A fractal-based relaxation algorithm for shape from terrain image

Liao, Iman Yi; Πέτρου, Μαρία; Zhao, Ran

doi:10.1016/j.cviu.2007.10.002

Cited by 9 publications

(7 citation statements)

References 43 publications

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“…Addressing fractals: Generating virtual maps based on fractal models is often used in movies and computer games [25]. Keim et al [26] first proposed a method based on the use of recursive patterns in the field of Information Visualization.…”

Section: Cartographic Maps Metaphormentioning

confidence: 99%

GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data

Auber

Huët

Lambert

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map.

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Section: Cartographic Maps Metaphormentioning

confidence: 99%

GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data

Auber

Huët

Lambert

et al. 2013

IEEE Trans. Visual. Comput. Graphics

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“…Most of the work (e.g., [23,25]) relies on variations of a fractal model. These techniques could provide additional photorealism, and may be used in future extention of our work.…”

Section: Related Workmentioning

confidence: 99%

GMap: Visualizing graphs and clusters as maps

Gansner

Kobourov

2010

2010 IEEE Pacific Visualization Symposium (PacificVis)

111

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Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these traditional methods often do not capture well the underlying structural information, clustering, and neighborhoods. In this paper, we describe GMap, a practical tool for visualizing relational data with geographic-like maps. We illustrate the effectiveness of this approach with examples from several domains. All the maps referenced in this paper can be found in www.research.att.com/˜yifanhu/GMap.

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“…Studies have shown that natural terrain has self-similarity, or scale independence, and the feature can be expressed by a stationary random process. Fractal theory is often used for digital terrain modeling [14,15]. Because of the self-similarity of terrain feature, fractal theory can approximate the terrain better and therefore has theoretical advantage.…”

Section: Kriging Interpolation Methodsmentioning

confidence: 99%

The Improved Kriging Interpolation Algorithm for Local Underwater Terrain Based on Fractal Compensation

Chen

Li²,

Su³

et al. 2014

Mathematical Problems in Engineering

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The interpolation-reconstruction of local underwater terrain using the underwater digital terrain map (UDTM) is an important step for building an underwater terrain matching unit and directly affects the accuracy of underwater terrain matching navigation. The Kriging method is often used in terrain interpolation, but, with this method, the local terrain features are often lost. Therefore, the accuracy cannot meet the requirements of practical application. Analysis of the geographical features is performed on the basis of the randomness and self-similarity of underwater terrain. We extract the fractal features of local underwater terrain with the fractal Brownian motion model, compensating for the possible errors of the Kriging method with fractal theory. We then put forward an improved Kriging interpolation method based on this fractal compensation. Interpolation-reconstruction tests show that the method can simulate the real underwater terrain features well and that it has good usability.

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A fractal-based relaxation algorithm for shape from terrain image

Cited by 9 publications

References 43 publications

GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data

GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data

GMap: Visualizing graphs and clusters as maps

The Improved Kriging Interpolation Algorithm for Local Underwater Terrain Based on Fractal Compensation

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