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

Background Landsat ETM 743, Kevo and digital elevation model

Background Tested methods: Lambertian cosine correction Minnaert correction Ekstrand correction Statistical Empirical correction C-correction Tests: Maximum Likelihood-classification to land cover classes Comparison of class statistics between and within classes Linear regression to estimate tree height, tree crown cover and vegetation cover Estimation of tree crown cover and height using Proba-software (VTT)

Topografic correction Imaging geometry changes locally causing unwanted brightness changes E.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 correction Intensities of image pixels are corrected according to the elevation variations, other properties of the surface are not taken into account The angle between the surface normal and incoming radiation is needed  ”Illumination image”

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

Example Landsat ETM (RGB: 743) and Illumination image

Example Correlation between pixel digital numbers vs. illumination varies between different channels

Lambert cosine correction It is supposed that the ground surface is lambertian, i.e. reflects radiation equal amounts to different directions L C = L O COS(sz) / COS(i) L O : original digital number or reflectance of pixel L C : corrected digital number sz: sun zenith angle i: angle between sun and local surface normal

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

Minnaert correction Constant k simulates the non-lambertian behaviour of the target surface L C = L O [ COS(sz) / COS(i) ] k Constant k is channel dependent and determined for each image

Minnaert correction Original and corrected ETM-image Still some overcorrection

Ekstrand correction Minnaert constant k varies according to illumination L C = L O [ COS(sz) / COS(i) ] k COS(i)

Ekstrand correction Original and corrected ETM-image

Determination of Minnaert constant k Linearization of Ekstrand correction equation: -ln L O = k cos i [ ln (cos(sz) / cos(i)) ] – ln L C Linear regression Line y = kx + b was adjusted to the digital numbers of the satellite image y = -ln L O x = cos i [ln(cos(sz) / cos(i))] b = -ln L C

Minnaert constant k Samples were taken from image Flat areas were removed from samples In order to study the effect of vegetation to the constant, samples were also stratified into classes according to the NDVI-value

Minnaert constant k NDVI classes and their number of samples ClassNDVINumber of samples ALL-1 < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < < NDVI < 0.958

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

Determination of Minnaert constant k Determined constants k and corresponding correlation coefficients r for different channels Ch1 kCh1 rCh2 kCh2 rCh3 kCh3 rCh4 kCh4 rCh5 kCh5 rCh7 kCh7 r ALL NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI<

Statistical-Empirical correction Statistical-empirical correction is statistical approach to model the relationship between original band and the illumination. L C = L O – m cos(i) m: slope of regression line Geometrically the correction rotates the regression line to the horizontal to remove the illumination dependence.

Statistical-Empirical correction Original and corrected ETM-image

C-correction C-correction is modification of the cosine correction by a factor C which should model the diffuse sky radiation. L C = L O [ ( cos(sz) + C ) / ( cos(i) + C ) ] C = b/m b and m are the regression coefficients of statistical- empirical correction method

C-correction Original and corrected image

Determination of slope m and intercept b Regression coefficients for Statistical- empirical and C-correction were determined using linear regression Slope 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 b Slopes m and correlation coefficients r for different channels Ch1 mCh1 rCh2 mCh2 rCh3 mCh3 rCh4 mCh4 rCh5 mCh5 rCh7 mCh7 r All NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI< <NDVI<

Maximum Likelihood-classification Ground truth: Lapland biotopemap ClassTree Crown Cover (%) Training compartments, number: pixels Test compartments, number: pixels Bare rock07: 4687: 487 Mineral soil07: 5137: 599 Lichen-Twig013: : 930 Lichen-Moss-Twig : : 869 Moss-Twig : 88012: 1101 Bogs with trees20-309: 6369: 708 Open bogs013: : 885

Maximum Likelihood-classification Accuracy measures: overall accuracy (OA), users’s and producer’s 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-classification In 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 statistics Jefferies-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 statistics Between-class-comparison 14 Biotopemapping classes separability should be as high as possible Within-class-comparison 7 Biotopemapping classes classes were divided into subclasses according to the direction of the main slope separability should be as low as possible

Comparison of class statistics Between-class-comparison Cosine correction and original image best Within-class-comparison Statistical-Empirical correction best, Cosine correction and original image worst The 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 regression Estimate tree height, tree crown cover and vegetation cover Ground survey 300 plots in Kevo region, Northern Lapland Information about vegetation and tree crown cover, tree height and species

Linear regression Tree height Statistical-Empirical best Stratification decreases the correlation a little Tree crown cover Cosine and C-correction best Stratification decreases the correlation a little Vegetation cover C- and Minnaert correction best

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

Estimation of tree crown cover and height Tree height C-correction best Topographic correction and stratification decreases estimation error Tree crown cover Ekstrand correction best Topographic correction and stratification decreases estimation error

Conclusion Topographic correction improves classification or estimation results But methods perform differently and their performence depends on task at hand In some cases correction even make results worse so it is difficult to choose the best method

Conclusion The 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