# topographic correction of landsat etm-images

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Topographic correction of Landsat ETM-images. Markus Törmä Finnish Environment Institute Helsinki University of Technology. Background. CORINE2000 classification of whole Finland Forested and natural areas are interpreted using Landsat ETM-image mosaics. Background. - PowerPoint PPT PresentationTRANSCRIPT

Topographic correction of Landsat ETM-images Markus TrmFinnish Environment InstituteHelsinki University of Technology

BackgroundCORINE2000 classification of whole FinlandForested and natural areas are interpreted using Landsat ETM-image mosaics

BackgroundEstimation of continuous variables like tree height and crown coverContinuous variables are transformed to discrete CORINE-classes using IF-THEN-rulesAccording to the test classificatios, there is need for a SIMPLE topographic correction method in Lapland

BackgroundLandsat ETM 743, Kevo and digital elevation model

BackgroundTested methods:Lambertian cosine correctionMinnaert correctionEkstrand correctionStatistical Empirical correctionC-correction

Tests:Maximum Likelihood-classification to land cover classesComparison of class statistics between and within classesLinear regression to estimate tree height, tree crown cover and vegetation coverEstimation of tree crown cover and height using Proba-software (VTT)

Topografic correctionImaging geometry changes locally causing unwanted brightness changesE.g. deciduous forest looks like more bright on the sunny side that the shadow side of the hill Reflectance is largest when the slope is perpendicular to the incoming radiation

Topografic correctionIntensities of image pixels are corrected according to the elevation variations, other properties of the surface are not taken into accountThe angle between the surface normal and incoming radiation is needed Illumination image

ExampleLandsat ETM (RGB: 743) and digital elevation model made by National Land Survey

ExampleLandsat ETM (RGB: 743) and Illumination image

ExampleCorrelation between pixel digital numbers vs. illumination varies between different channels

Lambert cosine correctionIt is supposed that the ground surface is lambertian, i.e. reflects radiation equal amounts to different directions

LC = LO COS(sz) / COS(i)

LO: original digital number or reflectance of pixelLC: corrected digital numbersz: sun zenith anglei: angle between sun and local surface normal

Lambert cosine correctionOriginal and corrected ETM-image Note overcorrection on the shadow side of hills

Minnaert correctionConstant k simulates the non-lambertian behaviour of the target surface

LC = LO [ COS(sz) / COS(i) ]k

Constant k is channel dependent and determined for each image

Minnaert correctionOriginal and corrected ETM-imageStill some overcorrection

Ekstrand correctionMinnaert constant k varies according to illumination

LC = LO [ COS(sz) / COS(i) ]k COS(i)

Ekstrand correctionOriginal and corrected ETM-image

Determination of Minnaert constant kLinearization of Ekstrand correction equation:-ln LO = k cos i [ ln (cos(sz) / cos(i)) ] ln LC

Linear regressionLine y = kx + b was adjusted to the digital numbers of the satellite imagey = -ln LOx = cos i [ln(cos(sz) / cos(i))] b = -ln LC

Minnaert constant kSamples were taken from imageFlat areas were removed from samplesIn order to study the effect of vegetation to the constant, samples were also stratified into classes according to the NDVI-value

Minnaert constant kNDVI classes and their number of samples

ClassNDVINumber of samplesALL-1 < NDVI < 1162601-1 < NDVI < 0.03520.0 < NDVI < 0.16630.1 < NDVI < 0.280540.2 < NDVI < 0.3259450.3 < NDVI < 0.4925360.4 < NDVI < 0.52780870.5 < NDVI < 0.64411080.6 < NDVI < 0.74567690.7 < NDVI < 0.821014100.8 < NDVI < 0.958

Minnaert constant kCorrelation between pixel digital numbers vs. illumination varies between different NDVI-classes on the channel 5

Determination of Minnaert constant kDetermined constants k and corresponding correlation coefficients r for different channels

Ch1 kCh1 rCh2 kCh2 rCh3 kCh3 rCh4 kCh4 rCh5 kCh5 rCh7 kCh7 rALL0.0584 0.06950.22900.19830.2491 0.11421.1042 0.49720.9846 0.38100.7099 0.2243NDVI

Statistical-Empirical correctionStatistical-empirical correction is statistical approach to model the relationship between original band and the illumination.

LC = LO m cos(i)

m: slope of regression lineGeometrically the correction rotates the regression line to the horizontal to remove the illumination dependence.

Statistical-Empirical correctionOriginal and corrected ETM-image

C-correctionC-correction is modification of the cosine correction by a factor C which should model the diffuse sky radiation.

LC = LO [ ( cos(sz) + C ) / ( cos(i) + C ) ]

C = b/m b and m are the regression coefficients of statistical-empirical correction method

C-correctionOriginal and corrected image

Determination of slope m and intercept bRegression coefficients for Statistical-empirical and C-correction were determined using linear regressionSlope of regression line m and intercept b were determined using illumination (cos(i)) as predictor variable and channel digital numbers as response variable

Determination of slope m and intercept bSlopes m and correlation coefficients r for different channels

Ch1 mCh1 rCh2 mCh2 rCh3 mCh3 rCh4 mCh4 rCh5 mCh5 rCh7 mCh7 rAll0.0302 0.07710.08510.19200.0799 0.12391.0043 0.54280.7055 0.44970.2768 0.2283NDVI

Maximum Likelihood-classificationGround truth: Lapland biotopemap

ClassTree CrownCover (%)Training compartments, number: pixelsTest compartments,number: pixelsBare rock07: 4687: 487Mineral soil07: 5137: 599Lichen-Twig013: 103012: 930Lichen-Moss-Twig20-3012: 103713: 869Moss-Twig30-4013: 88012: 1101Bogs with trees20-309: 6369: 708Open bogs013: 101012: 885

Maximum Likelihood-classificationAccuracy measures: overall accuracy (OA), userss and producers accuracies of classes for training (tr) and test (te) sets

Original image: Oatr 57.2%, Oate 48.2%Cosine correction: Oatr 60.9%, Oate 51.9%

Maximum Likelihood-classificationIn the case of test set, the correction methods usually increased classification accuracy compared to original image

Stratification using the NDVI-class increases classification accuracy of test pixels in the cases of Ekstrand and Statistical-Empirical correction.

Comparison of class statisticsJefferies-Matusita decision theoretic distance:distance between two groups of pixels defined by their mean vectors and covariancematrices

Distances were compared between classes and within individual classes

Comparison of class statisticsBetween-class-comparison14 Biotopemapping classes separability should be as high as possible

Within-class-comparison7 Biotopemapping classesclasses were divided into subclasses according to the direction of the main slope separability should be as low as possible

Comparison of class statisticsBetween-class-comparisonCosine correction and original image best

Within-class-comparisonStatistical-Empirical correction best, Cosine correction and original image worstThe effect of correction is largest for mineral soil classes and smallest for peat covered soils. Stratification using the NDVI-class decreases the separability of subclasses

Linear regressionEstimate tree height, tree crown cover and vegetation cover

Ground survey300 plots in Kevo region, Northern Lapland Information about vegetation and tree crown cover, tree height and species

Linear regressionTree heightStatistical-Empirical bestStratification decreases the correlation a little

Tree crown coverCosine and C-correction bestStratification decreases the correlation a little

Vegetation coverC- and Minnaert correction best

Estimation of tree crown cover and heightProba-software (Finnish National Research Center)Training (3386) and test (1657) compartments from Lapland Biotopemap, compartmentwise averagesTree height and crown cover were estimated for image pixels and compartment averages computedError measures: Bias, Root Mean Squared Error, Correlation Coefficient

Estimation of tree crown cover and heightTree heightC-correction bestTopographic correction and stratification decreases estimation error

Tree crown coverEkstrand correction bestTopographic correction and stratification decreases estimation error

ConclusionTopographic correction improves classification or estimation resultsBut methods perform differently and their performence depends on task at handIn some cases correction even make results worse so it is difficult to choose the best method

ConclusionThe best correction methods seem to be C-correction and Ekstrand correction

The stratification according to the NDVI-class improves results in some cases, depending on the used experiment

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