Tangential Distance Fields for Mesh Silhouette Problems
A We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, w...
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| Veröffentlicht in: | Computer graphics forum Jg. 28; H. 1; S. 84 - 100 |
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| Sprache: | Englisch |
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Blackwell Publishing Ltd
01.03.2009
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | A
We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a ‘tangential distance field’ (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi‐origin silhouette extraction in Hough space, silhouette‐based view point selection, camera path planning and light source placement. |
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| AbstractList | We consider a tangent-space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a 'tangential distance field' (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi-origin silhouette extraction in Hough space, silhouette-based view point selection, camera path planning and light source placement. Submitted March 2008Revised August2008 Accepted October 2008. A We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a ‘tangential distance field’ (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi‐origin silhouette extraction in Hough space, silhouette‐based view point selection, camera path planning and light source placement. We consider a tangent-space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a 'tangential distance field' (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi-origin silhouette extraction in Hough space, silhouette-based view point selection, camera path planning and light source placement. [PUBLICATION ABSTRACT] We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a ‘tangential distance field’ (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi‐origin silhouette extraction in Hough space, silhouette‐based view point selection, camera path planning and light source placement. |
| Author | Olson, M. Zhang, H. |
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| References_xml | – reference: Jones M. W., Baerentzen J. A., Sramek M.: 3d distance fields: A survey of techniques and applications. IEEE Transactions on Visualization and Computer Graphics 12, 4 (2006), 581-599. – reference: Koenderink J. J.: What does the occluding contour tell us about solid shape. Perception 13, (1984), 321-330. – reference: Harris J.: Algebraic Geometry: A First Course. Springer-Verlag, 1992. – reference: Olson M., Zhang H.: Silhouette extraction in hough space. Computer Graphics Forum 25, 3 (2006), 273-282. – reference: Su B., Liu D.: Computational Geometry: Curve and Surface Modeling. Academic Press, 1989. – reference: Vazquez P.: Automatic light source placement for maximum visual information recovery. Computer Graphics Forum (2006), 143-156. – reference: Sethi A., Renaudie D., Kriegman D., Ponce J.: Curve and surface duals and the recognition of curved 3d objects from their silhouettes. International Journal of Computer Vision 58, 1 (2004), 73-86. – reference: Christie M., Olivier P.: Camera control in computer graphics. Computer Graphics Forum, (2006), 247-256. – reference: Everitt B. S., Landau S., Leese M.: Cluster Analysis. Hodder Arnold Publishing and Oxford University Press, 2001. – reference: Gumhold S.: Maximum entropy light source placement. In IEEE Visualization (2002). – reference: Décoret X., Durand F., Sillion F. X., Dorsey J.: Billboard clouds for extreme model simplification. ACM TOG 22, 3 (2003), 689-696. – reference: Peternell M., Pottmann H., Steiner T.: Hough Transform and Laguerre Geometry for the Recognition and Reconstruction of Special 3D Shapes. Tech. Rep. 100, TU Vienna , 2003. – reference: Polonsky O., Patane G., Biasotti S., Gotsman C., Spagnuolo M.: What's in an image? Towards the computation of the "best" view of an object. The Visual Computer (2005). – reference: Johnstone J. K.: The bézier tangential surface system: a robust dual representation of tangent space. Computing 72, 1-2 (2004), 105-115. – start-page: 499 year: 2004 end-page: 508 – start-page: 517 year: 2000 end-page: 526 – start-page: 327 year: 2000 end-page: 334 – start-page: 143 year: 2006 end-page: 156 article-title: Automatic light source placement for maximum visual information recovery publication-title: Computer Graphics Forum – year: 2001 – year: 2007 – year: 1989 – year: 2003 – start-page: 71 year: 1992 end-page: 78 – volume: 13 start-page: 321 year: 1984 end-page: 330 article-title: What does the occluding contour tell us about solid shape publication-title: Perception – year: 1992 – volume: 4 start-page: 581 year: 2006 end-page: 599 article-title: 3d distance fields: A survey of techniques and applications publication-title: IEEE Transactions on Visualization and Computer Graphics 12 – start-page: 247 year: 2006 end-page: 256 article-title: Camera control in computer graphics publication-title: Computer Graphics Forum – start-page: 235 year: 1996 end-page: 253 – volume: 1–2 start-page: 105 year: 2004 end-page: 115 article-title: The bézier tangential surface system: a robust dual representation of tangent space publication-title: Computing 72 – year: 1959 – year: 2005 article-title: What's in an image? 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Towards the computation of the “best” view of an object publication-title: The Visual Computer – ident: e_1_2_10_17_2 doi: 10.1111/j.1467-8659.2006.00946.x – ident: e_1_2_10_9_2 doi: 10.1145/142920.134011 – ident: e_1_2_10_5_2 doi: 10.1145/882262.882326 – ident: e_1_2_10_3_2 – ident: e_1_2_10_14_2 doi: 10.1007/978-3-7091-7484-5_24 – start-page: 549 volume-title: SIGGRAPH year: 2006 ident: e_1_2_10_21_2 – year: 2002 ident: e_1_2_10_7_2 article-title: Maximum entropy light source placement publication-title: IEEE Visualization – ident: e_1_2_10_26_2 doi: 10.1023/B:VISI.0000016148.08046.fc – ident: e_1_2_10_13_2 doi: 10.1007/s00607-003-0050-2 – ident: e_1_2_10_8_2 doi: 10.1007/978-1-4757-2189-8 – volume-title: Hough Transform and Laguerre Geometry for the Recognition and Reconstruction of Special 3D Shapes year: 2003 ident: e_1_2_10_20_2 – volume-title: Computational Geometry: Curve and Surface Modeling year: 1989 ident: e_1_2_10_24_2 – ident: e_1_2_10_30_2 – ident: e_1_2_10_10_2 – ident: e_1_2_10_33_2 – ident: e_1_2_10_28_2 – ident: e_1_2_10_22_2 doi: 10.1145/344779.344935 – ident: e_1_2_10_32_2 – volume-title: Theoretical Computer Sciences ident: e_1_2_10_23_2 – ident: e_1_2_10_12_2 doi: 10.1109/TVCG.2006.56 – volume-title: SIGGRAPH year: 2007 ident: e_1_2_10_25_2 – start-page: 247 year: 2006 ident: e_1_2_10_4_2 article-title: Camera control in computer graphics publication-title: Computer Graphics Forum – ident: e_1_2_10_15_2 doi: 10.1068/p130321 – ident: e_1_2_10_27_2 – start-page: 143 year: 2006 ident: e_1_2_10_29_2 article-title: Automatic light source placement for maximum visual information recovery publication-title: Computer Graphics Forum – ident: e_1_2_10_16_2 – ident: e_1_2_10_11_2 doi: 10.1145/344779.345074 |
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We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such... We consider a tangent‐space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such... We consider a tangent-space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such... |
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| SubjectTerms | Algorithms and systems Computer graphics Hierarchy and geometric transformations I.3.5 Computational Geometry and Object Modelling - Geometric algorithms I.3.5 Computational Geometry and Object Modelling – Geometric algorithms, languages, and systems; Hierarchy and geometric transformations languages mesh triangles Optimization techniques Studies tangent space surface representations tangential distance field |
| Title | Tangential Distance Fields for Mesh Silhouette Problems |
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