### Citations

281 | Illustrating smooth surfaces. In:
- Hertzmann, Zorin
- 2000
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Citation Context ...ect-space silhouette detection under perspective projection is well studied. Many methods make use of mesh supporting planes under a planepoint transform to accelerate processing. Hertzmann and Zorin =-=[HZ00]-=- implement a dual-space approach in 4D homogeneous space. Pop et al. [PDB ∗ 01] use the classical point-plane duality in 3D projective space for efficient silhouette updates. In previous work [OZ06], ... |

240 |
Algebraic Geometry. A first course,
- Harris
- 1992
(Show Context)
Citation Context ...acement. We expect this to only be a partial list of potential applications of TDF. 2. Related Work Tangent-space representation of smooth surfaces has been studied in the field of algebraic geometry =-=[Har92]-=-. A related concept from convex geometry is that of the support function of a surface, defined as the dot product u(P) = P · N(P), where P is a point on the surface and N(P) is the unit surface normal... |

184 |
What does the occluding contour tell us about solid shape?
- Koenderink
- 1984
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Citation Context ...umbnail images may be generated for each entry and should allow the user to identify the mesh. 7.1. Selection criteria Silhouettes form one of the most important perceptual cues in object recognition =-=[Koe84]-=-. When humans sketch objects, they tend to define features by their silhouettes. Therefore, we seek to maximize the perceptual information provided by a set of viewpoints by choosing those viewpoints ... |

156 |
Machine Analysis of Bubble Chamber Pictures,
- Hough
- 1962
(Show Context)
Citation Context ...face can be mapped to a point H(P) which is the orthogonal projection of the origin onto the tangent plane at P; see Figure 1(d) for an illustration in the 2D case. This is called the Hough transform =-=[Hou59]-=- and the image of the mapping is called a pedal surface [Joh04]. The Hough transform, or its close relative, the dual transform, has been exploited to facilitate silhouette extraction [HZ00,PDB ∗ 01,O... |

110 | A planar-reflective symmetry transform for 3D shapes. - Podolak, Golovinskiy, et al. - 2006 |

102 | Silhouette Clipping”, - Sander, Gu, et al. - 2000 |

90 | Viewpoint Selection Using Viewpoint Entropy. Vision, Modeling and Visualization
- Vázquez, Feixas, et al.
- 2001
(Show Context)
Citation Context ...tween 23 times speed-up over [OZ06] in initial silhouette extraction. Viewpoint selection and camera path planning: The viewpoint selection problem has applications ranging from image-based modelling =-=[VFSH01]-=- to object recognition [YSY ∗ 06] and is also studied in robotics as the sensor placement problem [TL95]. Most approaches define a view quality metric and evaluate it over a set of candidate viewpoint... |

89 | Billboard clouds for extreme model simplification
- Décoret, Durand, et al.
(Show Context)
Citation Context ...f Hough and dual transforms for silhouette extraction [HZ00,PDB ∗ 01,OZ06]. Other uses of 3D Hough transforms include linear approximation of signed distance fields [WK03], billboard cloud generation =-=[DDSD03]-=-, recognition and reconstruction of surfaces [PPS03], and mesh retrieval [ZP01]. The dual transform has also been utilized for back-face culling [KMGL96]. While Hough and dual transforms are discrete ... |

74 | 3d distance fields: A survey of techniques and applications. Visualization and Computer Graphics
- Jones, Baerentzen, et al.
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Citation Context ...l-known scalar field defined for surfaces and it has many applications, including visibility analysis [TCO ∗ 05]. A thorough coverage on this subject can be found in the recent survey by Jones et al. =-=[JBS06]-=-. c○ 2008 The Author(s) Journal compilation c○ 2008 The Eurographics Association and Blackwell Publishing Ltd.sOlson and Zhang / Tangential Distance Fields for Mesh Silhouette Analysis Most relevant t... |

46 |
Maximum entropy light source placement.
- Gumhold
- 2002
(Show Context)
Citation Context ...lacement: Light source placement is generally studied alongside the viewpoint selection problem, and has applications ranging from edge-based object recognition [CM93] to perceptual scene enhancement =-=[Gum02]-=-. As with the viewpoint selection problem, light source placement algorithms generally define a quality metric and evaluate it over a set of candidate positions. Quality metrics can be quite similar t... |

41 | Upright orientation of man-made objects
- FU, COHEN-OR, et al.
- 2008
(Show Context)
Citation Context ...mative viewpoints, it does not compute a natural orientation for the camera. This is an interesting and difficult problem in its own right which is beginning to be addressed, for example by Fu et al. =-=[FCODS08]-=-. c○ 2008 The Author(s) Journal compilation c○ 2008 The Eurographics Association and Blackwell Publishing Ltd.sOlson and Zhang / Tangential Distance Fields for Mesh Silhouette Analysis Figure 18: Four... |

39 | Camera control in computer graphics”,
- Christie, Olivier, et al.
- 2008
(Show Context)
Citation Context ...ws for more efficient viewpoint search. Camera-path planning is a related problem. It has been studied in the context of motion planning and path finding [AVF04], as well as in digital cinematography =-=[CO06]-=-. We consider camera-path planning in the same context as viewpoint selection – selecting a camera path which conveys as much information as possible about a given model based again on silhouettes. Ou... |

30 | Hierarchical back-face computation.
- Kumar, Manocha, et al.
- 1996
(Show Context)
Citation Context ...ing is called a pedal surface [Joh04]. The Hough transform, or its close relative, the dual transform, has been exploited to facilitate silhouette extraction [HZ00,PDB ∗ 01,OZ06] or back face culling =-=[KMGL96]-=- over polygonal models. In this paper, we explore beyond low-level representations derived from tangent-space surface representations, such as a point cloud resulting from Hough transform. We introduc... |

27 | Automatic camera placement for robot vision tasks”,
- Triggs, Laugier
- 1995
(Show Context)
Citation Context ...planning: The viewpoint selection problem has applications ranging from image-based modelling [VFSH01] to object recognition [YSY ∗ 06] and is also studied in robotics as the sensor placement problem =-=[TL95]-=-. Most approaches define a view quality metric and evaluate it over a set of candidate viewpoints, essentially via an exhaustive search, choosing the candidate with the highest score as the best view.... |

19 |
Way-finder: guided tours through complex walkthrough models.
- ANDJAR, VAZQUEZ, et al.
- 2004
(Show Context)
Citation Context ...viewpoints and at reduced costs, as a TDF allows for more efficient viewpoint search. Camera-path planning is a related problem. It has been studied in the context of motion planning and path finding =-=[AVF04]-=-, as well as in digital cinematography [CO06]. We consider camera-path planning in the same context as viewpoint selection – selecting a camera path which conveys as much information as possible about... |

19 | Towards stable and salient multi-view representation of 3D shapes - Yamauchi, Saleem, et al. - 2006 |

17 |
Computational Geometry – Curve and Surface Modeling
- Su, Liu
- 1989
(Show Context)
Citation Context ... we have visited all viewpoints, we return to v1, closing the path. When following the path, we interpolate between the path nodes using cubic Bézier curves. By applying the methods from Chapter 4 of =-=[SL89]-=- – namely, by ensuring that control points across an endpoint are collinear and symmetric – we can ensure a smooth path between viewpoints with GC 2 continuity at its joints. 8. Placement of single li... |

17 | Curve and surface duals and the recognition of curved 3d objects from their silhouettes - Sethi, Renaudie, et al. |

14 | Efficient perspective-accurate silhouette computation and applications - Pop, Duncan, et al. - 2001 |

14 |
Hough transform-based 3D mesh retrieval
- Zaharia, Prêteux
- 2001
(Show Context)
Citation Context ... uses of 3D Hough transforms include linear approximation of signed distance fields [WK03], billboard cloud generation [DDSD03], recognition and reconstruction of surfaces [PPS03], and mesh retrieval =-=[ZP01]-=-. The dual transform has also been utilized for back-face culling [KMGL96]. While Hough and dual transforms are discrete representations derived from tangent-space surface representations, we are not ... |

11 | What is an image?: Towards the computation of the “best” view of an object,” The Visual Computer (Proc. Pacific Graphics - Polonsky, Patan, et al. - 2005 |

11 | Curves and surfaces represented by polynomial support functions.
- Sır, Gravesen, et al.
- 2008
(Show Context)
Citation Context ... that of the support function of a surface, defined as the dot product u(P) = P · N(P), where P is a point on the surface and N(P) is the unit surface normal at P. This has been adopted by Sir et al. =-=[SJGar]-=- to generate surface patches with elegant properties, including seamless support for surface offset. In computer vision, more specifically for recognition of curved objects, a close relationship betwe... |

11 | Piecewise Linear Approximation of Signed Distance Fields
- Wu, Kobbelt
- 2003
(Show Context)
Citation Context .... This is the idea behind the use of Hough and dual transforms for silhouette extraction [HZ00,PDB ∗ 01,OZ06]. Other uses of 3D Hough transforms include linear approximation of signed distance fields =-=[WK03]-=-, billboard cloud generation [DDSD03], recognition and reconstruction of surfaces [PPS03], and mesh retrieval [ZP01]. The dual transform has also been utilized for back-face culling [KMGL96]. While Ho... |

5 |
Cluster Analysis, A Hodder Arnold Publication
- Everitt, Landau, et al.
- 2001
(Show Context)
Citation Context ...rigin selection heuristic and rely on performance measurements to choose an appropriate k. In fact, this has been a well-practiced heuristic for choosing the number of clusters in clustering analysis =-=[ELL01]-=-. The origin selection algorithm above is concerned only with distances from origin to face supporting planes, or equivalently, distances from origin to Hough points. As previously noted, such distanc... |

5 |
H.: Silhouette Extraction in Hough Space
- OLSON, ZHANG
- 2006
(Show Context)
Citation Context ...n [HZ00] implement a dual-space approach in 4D homogeneous space. Pop et al. [PDB ∗ 01] use the classical point-plane duality in 3D projective space for efficient silhouette updates. In previous work =-=[OZ06]-=-, we advocate the use of 3D Hough transform of mesh faces, organized into a single octree, for efficient update and initial extraction of silhouette. Compared to the dual transform [PDB ∗ 01], the Hou... |

5 |
Automatic light source placement for maximum visual information recovery
- Vázquez
- 2007
(Show Context)
Citation Context ...acement algorithms generally define a quality metric and evaluate it over a set of candidate positions. Quality metrics can be quite similar to those for viewpoint selection. For example, [Gum02] and =-=[Vaz06]-=- use an entropy measure similar to [VFSH01]. Unlike viewpoint selection, however, the amount of information conveyed by a given light source placement can be affected by the light’s illumination param... |

4 | Hough Transform and Laguerre Geometry for the Recognition and - Peternell, Pottmann, et al. |

1 |
MODAYUR B.: Edge-based placec○ 2008 The Author(s) Journal compilation c○ 2008 The Eurographics Association and Blackwell Publishing Ltd. ment of camera and light source for object recognition and location
- COWAN
- 1993
(Show Context)
Citation Context ...ning such a camera path. Light source placement: Light source placement is generally studied alongside the viewpoint selection problem, and has applications ranging from edge-based object recognition =-=[CM93]-=- to perceptual scene enhancement [Gum02]. As with the viewpoint selection problem, light source placement algorithms generally define a quality metric and evaluate it over a set of candidate positions... |

1 | STUETZLE W.: Surface reconstruction from and Zhang / Tangential Distance Fields for Mesh Silhouette Analysis unorganized points - HOPPE, DEROSE, et al. - 1992 |

1 |
The bézier tangential surface system: a robust dual representation of tangent space
- JOHNSTONE
- 2004
(Show Context)
Citation Context ...ection of the origin onto the tangent plane at P; see Figure 1(d) for an illustration in the 2D case. This is called the Hough transform [Hou59] and the image of the mapping is called a pedal surface =-=[Joh04]-=-. The Hough transform, or its close relative, the dual transform, has been exploited to facilitate silhouette extraction [HZ00,PDB ∗ 01,OZ06] or back face culling [KMGL96] over polygonal models. In th... |

1 | Visualising duals of surfaces - MORRIS - 2002 |

1 |
Fast triangle order optimization for vertex locality and reduced overdraw
- SANDER, NEHAB, et al.
(Show Context)
Citation Context ...int-selection problem with a strong dependence upon planarity constraints, and is a clear candidate for our method. The occlusion potential characteristic in Sander et al.’s triangle reordering paper =-=[SNB07]-=- is also strongly dependent upon the ordering, position, and orientation of planar clusters. We may be c○ 2008 The Author(s) Journal compilation c○ 2008 The Eurographics Association and Blackwell Publ... |

1 | SAPIRO G.: Visibility and its dynamics in a pde-based implicit framework - TSAI, CHENG, et al. |