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## Visualization of Anatomic Tree Structures with Convolution Surfaces (2004)

Venue: | in Proc. Joint IEEE/EG Symposium on Visualization. Eurographics Association |

Citations: | 5 - 0 self |

### Citations

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A generalization of algebraic surface drawing
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Citation Context ... deformable objects, implicit surfaces unfold their full strength. James F. Blinn introduced implicit surfaces in computer graphics. He developed Blobby Molecules to visualize electron density fields =-=[Bli82]. -=-3.1. Implicit Surfaces: a Brief Introduction A classical example for an implicit equation is the description of a sphere with radius r: x 2 + y 2 + z 2 − r 2 = 0. This formula may be used to represe... |

144 |
Morphometric analysis of white matter lesions in MR images: Method and validation
- Zijdenbos, Dawant, et al.
- 1994
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Citation Context ...ased on this representation, measures can be derived which characterize the overlap of both sets of voxels or the distance between the contours. As a first attempt, we determined the similarity index =-=[ZDMP94]-=- between the segmentation result and convolution surface according to Eq. 13 and yielded a value of 0.88. This measure defines the volume overlap and is 1.0 if both sets are identical. The difference ... |

140 | An implicit surface polygonizer
- BLOOMENTHAL
- 1994
(Show Context)
Citation Context ... of a Geometric Model For the visualization of the vascular structures the convolution surface is transformed into a triangle mesh. We developed an object-oriented version of the Implicit Polygonizer =-=[Blo94]-=-. The implicit polygonizer partitions the space surrounding the surface based on a continuation scheme presented in [WMW86b]. An initial cube is centered at an arbitrary point on the convolution surfa... |

138 | Convolution surfaces
- Bloomenthal, Shoemake
- 1991
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Citation Context ...e structures in a mathematical sense. However, our method does not rely on this property. The visualization method applied here is based on Convolution Surfaces introduced by Bloomenthal and Shoemake =-=[BS91]-=-. As a difference to previous applications of convolution surfaces we shall faithfully represent the radius distribution given by the vessel analysis and we shall employ large datasets (>10K line segm... |

94 |
Animating soft objects
- Wyvill, McPheeters, et al.
- 1986
(Show Context)
Citation Context ...rd deviation σ. For several energy sources, the scalar value at p can be calculated as Eq. 3: F(p) = ∑ i (2) bie −σid2 i (3) Other popular field functions were presented in [NHK ∗ 85] (Metabal=-=ls) and [WMW86a]-=- (Soft Objects). Note that only scalar fields around point primitives were considered so far. 3.2. Convolution Surfaces Bloomenthal and Shoemake extended the concept to skeletal primitives of theoreti... |

88 | Object modeling by distribution function and a method of image generation - Nishimura, Hirai, et al. - 1985 |

41 |
Skeletal Design of Natural Forms.
- Bloomenthal
- 1995
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Citation Context ...olution: h ⊗ (S1 + S2) = (h ⊗ S1) + (h ⊗ S2) (6) This guarantees, for example, that two abutting, collinear segments [...] produce the same convolution as does the single segment that is their u=-=nion. [Blo95]-=- Furthermore, superposition has an impact on implementation issues and the modeling process. It permits the convolution of a complex object primitive by primitive in an arbitrary order instead of cons... |

36 | Geometric Methods for Vessel Visualization and Quantification - A Survey
- Bühler, Felkel, et al.
- 2002
(Show Context)
Citation Context ... by means of subdivision surfaces. The smoothness of the final model is dependent on the iteration depth of the refinement step. A comprehensive survey of methods for vessel visualization is given in =-=[BFLC]-=-. 3. Modeling of Tree-like Structures with Implicit Surfaces Implicit surfaces offer an alternative to explicitly constructing the surface of an object by a set of polygons or parametric patches. They... |

35 | Symbolic description of 3-D structures applied to cerebral vessel tree obtained from MR Angiography volume data,”, - Gerig - 1993 |

27 | Implicit surfaces: Appearance, blending and consistency
- Opalach, Maddock
- 1993
(Show Context)
Citation Context ...hapes it is essential to control the blending between certain parts of the object. Concerning vascular structures, vessel segments whose skeleton is not connected should not blend with each other. In =-=[OM93]-=- the use of a restricted blending graph was suggested to overcome this problem. Based on the topology of the given skeleton, primitives are classified into blendinggroups of the following types: all p... |

26 |
WYVILL B.: Data Structure for Soft Objects
- WYVILL, MCPHEETERS
- 1986
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Citation Context ...le mesh. We developed an object-oriented version of the Implicit Polygonizer [Blo94]. The implicit polygonizer partitions the space surrounding the surface based on a continuation scheme presented in =-=[WMW86b]-=-. An initial cube is centered at an arbitrary point on the convolution surface. We use the root in our tree data structure as seed point for computing the position of the initial cube. The size of the... |

18 |
Bulge elimination in convolution surfaces
- BLOOMENTHAL
- 1997
(Show Context)
Citation Context ...e might be easily mistaken for a pathological variation, e.g. an aneurysm. Even though our visualization method is not targeted at supporting vascular diagnostics, we shall minimize this drawback. In =-=[Blo97], -=-two methods are described that address the bulging problem. • combination surfaces which are an interpolation between union surface (distance surface with the maximumoperator as a blending function)... |

13 | Convolution Surfaces for Line Skeletons with Polynomial Weight Distributions - Jin, Tai, et al. - 2001 |

12 | Surface Reconstruction of the Branching Vessels for Augmented Reality Aided Surgery
- Felkel, Fuhrmann, et al.
- 2002
(Show Context)
Citation Context ...e used to represent the diminutions of the vessel diameter faithfully. However, the fitting of primitives to one another does not generate smooth transitions between vessel segments at branchings. In =-=[FFKW02]-=-, branchings are treated separately to avoid rendering discontinuities and the construction of objectionable structures inside the geometric model. Along straight parts, a vessel segment is approximat... |

8 |
Convolution Surfaces in Computer Graphics.
- Sherstyuk
(Show Context)
Citation Context ...nd the modeling process. It permits the convolution of a complex object primitive by primitive in an arbitrary order instead of considering the skeleton as a whole. 3.3. Filter Selection According to =-=[She98]-=-, an appropriate filter function should be continuous and monotonic. Furthermore, it should have finite support (or be negligible beyond a certain distance), and exhibit zero or near zero gradient at ... |

7 |
Masamune K, Dohi T. Region-growing-based feature extraction algorithm for tree-like objects
- Masutani
- 1996
(Show Context)
Citation Context ...uctures in general and vascular trees in particular. Our visualization technique is based on the model assumption that cross sections of non-pathologic vessels have a circular shape, as disscussed in =-=[MMD96]-=-. Masutani et al. fitted cylinders along the skeleton to visualize vascular structures. The drawback of this method is that discontinuities at branchings arise where cylinders with different diameters... |

5 |
CANI M.-P.: Implicit modeling with skeleton curves: Controlled blending in contact situations
- ANGELIDIS, JEPP
- 2002
(Show Context)
Citation Context ...ing types: all primitives blendable, all primitives unblendable, blendable and unblendable primitives. Unfortunately, this solution does not ensure C 1 continuity of the shape. A more recent approach =-=[AJC02]-=- introduces local convolution. This concept is based on defining a restricted skeleton range for computing the scalar value at a certain point in space. It prevents blending even between small folds o... |

5 |
PEITGEN H.-O.: Analysis of vasculature for liver surgical planning
- SELLE, PREIM, et al.
(Show Context)
Citation Context ...fferent types of branchings and produces smooth surfaces even at endpoints and branchings. The vessel skeleton serves as the input for the visualization process. It is represented as a directed graph =-=[SPSP02]-=-. Edges of this graph are approximated by line segments connecting adjacent voxels. Each segment is described by its two endpoints and one associated radius (the radius of the largest circle completel... |

4 |
CANI M.-P.: Implicit modelling using subdivision curves
- HORNUS, ANGELIDIS
- 2003
(Show Context)
Citation Context ...y are inadequate for modeling surfaces that exactly converge against a given radius. As far as we know, solely in [Blo95] c○ The Eurographics Association 2004. Oeltze et al / Convolution Surfaces an=-=d [HAC03] appr-=-oaches have been published that concentrate on this problem. In [Blo95] a Gaussian function is utilized for convolution (see Fig. 1(a)). h(p) = e −d2 ω , ω = ln2, d > 0 (7) ω is known as the widt... |

4 |
PEITGEN H.-O.: Visualization and interaction techniques for the exploration of vascular structures
- HAHN, PREIM, et al.
(Show Context)
Citation Context ... pathologic situations, such as aneurysms and stenosis, and fitted these models to the patient specific data at hand. The focus of her work is on the geometric continuity and on realistic shading. In =-=[HPSP01]-=- a vessel visualization pipeline has been introduced. The skeleton and the local vessel diameter determined in the image analysis stage are smoothed with a [121] binomial filter. Special care is taken... |

3 | An overview of implicit surfaces
- Opalach, Maddock
- 1995
(Show Context)
Citation Context ...l points p(x,y,z) in space which are on the surface of a sphere with radius r. Furthermore, it facilitates point classification by simply checking the sign of the resulting scalar value. According to =-=[OM95], -=-the above equation can be rewritten as Eq. 1: F(p) − Iso = 0 (1) F(p) is called the scalar field function because a scalar value may be computed for each point p. Iso denotes the isovalue for genera... |

2 |
Tost D, Navazo I. An Interactive Cerebral Blood Vessel Exploration System
- Puig
- 1997
(Show Context)
Citation Context ...this method is that discontinuities at branchings arise where cylinders with different diameters coincide. A special problem, the visualization of cerebral structures, has been tackled by Puig et al. =-=[PTN97]-=-. She modeled typical bifuractions and pathologic situations, such as aneurysms and stenosis, and fitted these models to the patient specific data at hand. The focus of her work is on the geometric co... |