Topographic correction of Landsat ETM-images Markus Törmä Finnish Environment Institute Helsinki University of Technology
Jan 13, 2016
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