Soucy, M. and Laurendeau, D. (1996). Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1---14.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to a function sampled at scattered points. We also propose a second adaptive thinning algorithm (denoted by AT3) which is less accurate but much faster. Though we have not found papers in which the thinning algorithm AT1 appears, it is close to the simpli cation algorithm of Soucy and Laurendeau [ 12 ], designed for free form 3D triangle meshes. To gain some insight into the nature of our algorithm, it is proved that for data sampled from a convex function, with the strategy of convex triangulation, minimization of our preferred anticipated error yields the same sequence of removed points, as ....

....of corresponding triangulations TK ; TN . This thinning algorithm will be the subject of most of this paper so let us pause to make some observations. Remarks 1. The basic principles of this thinning algorithm are similar to those of the algorithm proposed by Soucy and Laurendeau [ 12 ] for the simpli cation of free form triangle meshes in 3D, where the retriangulation of a cell is done by a local projection into a locally de ned plane. 2. By changing the de nition of a removable point and or by changing the strategy of triangulation, various alternative thinning algorithms ....

M. Soucy and D. Laurendeau, Multiresolution Surface Modeling Based on Hierarchical Triangulation, Computer Vision and Image Understanding 63 (1996), 1-14.

....are added to the front of the model providing the inflation force needed to successfully segment the long narrow feature. Both subdivision criteria can be used in conjunction to minimise the polygon count of a mesh, removing the need for post processing techniques such as Delaunay Triangulation [7]. An edge is subdivided only if it exceeds both a distance and a curvature threshold. Polygons on parts of the surface with low curvature grow beyond the threshold keeping polygon counts to a minimum. Therefore, areas of high curvature have larger numbers of small polygons that better model the ....

Soucy, M., and Laurendeau, D., "Multiresolution Surface Modeling Based on Hierarchical Traingulation.", Computer Vision and Image Understanding, 63(1), 1996, 1-14.

....to a function sampled at scattered points. We also propose a second adaptive thinning algorithm (denoted by AT3) which is less accurate but much faster. Though we have not found papers in which the thinning algorithm AT1 appears, it is close to the simplification algorithm of Soucy and Laurendeau [ 12 ], designed for free form 3D triangle meshes. To gain some insight into the nature of our algorithm, it is proved that for data sampled from a convex function, with the strategy of convex triangulation, minimization of our preferred anticipated error yields the same sequence of removed points, as ....

....of corresponding triangulations TK ; TN . This thinning algorithm will be the subject of most of this paper so let us pause to make some observations. Remarks 1. The basic principles of this thinning algorithm are similar to those of the algorithm proposed by Soucy and Laurendeau [ 12 ] for the simplification of free form triangle meshes in 3D, where the retriangulation of a cell is done by a local projection into a locally defined plane. 2. By changing the definition of a removable point and or by changing the strategy of triangulation, various alternative thinning algorithms ....

M. Soucy and D. Laurendeau, Multiresolution Surface Modeling Based on Hierarchical Triangulation, Computer Vision and Image Understanding 63 (1996), 1--14.

....issues behind the solution here is how to adaptively control the levels of detail (LODs) of the model by exploiting task oriented heuristics. The following heuristics have been widely used in disciplines involving such a geometric modeling process: 1) complexity of local shapes of object surfaces [21, 20, 24]; 2) image space constraints on illumination, radiometry and textures [7, 15, 22, 4] 3) view dependent criteria such as visibility or relative locations of objects and viewers [14, 11, 3] On the other hand, perceptual gaze provides another nice cue for minimizing visual complexity of virtual ....

M. Soucy and D. Laurendeau. Multi-resolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63:1--14, 1996.

....simplification [7] are vertex clustering, vertex decimation, edge contraction, and patch decimation. Vertex clustering [8, 9] means that some close vertices are clustered and represented by a single vertex. This technique is fast, but with low quality on the simplified result. Vertex decimation [10, 11] is a technique by destroying a vertex, and retriangulating the hole. And edge contraction [2, 3, 4, 5, 6] is by contracting an edge to a vertex recursively. The most well known algorithm is the quadric error metric edge contraction proposed by Garland and Heckbert [2] which is efficient and have ....

M. Soucy and D. Laurendeau. Multiresolution Surface Modeling Based on Hierarchical Triangulations. Computer Vision and Image Understanding, 63(1):1-14, 1996.

....of the mesh. To avoid self intersections, additional geometric tests are required. The selection of the vertex to be removed is commonly based on a curvature estimation at the vertex. Vertices with low curvature values are removed first. The vertex removal operator is used in [SZL92] Cea96] SL96] and in most terrain simplification methods. ffl edge collapse The edge collapse operator takes as parameter the edge to be collapsed, or its equivalent, a pair of vertices sharing an edge. The two vertices are collapsed in one vertex. As a result of this collapse, the triangles sharing the ....

.... Terrain [SR94] PM92] Mesh simplif 8 : Bottom up: Vel93] Clustering: RB93] Red96] Tan97] GH97] Incremental 8 : vertex: SZL92] Cea96] SL96] edge: Gue96] RR96] AS96] HDD 93] Hop96] Hop97] PH97] face: Ham94] faces: DZ91] KCHN91] HH93] KT96] KT93] edge flip: CCMS97] BBCS96] Re tiling: Tur92] Wavelets: DLW94] Eea95] CPD 96] GSG96] Based on SDM ( Octrees: AAB95a] JAS95] AAB ....

Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding: CVIU, 63(1):1--14, January 1996.

....to a function sampled at scattered points. We also propose a second adaptive thinning algorithm (denoted by AT3) which is less accurate but much faster. Though we have not found papers in which thinning algorithm AT1 appears, it is close to the simpli cation algorithm of Soucy and Laurendeau [ 11 ], designed for free form 3D triangle meshes. To gain some insight into the nature of our algorithm, it is proved that for data sampled from a convex function, with the strategy of convex triangulation, minimization of our preferred anticipated error yields the same sequence of removed points, as ....

....of corresponding triangulations TK ; TN . This thinning algorithm will be the subject of most of this paper so let us pause to make some observations. Remarks 1. The basic principles of this thinning algorithm are similar to those of the algorithm proposed by Soucy and Laurendeau [ 11 ] for the simpli cation of free form triangle meshes in 3D, where the retriangulation of a cell is done by a local projection into a locally de ned plane. 2. By changing the de nition of a removable point and or by changing the strategy of triangulation, various alternative thinning algorithms can ....

M. Soucy and D. Laurendeau, Multiresolution Surface Modeling Based on Hierarchical Triangulation, Computer Vision and Image Understanding 63 (1996), 1-14.

....a set of dense points, an explicit 3 D model should be obtained for further high level processing. Thus, the modeling technique to convert the raw range data into a suitable surface model is quite of important issue, and much efforts have been made to develop such techniques so far [1] 5] [7], 9] 12] Applications of this technique can be found in the field of 3 D modeling, including reverse engineering and virtual environments, as well as 3 D video Manuscript received March 15, 1999; revised September 30, 1999. This paper was recommended by Guest Editor K. N. Ngan I. K. Park and ....

....acquisition and display. Note that in the field of 3 D video technology [21] 22] the representation of the 3 D model is quite an important issue for data compression and transmission. Among several 3 D models, the triangular mesh model has been commonly used in many previous works [1] 3] [7], 9] 10] 12] Since the range image is acquired in a grid array, the mesh model can be obtained by utilizing the connectivity information. The triangular mesh model has been the most popular 3 D model in the fields of computer vision and graphics, as the triangular mesh model is easy to ....

M. Soucy and D. Laurendeau, "Multiresolution surface modeling based on hierarchical triangulation," CVGIP: Image Understanding, vol. 63, no. 1, pp. 1--14, Jan. 1996.

.... makes the entropy coding of the corrective vectors, discussed above, very effective, bringing the vertex location storage to between 12 and 18 bits per vertex for uniform tessellations of smooth surfaces [THLR98] The mesh may be simplified by coalescing vertices [RB93] by decimating them [SL96, SZL92], or by collapsing edges [HRD 93, RR96, GH97] A more complete discussion may be found in [HG97] Most of these techniques remove vertices one at a time in an order that attempts to maximize the accuracy of the approximating model at each stage. Saving intermediate results generates a ....

M. Soucy and D. Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Comput. Vision Image Understanding, 63():1--14, January 1996.

....on generating levels of detail, or LODs, of a given object. Different algorithms vary in terms of quality of approximation, efficiency, simplification operations, and assumptions on the input model. The common set of geometric operations correspond to vertex removal and retriangulating holes [Bajaj96, Kalvin94, Schroeder92, Soucy96, Turk92], edge collapses [Cohen97, Cohen98, Guziec95, Hoppe93, Hoppe96, Kobbelt98, Lindstrom98, Ronfard96] and triangle removal [Hamann94] Many of the earlier algorithms assume that the input model is a manifold and represented as a valid mesh. Other algorithms include those based on multiresolution ....

Soucy, M., and Laurendeau, D. "Multi-Resolution Surface Modeling Based on Hierarchical Triangulation," Computer Vision and Image Understanding, vol. 63, 1-14, 1996.

....to our work can be broadly categorized into 3 classes: Vertex Decimation. Schroeder et al. 9] describe an algorithm whichwewouldtermvertex decimation. Their method iteratively selects a vertex for removal, removes all adjacent faces, and retriangulates the resulting hole. Soucy and Laurendeau [10] described a more sophisticated, but essentially similar algorithm. While they provide reasonable efficiency and quality, these methods are not really suited for our purpose. Both methods use vertex classification and retriangulation schemes which are inherently limited to manifold surfaces, and ....

Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1--14, 1996.

....coding of the corrective vectors, discussed above, very effective, bringing the vertex location storage to about 12 bits per vertex for uniform tessellations of smooth surfaces [THLR98] 0. 2 k [ Overview 4 . The mesh may be simplified by coalescing vertices [RB93] by decimating them [SL96, SZL92], or by collapsing edges [HRD 93, RR96, GH97] A more complete discussion may be found in [HG97] Most of these techniques remove vertices one at a time in an order that attempts to maximize the accuracy of the approximating model at each stage. Saving intermediate results generates a ....

M. Soucy and D. Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Comput. Vision Image Understanding, 63():1--14, January 1996.

....approaches. Although some bottom up methods exist [Vel93] most methods follow a top down strategy, performing a face reduction directly on the mesh by the iterative application of reduction operators (incremental methods) Different operators have been proposed: vertex removal [SZL92] ea96] SL96] edge collapse [RR96] Gue96] AS96] Hop96] Hop97] face removal [Ham94] superfaces merging [KT93] KT96] and edge flipping 1 [CCMS97] BBCS96] These operators are reviewed in Section 1.2.2. Other mesh simplification methods are based on re tiling techniques [Tur92] and ....

....of the mesh. To avoid self intersections, additional geometric tests are required. The selection of the vertex to be removed is commonly based on a curvature estimation at the vertex. Vertices with low curvature values are removed first. The vertex removal operator is used in [SZL92] ea96] SL96] and in most terrain simplification methods. 5 ffl edge collapse The edge collapse operator takes as parameter the edge to be collapsed, or its equivalent, a pair of vertices sharing an edge. The two vertices are collapsed in one vertex. As a result of this collapse, the triangles sharing the ....

Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding: CVIU, 63(1):1--14, January 1996.

....of the mesh. To avoid self intersections, additional geometric tests are required. The selection of the vertex to be removed is commonly based on a curvature estimation at the vertex. Vertices with low curvature values are removed first. The vertex removal operator is used in [SZL92] ea96] SL96] and in most terrain simplification methods. ffl edge collapse The edge collapse operator takes as parameter the edge to be collapsed, or its equivalent, a pair of vertices sharing an edge. The two vertices are collapsed in one vertex. As a result of this collapse, the triangles sharing the ....

.... : Terrain [SR94] Mesh simplif 8 : Bottom up: Vel93] Clustering: RB93] Red96] Tan97] GH97] Incremental 8 : vertex: SZL92] ea96] SL96] edge: Gue96] RR96] AS96] HDD 93] Hop96] Hop97] PH97] face: Ham94] faces: DZ91] KCHN91] HH93] KT96] KT93] edge flip: CCMS97] BBCS96] Re tiling: Tur92] Wavelets: DLW94] Eea95] CPD 96] GSG96] Based on SDM ( Voxels: HHK 95] Hea96] MSS94] ....

Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding: CVIU, 63(1):1--14, January 1996.

....fields, it uses a less expensive and less accurate error measure, and it deletes multiple vertices per pass. Consequently, it is faster, but probably has lower quality. Soucy and Laurendeau 92. To simplify manifolds with boundary, Soucy and Laurendeau also developed a vertex decimation algorithm [118, 119]. Their application was the construction of surface models from multiple range views. On each pass, the vertex with least error is deleted, and its neighborhood (the set of adjacent triangles) is retriangulated. The process stops when the error rises above a specified tolerance or the desired size ....

....uses a regularization step that moves the vertex towards the barycenter, but constrains the vertex to move parallel to the average plane of its neighbors. Klein Liebich Strasser 96. The algorithm described by Klein, Liebich, and Strasser [69] is very similar to the method of Soucy and Laurendeau [119]. It simplifies an oriented manifold by iteratively removing a vertex a retriangulating the resulting hole using a constrained Delaunay triangulation. Each deleted vertex is linked to the closest face in the approximation. These links are used to compute the distance between the original and ....

Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1--14, 1996.

.... the simplified mesh to lie between two offset surfaces (but it works only on orientable manifold surfaces) Some other methods adopt heuristics for the evaluation of the global error introduced by each vertex removal and re triangulation step, and work under an incremental simplification framework [42, 5, 3, 29, 36, 15]; controlled local modifications of re triangulated patches, based on edge flipping, have been proposed to improve approximation accuracy in mesh decimation [3, 5] the decimation approach has also been generalized to the simplification of 3D simplicial decompositions (tetrahedral sets) ....

....Geom. Opt. 24] Min # f x no yes unch. yes 0.7 2.7 not avail. Superfaces [27] Min # f x yes yes unch. yes 0.3 0.8 not avail. Decimation Approaches Mesh Decimat. 40] Min x v x no yes unch. yes 2. 2.5 publ.dom. Triangle Remov. 17] Min # x f x no yes unch. yes not avail. Hierarch.Triang. [42] Min # x v x yes yes unch. yes comm.prod. Err.Bound.TMR [3] Min # x v x yes yes unch. yes not avail. Multires.Dec. 5] both x v x yes x yes unch. yes 0.15 0.2 publ.dom. Hausd.Distance [29] Min # x v x yes yes unch. yes not avail. Simpl.Envelop. 8] Min # v x yes yes unch. yes 0.07 0.09 ....

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Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1--14, 1996.

.... the simplified mesh to lie between two offset surfaces (but it works only on orientable manifold surfaces) Some other methods adopt heuristics for the evaluation of the global error introducedby each vertex removal and re triangulation step, and work under an incremental simplification framework [98, 11, 3, 62, 87, 44]; controlled local modifications of re triangulated patches, based on edge flipping, have been proposed to improve approximation accuracy in mesh decimation [11, 3] the decimation approach has also been generalized to the simplification of 3D simplicial decompositions (tetrahedral sets) ....

....to detect removable triangles seems not very computationally efficient The new mesh will contain new vertices which are relocated on the removed surface patch. Times: no info is reported. Hierarchical Triangulation Modeling (Soucy Laurendeau) The Hierarchical Triangulation Modeling method [98] extends the Schroeder et al. approach [96] by providinga global error management. In particular, for each face of the intermediate simplified mesh it stores all of the removed vertices which project on the face. A global error approximation is evaluated by computing for each face of a new patch ....

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Marc Soucy and Denis Laurendeau. Multiresolutionsurface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1--14, 1996.

.... to improve either the model accuracy or its descriptiveness (there were some attempts to do this in triangulations [32, 5] or for (2) removing redundant primitives to increase the ratio of descriptiveness over the description length of the the final representation (some attempts are reported in [1, 27]) The bottom up approach known as reconstruction from unorganized points is much more difficult and has not been treated as often. Tonnessen and Szeliski proposed modeling objects (surfaces) as collections of (isolated) oriented particles [29] which was a generalization of the particles of ....

M. Soucy and D. Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision, Graphics, and Image Processing, 63(1):1--14, 1996.

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Soucy, M. and Laurendeau, D. (1996). Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1---14.

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M. Soucy, D. Laurendeau. "Multiresolution surface modeling based on hierarchical triangulation", Computer Vision and Image Understanding 63(1), pp. 1--14, January, 1996.

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Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1-- 14, 1996.

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M. Soucy, D. Laurendeau, "Multiresolution surface modeling based on hierarchical triangulation", Computer Vision and Image Understanding 63(1), 1--14, 1996.

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