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3874 | Snakes: Active contour models,”
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...l. It can produce models of varying resolution and can remove noise much easier. In the category of dynamic approaches, the most famous one is the snake model proposed by Kass, Witkin and Terzopoulos =-=[4]-=-. A snake is essentially a spline that minimizes the energy associated with the spline. The total energy of the snake model is contributed from three different sources: (1) the internal energy of the ... |

2653 | Marching Cubes: A High Resolution 3D Surface Construction Algorithm
- Lorensen, Cline
- 1987
(Show Context)
Citation Context ...he main drawback of this approach is that the user must manually identify a contour in every slice that comprises the object. Later on, Lorenson and Cline developed an algorithm called marching cubes =-=[6]-=- that has proven very useful for generating threedimensional polygonal surface from volume data with no connectivity information. In their algorithm, a cube is bounded by eight pixels located on two a... |

1410 | Geodesic active contours.
- Caselles, Kimmel, et al.
- 1997
(Show Context)
Citation Context ...mation, i.e., only geometric aspects of the underlying dataset are reconstructed through energy-based simulation. To overcome this limitation, several researchers have proposed implicit-based methods =-=[1, 7, 21]-=-. The key part of these schemes is the modeling of an evolving level set of some implicitly defined function. Despite the advantages of topological and geometric flexibility, implicit models are in ge... |

871 | K.: Elastically deformable models
- TERZOPOULOS, PLATT, et al.
- 1987
(Show Context)
Citation Context ...ther irregularities on object boundaries. Hence, model-based approaches are more robust, especially for noise-corrupted datasets. Among the wide spectrum of model-driven techniques, deformable models =-=[3, 15, 16, 17]-=- have been extremely popular and successful primarily because they offer a unified and powerful approach that combines the knowledge from geometry, physics, approximation theory, and functional analys... |

798 | Shape modeling with front propagation: A level set approach
- Malladi, Sethian, et al.
- 1995
(Show Context)
Citation Context ...mation, i.e., only geometric aspects of the underlying dataset are reconstructed through energy-based simulation. To overcome this limitation, several researchers have proposed implicit-based methods =-=[1, 7, 21]-=-. The key part of these schemes is the modeling of an evolving level set of some implicitly defined function. Despite the advantages of topological and geometric flexibility, implicit models are in ge... |

616 | Smooth subdivision surfaces based on triangles - LOOP - 1987 |

392 |
Dynamic 3D models with local and global deformations: Deformable superquadrics.
- Terzopoulos, Metaxas
- 1991
(Show Context)
Citation Context ...ther irregularities on object boundaries. Hence, model-based approaches are more robust, especially for noise-corrupted datasets. Among the wide spectrum of model-driven techniques, deformable models =-=[3, 15, 16, 17]-=- have been extremely popular and successful primarily because they offer a unified and powerful approach that combines the knowledge from geometry, physics, approximation theory, and functional analys... |

238 | T-snakes: Topology adaptive snakes
- McInerney, Terzopolous
- 2000
(Show Context)
Citation Context ...l and geometric flexibility, implicit models are in general not very convenient for shape analysis and visualization, and also very difficult for user interaction. Recently, McInerney and Terzopoulos =-=[11]-=- proposed topological adaptable snake, which is a parametric snakes model that has the power of an implicit formulation. The basic idea is to superimpose a simplicial grid on the image domain and iter... |

201 |
Optimal Surface Reconstruction from Planar Contours
- Fuchs, Kedem, et al.
- 1977
(Show Context)
Citation Context ...ther irregularities on object boundaries. Hence, model-based approaches are more robust, especially for noise-corrupted datasets. Among the wide spectrum of model-driven techniques, deformable models =-=[3, 15, 16, 17]-=- have been extremely popular and successful primarily because they offer a unified and powerful approach that combines the knowledge from geometry, physics, approximation theory, and functional analys... |

194 | Finite element methods for active contour models and ballons for 2-d and 3-d images
- COHEN, COHEN
- 1993
(Show Context)
Citation Context ...mensional image by modeling an axissymmetric elastic skin spread over a flexible spine. Finite element methods are also explored in deformable models by several researchers, including Cohen and Cohen =-=[2]-=-, Terzopoulos and Metaxas [17], and McInerney and Terzopoulos [10]. On the other hand, Miller et al. [12, 13] proposed a polygon-based deformable model. The behavior of the model is determined by a lo... |

194 | A level-set approach to 3D reconstruction from range data
- Whitaker
- 1998
(Show Context)
Citation Context ...mation, i.e., only geometric aspects of the underlying dataset are reconstructed through energy-based simulation. To overcome this limitation, several researchers have proposed implicit-based methods =-=[1, 7, 21]-=-. The key part of these schemes is the modeling of an evolving level set of some implicitly defined function. Despite the advantages of topological and geometric flexibility, implicit models are in ge... |

163 | Free-form shape design using triangulated surfaces
- Welch, Witkin
- 1994
(Show Context)
Citation Context ...m volume data and the initial model is automatically placed within the dataset. Besides the aforementioned work, two other research advances are also of relevance. One is the work of Welch and Witkin =-=[19, 20]-=-. They use a triangle mesh to approximate the underlying smooth variational surface for freeform surface design. Another one is the more recent work called "skin" algorithm proposed by Marksoian et al... |

136 | Symmetry-seeking models for 3D object reconstruction
- Terzopoulos, Witkin, et al.
- 1987
(Show Context)
Citation Context ...l only behaves and deforms on a 2-D plane, and can only model the topology of simple 2-D objects. Later on, Terzopoulos, Kass and Witkin generalized the concept of snakes into symmetry-seeking models =-=[18]-=-. They derive a three-dimensional shape from a two-dimensional image by modeling an axissymmetric elastic skin spread over a flexible spine. Finite element methods are also explored in deformable mode... |

134 | A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis
- McInerney, Terzopoulos
- 1995
(Show Context)
Citation Context ...over a flexible spine. Finite element methods are also explored in deformable models by several researchers, including Cohen and Cohen [2], Terzopoulos and Metaxas [17], and McInerney and Terzopoulos =-=[10]-=-. On the other hand, Miller et al. [12, 13] proposed a polygon-based deformable model. The behavior of the model is determined by a local cost function associated with each model vertex. The cost func... |

114 |
Geometrically Deformed Models: A Method of Extracting Closed Geometric Models from Volume Data
- Miller, Breen, et al.
- 1991
(Show Context)
Citation Context ...ethods are also explored in deformable models by several researchers, including Cohen and Cohen [2], Terzopoulos and Metaxas [17], and McInerney and Terzopoulos [10]. On the other hand, Miller et al. =-=[12, 13]-=- proposed a polygon-based deformable model. The behavior of the model is determined by a local cost function associated with each model vertex. The cost function is a weighted linear combination of th... |

77 |
Modeling surfaces of arbitrary topology with dynamic particles
- Szeliski, Tonnesen, et al.
- 1993
(Show Context)
Citation Context |

68 | Skin: A constructive approach to modeling free-form shapes
- Markosian, Cohen, et al.
- 1999
(Show Context)
Citation Context ...They use a triangle mesh to approximate the underlying smooth variational surface for freeform surface design. Another one is the more recent work called "skin" algorithm proposed by Marksoian et al. =-=[9]-=-. Their goal is to generate a triangle mesh to approximate the surface implicitly defined by the "skeletons". 3. ENERGY-BASED OPTIMIZATION The deformable behavior of the model is governed by the princ... |

40 | Dynamic Catmull-Clark subdivision surfaces
- Qin, Mandal, et al.
- 1998
(Show Context)
Citation Context ... centroid of its neighbors. Similar to the snake model, the topological variation in Miller et al.'s work is not allowed. The modeled dataset must be homomorphic to a sphere. Recently, Qin and Mandal =-=[14, 8]-=- proposed dynamic subdivision surfaces for surface reconstruction. Their approaches combine the advantages of free-form deformable models with the nice properties of subdivision surfaces, and their al... |

37 | B.: A novel FEM-based dynamic framework for subdivision surfaces
- Mandal, Qin, et al.
- 2000
(Show Context)
Citation Context ... centroid of its neighbors. Similar to the snake model, the topological variation in Miller et al.'s work is not allowed. The modeled dataset must be homomorphic to a sphere. Recently, Qin and Mandal =-=[14, 8]-=- proposed dynamic subdivision surfaces for surface reconstruction. Their approaches combine the advantages of free-form deformable models with the nice properties of subdivision surfaces, and their al... |

15 |
Serious Putty: Topological Design for Variational Curves and Surfaces
- Welch
- 1995
(Show Context)
Citation Context ...m volume data and the initial model is automatically placed within the dataset. Besides the aforementioned work, two other research advances are also of relevance. One is the work of Welch and Witkin =-=[19, 20]-=-. They use a triangle mesh to approximate the underlying smooth variational surface for freeform surface design. Another one is the more recent work called "skin" algorithm proposed by Marksoian et al... |

14 | On GDM’s: Geometrically deformed models for the extraction of closed shapes from volume data
- Miller
- 1990
(Show Context)
Citation Context ...ethods are also explored in deformable models by several researchers, including Cohen and Cohen [2], Terzopoulos and Metaxas [17], and McInerney and Terzopoulos [10]. On the other hand, Miller et al. =-=[12, 13]-=- proposed a polygon-based deformable model. The behavior of the model is determined by a local cost function associated with each model vertex. The cost function is a weighted linear combination of th... |