P. Uselton. Optimal surface reconstruction from planar contours. Communications of the ACM, 20(10):693--702, October 1977.

....We solve this problem using the dynamic programming technique. When the curves are open curves, we use a constraint that the end points of the source and the target curves correspond alternately. If the curves are closed curves, then the global minimum can be calculated using the algorithm in [4] without having the user specifying the initial correspondence. Figure 2 shows an example of shape interpolation between a turtle and a wolf (same as the example in [25] The correspondence between the turtle and the wolf are calculated by using our algorithm. In the shape interpolation process, ....

H. Fuchs, Z.M. Kedem, and S.P. Uselton. Optimal surface reconstruction from planar contours. In ACM of Communications, Vol. 20, No. 10, pages 693-702, 1977.

....correspondencebetween the vertices (samples) of the two signals: to each vertex of one signal, assign (at least) a vertex in the other signal such that a global cost function measuring the difference of the two signals is minimized. In this sense, the problem is related to contour triangulation [10] and shape blending [24] and is solved by dynamic programming optimization techniques. The solution spacecan be represented as a two dimensional grid, where eachnode corresponds to one possible vertex assignment (see Figure 10) The optimal vertex correspondence solution is illustrated in the ....

....of each signal. Intuitively, the larger the difference in distance between two adjacent vertices of 4 This holds for the vertex correspondence problem,where we favor a diagonal move in the graph over a south followed by east moveor an east followed by a south move. For contour triangulation [10], where diagonal moves are denied, the complexity is O(#2n# ##n n #) 0 1 2 3 4 5 6 7 8 9 cost function terms: stretching work between 2 adjacent vertices in signal (difference in segment lengths) bending work between 3 adjacent vertices in signal (difference in angles) B A i signal ....

FUCHS,H.,KEDEM,Z.,AND USELTON, S. Optimal surface reconstruction from planar contours. Communications of the ACM 10, 10 (1977), 693--702.

....Reynolds, and Udupa [11] voxels which intersect the iso surface of interest are detected; the voxel faces are rendered as a connected mesh of small squares. A mesh of triangles that approximates the iso surface can be generated by connecting a stack of planar contours (Fuchs, Kedem, and Uselton [33]) or by finding a linear approximation to the surface inside each voxel (Lorensen and Cline s marching cubes technique [60] In the dividing cubes method (Cline, Lorensen, Ludke, and Teeter [12] a mesh of point primitives is generated from the iso surface. 1.1.2 Volume Rendering Algorithms ....

Fuchs, H., Kedem, Z. M., and Uselton, S. P., "Optimal Surface Reconstruction from Planar Contours", Communications of the ACM, 20(10), October 1977, pp. 693--702.

....ffl Self intersecting shapes. In most applications, it is desirable that the reconstructed shape is simple, i.e. free of self intersection. However, some existing algorithms do not guarantee this property. As pointed out in [1] it is possible that the output of the toroidal graph method [13] can have a selfintersection for a pair of dissimilar contours, even when it is possible to construct an intersection free shape by using the same pair of contours by a different approach. For a certain pair of contours, it is not possible to construct a simple polyhedron at all only by using ....

....and an analysis of the algorithm are shown in Sections 5 and 6, respectively. Section 7 contains some remarks on the method and Section 8 concludes the paper. 2 Background 2. 1 Related Work Reconstructing a 3D solid from a series of contour data was first formulated by using the toroidal graph [13, 21]. In this approach, a triangular tiling is represented as a path in the graph. Then, the shortest path is sought in the graph to generate a tiling such that some global property is minimized such as the total surface area and the total volume enclosed by the solid. Some variations have also been ....

[Article contains additional citation context not shown here]

H. Fuchs, Z. Kedem, and S. Uselton. Optimal surface reconstruction from planar contours. Communications of the ACM, 20(10):693--702, 1977.

....to facilitate understanding of the underlying three dimensional structure and aid in pre surgical planning [Gold85] Techniques for viewing three dimensional data volumes have evolved from image processing and data conversion. A few examples would be extracting contour edges and surface tiling [Fuch77], finding isosurfaces with the marching cubes algorithm [Lore87] and 3D surface shading in the cuberille and voxel environment [Chen85, Kauf88, Levo88] and finally to direct volume visualization that simulates the amount of material traversed by a light ray in an opacity parameter [Dreb88, ....

Fuchs, H., Z. M. Kedem, and S. P. Uselton, "Optimal Surface Reconstruction from Planar Contours," Communications of the ACM 20(10), pp. 693-702 (1977).

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FUCHS H., KEDEM Z., USELTON S., "Optimal surface reconstruction from planar contours", Communications of the ACM, vol. 20, num. 10, 1977, p. 693-702.

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H. Fuchs, Z.M. Kedem, and S.P. Uselton. Optimal surface reconstruction from planar contours. Communications of the ACM, 20(10):693--702, Oct. 1977.

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H. Fuchs, Z. M. Kedem, and S. P. Uselton, "Optimal surface reconstruction from planar contours," Commun. ACM, vol. 20, pp. 693--702, 1977.

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Fuchs, H., Kedem, Z. M., and Uselton, S. P., "Optimal Surface Reconstruction from Planar Contours", Communications of the ACM, 20(10), October 1977, pp. 693--702.

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Fuchs, H., Kedmen, Z., and Uselton, S., "Optimal Surface Reconstruction from Planar Contours", Communications of the ACM, Volume 20, Number 10, October 1977, pages 693--702.

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H. Fuchs, Z. M. Kedem and S. P. Uselton. Optimal surface reconstruction from planar contours. Commun. ACM, 20:693-702, 1977.

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H. Fuchs, Z.M. Kedem, and S.P. Uselton. Optimal surface reconstruction from planar contours. Communications ACM, 20(10):693--702, 1977.

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H. Fuchs, Z.M. Kedem, and S.P. Uselton. Optimal surface reconstruction from planar contours. Commun. ACM, 20:693#702, 1977.

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Fuchs H, Kedem Z, Uselton S. Optimal surface reconstruction from planar contours. Communications of the ACM

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Henry Fuchs, Zvi Kedem, and Samuel Uselton. Optimal surface reconstruction from planar contours. Communications of the ACM, 20(10):693--702, October 1977. ACM SIGGRAPH Conference Proceedings.

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H. Fuchs, Z.M. Kedem, and S.P. Uselton, "Optimal Surface Reconstruction from Planar Contours," Communications of the ACM, vol. 20, no. 10, pp. 693-702, October 1977.

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Fuchs H, Kedem ZM, Uselton SP (1977) Optimal surface reconstruction from planar contours. Comm. of the ACM 20:693--702

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