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![Page 1: U.S. Department of the Interior U.S. Geological Survey Accurate Projection of Small-Scale Raster Datasets 21 st International Cartographic Conference 10.](https://reader035.fdocuments.in/reader035/viewer/2022062500/56649e605503460f94b5a4fb/html5/thumbnails/1.jpg)
U.S. Department of the InteriorU.S. Geological Survey
Accurate Projection of Small-Scale Raster Datasets
21st International Cartographic Conference
10 – 16 Aug 2003Durban, South Africa
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Accurate Projection of Small-Scale Raster Datasets
E. Lynn Usery, USGS, Mid-Continent Mapping Center, Rolla, MOJeong Chang Seong, Northern Michigan University, Marquette, MIDan Steinwand, Science Applications International Corp., EROS Data Center, Sioux Falls, SD Michael P. Finn, USGS, MCMC, Rolla
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OutlineMotivationObjectivesApproachMethodsResultsConclusions
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Motivation – What is the Problem?Projection of global datasets with conventional GIS software results in errorErrors affect global models and invalidate results
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ObjectivesDevelop a dynamic projection for raster data Determine methods to measure error and apply error correction Develop a better categorical resamplerDevelop an system to support map projection selection
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ApproachEmpirical TestingCompute exact areas in spherical coordinates and replicate cell-by-cell in projected dataDevelop error theory using horizontal and vertical scale factorsDevelop a categorical resampler with user selection of output pixel on down-samplingDesign and Implement a Decision Support System
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Empirical TestingMultiple Datasets
Global land cover, 30 arc-secGlobal Life (ecological) Zones, ½ degreeGlobal vegetation, 1 degree
Multiple ProjectionsEckert IVHammerSinusoidal MollweideGoode HomolosineWagner IVRobinson (non-equal area)
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Empirical Test ResultsUse of Commercial GIS Software
Software is not always reliable for global projectionSome projections do not run to completionInverse projection results in extension of raster areas to 0-degree linesRepeat areas at edges of projectionComputation times extensive
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Mollweide from Commercial Software
Michael P. Finn:
Michael P. Finn:
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Mollweide from USGS mapimg
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Dynamic Projection of Raster CellsCompute areas of pixels in geographic coordinatesMap each raster line to appropriate areaResult is accurate for computation and analysis, but each raster line has different size
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Areas of Single Pixels Computed from Spherical Coordinates (in meters2)
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Error Theory and ModelingBest projection for global scale
CriteriaIt shouldn’t lose pixel values when a local-scale dataset is projected to the global-scale projection It shouldn’t lose pixel values when a dataset in the global-scale projection is projected at a very accurate local-scale projection
Efficient storage
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Reprojection accuracies between global and local projections
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Accuracy increase due to the change of skew angle
1
1.4
1.8
2.2
2.6 3
3.4
3.8
4.2
4.6 5
5.4
5.8
6.2
6.6 7
7.4
7.8
8.2
8.6 9
9.4
9.8
S1
S4
S7
S10
S13
S16
S19
S22
S25
S28
S31
S34
S37
S40
S43
S46
S49
S52
S55
S58
S61
S64
S67
S70
S73
S76
S79
Scale Factor
Skew Angle
0.6000-0.8000
0.4000-0.6000
0.2000-0.4000
0.0000-0.2000
-0.2000-0.0000
SkewModel.Xls
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Error Theory and Modeling Summary
Scale factor model explains most pixel value changesThe change of pixel values occurs regardless of pixel resolutionsSignificant change as category numbers increaseSignificant change due to skewing
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Categorical ResamplingDown-sampling to larger pixel size
aggregating multiple input pixels to one output pixel
Nearest neighbor selects one pixel valueMany pixels involved
use simple statistical methods to determine output image pixels based on the area the pixel coverage in the input image
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Extreme Downsampling and Reprojection with the Nearest Neighbor
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Extreme Downsampling and Reprojection with the New Algorithm
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Decision Support System for Map Projection Selection
Global, continental, regional (10 ° min)Preserve shape, area, compromiseData type – raster or vectorUser input determines projection selection
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ConclusionsProjection of global raster data is a significant problemArea preservation in raster data is possible for computation and analysis, not for displayA scale factor model accounts for most error and shows the sinusoidal projection to preserve areas better than othersCategorical resampling with modal categories yields better results than nearest neighbor methodsA Decision Support System is needed and now available
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Addition InformationAvailable at:
http://mcmcweb.er.usgs.gov/carto_research/projection/index.htmlE-mail: [email protected]
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U.S. Department of the InteriorU.S. Geological Survey
Accurate Projection of Small-Scale Raster Datasets
21st International Cartographic Conference
10 – 16 Aug 2003Durban, South Africa