## Imaging Vector Fields Using Line Integral Convolution

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### BibTeX

@MISC{_imagingvector,

author = {},

title = {Imaging Vector Fields Using Line Integral Convolution},

year = {}

}

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### Abstract

Imaging vector fields has applications in science, art, image processing and special effects. An effective new approach is to use linear and curvilinear filtering techniques to locally blur textures along a vector field. This approach builds on several previous texture

### Citations

1106 |
The Visual Display of Quantitative Information
- Tufte
- 1983
(Show Context)
Citation Context ...gorithms. Most vector visualization algorithms use spatial resolution to represent the vector field. These include sampling the field, such as with stream lines[12] or particle traces, and using icons=-=[19]-=- at every vector field coordinate. Stream lines and particle tracing techniques depend critically on the placement of the “streamers” or the particle sources. Depending on their placement, eddies or c... |

692 |
An Introduction to Wavelets
- Chui
- 1992
(Show Context)
Citation Context ...7. This abrupt cutoff is noticeable as spatio-temporal artifacts in animations that vary the phase as a function of time. One solution to this problem is to use a Gaussian window as suggested by Gabor=-=[4]-=-. 3 By multiplying, or windowing, the Hanning function by a Gaussian, these cutoffs are smoothly attenuated to zero. However, a Gaussian windowed Hanning function does not have a simple closed form in... |

537 |
An Image Synthesizer
- PERLIN
- 1985
(Show Context)
Citation Context ...e new approach is to use linear and curvilinear filtering techniques to locally blur textures along a vector field. This approach builds on several previous texture generation and filtering techniques=-=[8, 9, 11, 14, 15, 17, 23]-=-. It is, however, unique because it is local, one-dimensional and independent of any predefined geometry or texture. The technique is general and capable of imaging arbitrary two- and three-dimensiona... |

381 | Volume rendering
- Drebin, Carpenter, et al.
- 1988
(Show Context)
Citation Context ...e-dimensional. The output of the three-dimensional LIC algorithm is a three-dimensional image or scalar field. This field is rendered using volume rendering techniques such as those found in [21] and =-=[6]-=-. Figure 14 is a three-dimensional rendering of an electrostatic field with two point charges placed a fixed distance apart from one another. In this volumetric rendering, the magnitude of the vector ... |

285 |
Algorithm for Computer Control of a Digital Plotter
- Bresenham
- 1965
(Show Context)
Citation Context ...d can work in two and three dimensions. Such a technique would be very general and have wide application. 3. DDA CONVOLUTION One approach is a generalization of traditional DDA line drawing techniques=-=[1]-=- and the spatial convolution algorithms described by Van Wijk[23] and Perlin[14]. Each vector in a field is used to define a long, narrow, DDA generated filter kernel tangential to the vector and goin... |

238 | Artificial Evolution for Computer Graphics
- Sims
- 1991
(Show Context)
Citation Context ...e new approach is to use linear and curvilinear filtering techniques to locally blur textures along a vector field. This approach builds on several previous texture generation and filtering techniques=-=[8, 9, 11, 14, 15, 17, 23]-=-. It is, however, unique because it is local, one-dimensional and independent of any predefined geometry or texture. The technique is general and capable of imaging arbitrary two- and three-dimensiona... |

230 | Generating textures on arbitrary surfaces using reaction-diffusion
- TURK
- 1991
(Show Context)
Citation Context ...ly, it does not easily generalize to other forms of textures that might be better suited to a particular class of vector data (such as fluid flow versus electromagnetic). Reaction diffusion techniques=-=[20, 24]-=- also provide an avenue for visualizing vector fields since the controlling differential equations are inherently vector in nature. It is possible to map vector data onto these differential equations ... |

209 | Rendering Fur with ThreeDimensional Textures
- Kajiya
- 1989
(Show Context)
Citation Context ...e new approach is to use linear and curvilinear filtering techniques to locally blur textures along a vector field. This approach builds on several previous texture generation and filtering techniques=-=[8, 9, 11, 14, 15, 17, 23]-=-. It is, however, unique because it is local, one-dimensional and independent of any predefined geometry or texture. The technique is general and capable of imaging arbitrary two- and three-dimensiona... |

206 |
Paint by Numbers: Abstract Image Representation
- Haeberli
- 1990
(Show Context)
Citation Context |

144 |
Spot noise: Texture synthesis for data visualization
- Wijk
- 1991
(Show Context)
Citation Context |

129 | Reaction-diffusion textures - Witkin, Kass - 1991 |

116 |
V-BUFFER: Visible Volume Rendering
- Upson, Keeler
- 1988
(Show Context)
Citation Context ...t be three-dimensional. The output of the three-dimensional LIC algorithm is a three-dimensional image or scalar field. This field is rendered using volume rendering techniques such as those found in =-=[21]-=- and [6]. Figure 14 is a three-dimensional rendering of an electrostatic field with two point charges placed a fixed distance apart from one another. In this volumetric rendering, the magnitude of the... |

49 |
Filtering by repeated integration
- Heckbert
- 1986
(Show Context)
Citation Context ...ith L equal to 0, the input image is passed through unchanged. As the value of L increases, the input image is blurred to a greater extent, giving an impressionistic result. Here, a biased ramp filter=-=[10]-=- is used to roughly simulate a brush stroke. Figures 2, 4, 8, 9 and 11 were generated using white noise input images. Aliasing can be a serious problem when using LIC with a high frequency source imag... |

44 | Direct volume visualization of three-dimensional vector fields
- Crawfis, Max
- 1992
(Show Context)
Citation Context ...pling surface. The technique presented by Haeberli[9] for algorithmicly generating “paintings” via vector-like brush strokes can also be thought of as a vector visualization technique. Crawfis and Max=-=[5]-=-sdescribe a three-dimensional variation on this in which blurred cylinders represent three-dimensional brush strokes whose directions and colors are controlled by a three-dimensional vector field. Bot... |

38 | Motion without movement
- FREEMAN, ADELSON, et al.
- 1991
(Show Context)
Citation Context |

23 |
A 3-D Streamline Tracking Algorithm Using Dual Stream Functions
- Kenwright, Mallinson
- 1992
(Show Context)
Citation Context ... (512x512 or greater) strain existing algorithms. Most vector visualization algorithms use spatial resolution to represent the vector field. These include sampling the field, such as with stream lines=-=[12]-=- or particle traces, and using icons[19] at every vector field coordinate. Stream lines and particle tracing techniques depend critically on the placement of the “streamers” or the particle sources. D... |

14 |
Digital Image Processing (2nd ed
- Pratt
- 1991
(Show Context)
Citation Context ...ch of the form and shape in our environment is a function of not only image intensity and color, but also of directional information such as edges. Painters, sculptors, photographers, image processors=-=[16]-=- and computer graphics researchers[9] have recognized the importance of direction in the process of image creation and form. Hence, algorithms that can image such directional information have wide app... |

13 |
Interactive Animated Visualization of Flow Fields
- Gelder, Wilhelms
- 1992
(Show Context)
Citation Context ...cal vector field tangents, but not their direction. Freeman, et al[8] describe a technique which simulates motion by use of special convolutions. A similar technique is used by Van Gelder and Wilhelms=-=[22]-=- to show vector field flow. This technique can be extended and used to represent the local vector field direction via animation of successive LIC imaged vector fields using varying phase shifted perio... |

8 |
Choreographed Image Flow
- Sims
- 1992
(Show Context)
Citation Context ... could be warped along transverse field lines. However, an algorithm to perform this task for an arbitrary local stream line would be inherently more expensive and complex than the LIC algorithm. Sims=-=[18]-=- describes an alternative technique which produces results similar to LIC. This alternative approach warps or advects texture coordinates as a function of a vector field. The similarity between the tw... |

2 |
Fundamentals Handbook of Electrical Engineering and Computer Engineering
- Chang
- 1982
(Show Context)
Citation Context ...(7) (8) 267 Figure 7: Phase shifted Hanning ripple functions(top), a Hanning windowing function(middle), and Hanning ripple functions multiplied by the Hanning window function(bottom). apparent motion=-=[3]-=-. A low frequency ripple function results in a windowed filter whose frequency response noticeably changes as a function of phase. This appears as a periodic blurring and sharpening of the image as th... |

2 |
Study of Field Bifurcations
- Dumortier, Roussarie, et al.
- 1991
(Show Context)
Citation Context ...ior would require a global analysis of the field. Such techniques currently do not exist for arbitrary vector fields, would most likely be expensive to calculate[13] and are an area of active research=-=[7]-=-. 4. LINE INTEGRAL CONVOLUTION The local behavior of the vector field can be approximated by computing a local stream line that starts at the center of pixel (x, y) and moves out in the positive and n... |