Topographic correction of Landsat ETM-images

Markus TörmäFinnish 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

BackgroundTested 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

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

• LO: original digital number or reflectance of pixel

• LC: 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

LC = LO [ 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

LC = LO [ 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 LO = k cos i [ ln (cos(sz) / cos(i)) ] – ln LC

• Linear regression• Line y = kx + b was adjusted to the digital numbers of

the satellite image

y = -ln LO

x = cos i [ln(cos(sz) / cos(i))]

b = -ln LC

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

Class NDVI Number of samples

ALL -1 < NDVI < 1 16260

1 -1 < NDVI < 0.0 35

2 0.0 < NDVI < 0.1 66

3 0.1 < NDVI < 0.2 805

4 0.2 < NDVI < 0.3 2594

5 0.3 < NDVI < 0.4 9253

6 0.4 < NDVI < 0.5 27808

7 0.5 < NDVI < 0.6 44110

8 0.6 < NDVI < 0.7 45676

9 0.7 < NDVI < 0.8 21014

10 0.8 < NDVI < 0.9 58

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 k Ch1 r Ch2 k Ch2 r Ch3 k Ch3 r Ch4 k Ch4 r Ch5 k Ch5 r Ch7 k Ch7 r

ALL 0.0584 0.0695 0.2290 0.1983 0.2491 0.1142 1.1042 0.4972 0.9846 0.3810 0.7099 0.2243

NDVI<0 0.4227 0.4903 1.1120 0.5986 1.8703 0.5757 1.6927 0.5264 1.6243 0.3434 1.7972 0.3379

0<NDVI<0.1 0.6439 0.2066 1.1224 0.2469 1.3756 0.2257 1.2230 0.2070 0.7187 0.0805 0.8029 0.0851

0.1<NDVI<0.2 0.4401 0.4332 0.7655 0.4599 0.9492 0.3860 1.0039 0.3951 1.1287 0.2672 1.1331 0.2515

0.2<NDVI<0.3 0.4227 0.5298 0.7351 0.5510 0.9682 0.4940 0.9894 0.4902 1.3039 0.3817 1.3444 0.3718

0.3<NDVI<0.4 0.3216 0.5066 0.6007 0.5646 0.8414 0.5377 0.8888 0.5367 1.3145 0.5004 1.3327 0.4878

0.4<NDVI<0.5 0.2900 0.4714 0.5360 0.5256 0.7956 0.5134 0.8466 0.5624 1.3609 0.5322 1.3819 0.5102

0.5<NDVI<0.6 0.1832 0.4284 0.3902 0.4997 0.6777 0.4882 0.7778 0.5289 1.2547 0.4979 1.2631 0.4825

0.6<NDVI<0.7 0.1536 0.4664 0.3033 0.5941 0.6188 0.6094 0.7114 0.6045 1.1705 0.6515 1.1897 0.6335

0.7<NDVI<0.8 0.1054 0.4110 0.2473 0.6474 0.4642 0.6462 0.8001 0.7562 0.9938 0.8356 0.8946 0.7538

0.8<NDVI<0.9 0.0269 0.1167 -0.0183 -0.0548 0.1420 0.2915 0.1608 0.2594 0.2382 0.4645 0.1863 0.2941

Statistical-Empirical correction

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

LC = LO – 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.

LC = LO [ ( 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 m Ch1 r Ch2 m Ch2 r Ch3 m Ch3 r Ch4 m Ch4 r Ch5 m Ch5 r Ch7 m Ch7 r

All 0.0302 0.0771 0.0851 0.1920 0.0799 0.1239 1.0043 0.5428 0.7055 0.4497 0.2768 0.2283

NDVI<0 0.1031 0.4213 0.2021 0.5286 0.2517 0.4828 0.2380 0.4508 0.1533 0.2976 0.1252 0.2960

0<NDVI<0.1 0.3574 0.1893 0.5389 0.2404 0.5903 0.2450 0.6277 0.2331 0.5365 0.1827 0.5132 0.1908

0.1<NDVI<0.2 0.2305 0.5159 0.3396 0.5741 0.4127 0.5499 0.6302 0.5644 1.0392 0.5565 0.8427 0.5519

0.2<NDVI<0.3 0.2114 0.5999 0.3084 0.6436 0.3790 0.6298 0.6672 0.6305 1.0997 0.6408 0.8282 0.6337

0.3<NDVI<0.4 0.1562 0.5551 0.2408 0.6295 0.3056 0.6393 0.6801 0.6466 1.1082 0.6973 0.7232 0.6733

0.4<NDVI<0.5 0.1287 0.4841 0.1945 0.5477 0.2500 0.5534 0.6881 0.6118 1.0569 0.6143 0.6173 0.5857

0.5<NDVI<0.6 0.0758 0.4302 0.1295 0.5000 0.1785 0.4972 0.6627 0.5412 0.8616 0.5214 0.4577 0.5020

0.6<NDVI<0.7 0.0592 0.4525 0.0944 0.5776 0.1393 0.6036 0.6849 0.6030 0.7528 0.6618 0.3670 0.6337

0.7<NDVI<0.8 0.0412 0.3739 0.0789 0.6149 0.0982 0.6319 0.9540 0.7176 0.6588 0.8266 0.2625 0.7381

0.8<NDVI<0.9 0.0036 0.0434 -0.0076 -0.0753 0.0160 0.1875 0.1221 0.1373 0.1248 0.3526 0.0384 0.2160

Maximum Likelihood-classification• Ground truth: Lapland biotopemap

Class Tree Crown

Cover (%)

Training compartments, number: pixels

Test compartments,

number: pixels

Bare rock 0 7: 468 7: 487

Mineral soil 0 7: 513 7: 599

Lichen-Twig 0 13: 1030 12: 930

Lichen-Moss-Twig 20-30 12: 1037 13: 869

Moss-Twig 30-40 13: 880 12: 1101

Bogs with trees 20-30 9: 636 9: 708

Open bogs 0 13: 1010 12: 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 regressionTree 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