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

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

OutlineMotivationObjectivesApproachMethodsResultsConclusions

Motivation – What is the Problem?Projection of global datasets with conventional GIS software results in errorErrors affect global models and invalidate results

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

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

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)

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

Mollweide from Commercial Software

Michael P. Finn:

Michael P. Finn:

Mollweide from USGS mapimg

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

Areas of Single Pixels Computed from Spherical Coordinates (in meters2)

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

Reprojection accuracies between global and local projections

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

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

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

Extreme Downsampling and Reprojection with the Nearest Neighbor

Extreme Downsampling and Reprojection with the New Algorithm

Decision Support System for Map Projection Selection

Global, continental, regional (10 ° min)Preserve shape, area, compromiseData type – raster or vectorUser input determines projection selection

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

Addition InformationAvailable at:

http://mcmcweb.er.usgs.gov/carto_research/projection/index.htmlE-mail: mfinn@usgs.gov

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