agreement at multiple resolutions for real and categorical maps chris ayres – george kariuki...
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Agreement at Multiple Resolutions for Real and
Categorical Maps
Chris Ayres – George Kariuki Kristopher Kuzera
[email protected], [email protected], [email protected]
GEOG 360 Quantitative ModelingFinal Project - Spring 2004
REALMULTIRES, SOFTMULTIRES
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Lessons
• Currently, there is no known program available to perform and interpret a MULTIPLE-RESOLUTION ANALYSIS for real and categorical data.
• Automation of these processes allows for efficient production and replication of methodologies, with a minimization of human error.
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Multiple Resolution Analysis
• Multiple resolution analysis compares corresponding pixels of two maps over varying resolutions ranging from fine to coarse.
• This helps locate spatial patterns within the dataset and allows for ease in interpretability of the data.
• The analysis can distinguish disagreement of quantity from disagreement of location.
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Forest 1999Urban 1971
Multiple Resolution Example
Maps of categorical disagreement from fine to coarse resolutions
Worcester County, MA
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MULTIRES Programs
1971
1999
Actual
Predicted
• REALMULTIRES– Real variables
• SOFTMULTIRES– Categorical variables
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Characteristic REAL-MULTIRES
SOFT-MULTIRES
Performs MULTIPLE RESOLUTION ANALYSIS of three different SOFT-CLASSIFIED OPERATORS to compare two categorical maps.
Yes
Compares two maps of a common real variable (NDVI, SST) at multiple spatial-resolutions using various components of two measures of accuracy: (1) Root Mean Square Error (RMSE) (2) Mean Absolute Error (MAE)
Yes
Uses IDRISI to carry out raster functions: CONTRACT, RECLASS, OVERLAY, EXTRACT, WINDOW, CONVERT, TRANSFORM
Yes Yes
Calculates COEFFICIENTS OF AGREEMENT from generated cross-tabulation matrices of agreement and disagreement.
Yes
Graphically displays results over all resolutions. Yes Yes
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NDVI deviation at 1x1 km
Null model would predict zero everywhere.
Drought Prediction in Southern Africa
Actual Map Predicted Map
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NDVI deviation at 4x4 km
Null model would predict zero everywhere.
Drought Prediction in Southern Africa
Actual Map Predicted Map
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NDVI deviation at 16x16 km
Null model would predict zero everywhere.
Drought Prediction in Southern Africa
Actual Map Predicted Map
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Program Implementation: RMSE
Perfect Posterior PriorINFORMATION OF QUANTITY
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Program Implementation: MAE
Perfect Posterior PriorINFORMATION OF QUANTITY
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Interface for REALMULTIRES• Inputs
– Working Folder– Actual map– Prediction map– Mask Map– No. of Rows– No. of Cols– Range of resolutions
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Budget Results:Null versus Prediction
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Resolution
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. Agreement dueto LocationDisagreementdue to LocationDisagreementdue to Quantity
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Resolution
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Agreement due toLocation
Disagreement due toLocation
Disagreement due toQuantity
0.465
0.47
0.475
0.48
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0.49
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Resolution
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Agreement due toLocation
Disagreement due toLocation
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REALMULTIRESAutomation Benefits
• Huge time savings– 2 WEEKS manually becomes 1½ MINUTES automatically.
• Minimize Chance of Error, Maximize Efficiency– Repetitive tasks are prone to human error such as typos that
could have a big unwanted impact on the results.
• RMSE and MAE have great potential for accuracy assessment (drought prediction)The two methods are better than regression at giving useful information to evaluate drought prediction in Africa.
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SOFTMULTIRESFlow Chart
Whichoperator?
MULTIPLICATION COMPOSITE
MINIMUM
Calculate minimum valuesof similar classes atresolutions. (MINIMUM)
Create gains and lossesmaps at resolutions.(ADD / SUBTRACT)
Multiply gains and lossesover 1 - agreement
Multiply each map withevery other at resolutions.(MULTIPLY)
Calculate minimum valuesof comparing maps atresolutions. (MINIMUM)
Calculate sumof pixels. (EXTRACT)
Calculate sumof pixels. (EXTRACT)
Calculate sumof pixels. (EXTRACT)
Calculate sumof pixels. (EXTRACT)
STARTRead the following variables frominput sheet: Comparison Year,Reference Year, Map files, Operators,Number of Categories
Create soft-classified resolution maps for eachclass at each year. (CONTRACT)
Read RDC file to determinenumber of resolutions, rows,and columns.
END
Sums entered in contingencytable at resolutions.
Derive statisticsfrom matrices.
Graph statisticsover resolutions.
IDRISI Kilimanjaro
Another operator?
NOYES
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SOFTMULTIRESSoft-Classified Operators
• Soft-classified operators allow for multiple class membership per pixel. The pixels are considered “soft”.
• Different operators have different interpretations of class membership and location within a pixel.
• SOFTMULTIRES allows user to choose any or all operators for their analysis.
OPERATOR AGREEMENT DISAGREEMENT
Multiplication multiply multiply
Minimum minimum minimum
Composite minimum multiply / ratio
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• Coefficients of agreement determine agreement based on the proportions of categories correctly classified.
• These vary depending on which cells of the cross-tabulation matrix are used for calculation.
• SOFTMULTIRES derives the above coefficients from generated cross-tabulation matrices.
OVERALL COEFFICIENTS OF AGREEMENT
CATEGORICAL COEFFICIENTS OF AGREEMENT
Overall Proportion Correct User’s Accuracy
Nishii-Tanaka Producer’s Accuracy
Cramer’s VConditional Kappa
(by row and column)
SOFTMULTIRESCoefficients of Agreement
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Interface for SOFTMULTIRES• Inputs
– Comparison map year– Reference map year– Number of Categories (maximum 15)– Operator (Multiplication, Minimum, and/or Composite)– Path Directory– Boolean raster images for each category
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Cross-Tabulation Matrix
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Graphical Output
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SOFTMULTIRESAutomation Benefits
• SOFTMULTIRES allows for simple recreation of methodology for any two categorical maps.
• SOFTMULTIRES produces many coefficients for ease of interpretability.
• SOFTMULTIRES reduces processing time.– 40 HOURS manually becomes 10 MINUTES automatically.
• SOFTMULTIRES produces hundreds of maps quickly.4 reference categories x 4 comparison categories
x 10 resolutions x 3 operators =
480 images
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Lessons
• Currently, there is no known program available to perform and interpret a MULTIPLE-RESOLUTION ANALYSIS for real and categorical data.
• Automation of these processes allows for efficient production and replication of methodologies, with a minimization of human error.
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• REALMULTIRES method is based on:• Pontius. 2002. Statistical methods to partition effects of quantity and location during
comparison of categorical maps at multiple resolutions. Photogrammetric Engineering & Remote Sensing 68(10). pp. 1041-1049.
• SOFTMULTIRES method is based on:• Kuzera, K. and Pontius, R. G. Jr. 2004. Categorical Coefficients of Agreement for Assessing
Soft-Classified Maps at Multiple Resolutions. In proceedings TIES 2004.
• Special thanks to: • Clarklabs (www.clarklabs.org) who is incorporating the validation method and the multiple-
resolution analysis of categorical maps into the GIS software Idrisi.• Ron Eastman who supplied data of NDVI images.• Human-Environment Regional Observatory Network for providing Worcester categorical data.• Gil Pontius for advising.• Olufunmilayo E. Thontteh for collaboration. More information available at the presentation of
her Masters Thesis work: “Verification Of Vegetation Index Predictions Using Multiple Resolution Images”.
Plugs & Acknowledgements