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Minimum spanning trees for valley and ridge characterization in digital elevation maps
conference contribution
posted on 2010-01-01, 00:00 authored by Shaun BangayShaun Bangay, D de Bruyn, K GlassTexture synthesis employs neighbourhood matching to generate appropriate new content. Terrain synthesis has the added constraint that new content must be geographically plausible. The profile recognition and polygon breaking algorithm (PPA) [Chang et al. 1998] provides a robust mechanism for characterizing terrain as systems of valley and ridge lines in digital elevation maps. We exploit this to create a terrain characterization metric that is robust, efficient to compute and is sensitive to terrain properties.
Terrain regions are characterized as a minimum spanning tree derived from a graph created from the sample points of the elevation map which are encoded as weights in the edges of the graph. This formulation allows us to provide a single consistent feature definition that is sensitive to the pattern of ridges and valleys in the terrain Alternative formulations of these weights provide richer characteristicmeasures and we provide examples of alternate definitions based on curvature and contour measures.
We show that the measure is robust, with a significant portion derived directly from information local to the terrain sample. Global terrain characteristics introduce the issue of over- and underconnected valley/ridge lines when working with sub-regions. This is addressed by providing two graph construction strategies, which respectively provide an upper bound on connectivity as a single spanning tree, and a lower bound as a forest of trees.
Efficient minimum spanning tree algorithms are adapted to the context of terrain data and are shown to provide substantially better performance than previous PPA implementations. In particular, these are able to characterize valley and ridge behaviour at every point even in large elevation maps, providing a measure sensitive to terrain features at all scales.
The resulting graph based formulation provides an efficient and elegant algorithm for characterizing terrain features. The measure can be calculated efficiently, is robust under changes of neighbourhood position, size and resolution and the hybrid measure is sensitive to terrain features both locally and globally.
Terrain regions are characterized as a minimum spanning tree derived from a graph created from the sample points of the elevation map which are encoded as weights in the edges of the graph. This formulation allows us to provide a single consistent feature definition that is sensitive to the pattern of ridges and valleys in the terrain Alternative formulations of these weights provide richer characteristicmeasures and we provide examples of alternate definitions based on curvature and contour measures.
We show that the measure is robust, with a significant portion derived directly from information local to the terrain sample. Global terrain characteristics introduce the issue of over- and underconnected valley/ridge lines when working with sub-regions. This is addressed by providing two graph construction strategies, which respectively provide an upper bound on connectivity as a single spanning tree, and a lower bound as a forest of trees.
Efficient minimum spanning tree algorithms are adapted to the context of terrain data and are shown to provide substantially better performance than previous PPA implementations. In particular, these are able to characterize valley and ridge behaviour at every point even in large elevation maps, providing a measure sensitive to terrain features at all scales.
The resulting graph based formulation provides an efficient and elegant algorithm for characterizing terrain features. The measure can be calculated efficiently, is robust under changes of neighbourhood position, size and resolution and the hybrid measure is sensitive to terrain features both locally and globally.
History
Event
International conference on computer graphics, virtual reality, visualisation and interaction in Africa (7th : 2010 : Franschhoek, South Africa)Series
ACM conference proceedings seriesPagination
73 - 82Publisher
Association for Computing MachineryLocation
Franschhoek, South AfricaPlace of publication
New York, N.Y.Publisher DOI
Start date
2010-06-21End date
2010-06-23ISBN-13
9781450301183ISBN-10
1450301185Language
engPublication classification
E1.1 Full written paper - refereedCopyright notice
2010, Association for Computing MachineryEditor/Contributor(s)
S SpencerTitle of proceedings
Afrigraph 2010 : proceedings of the 7th international conference on computer graphics, virtual reality, visualisation and interaction in AfricaUsage metrics
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