Transcript Topographic correction of Landsat ETM

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 ETMimage mosaics
Background
• Estimation of continuous variables like tree
height and crown cover
• Continuous variables are transformed to
discrete CORINE-classes using IF-THENrules
• 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
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 statisticalempirical correction method
C-correction
• Original and corrected image
Determination of slope m and
intercept b
• Regression coefficients for Statisticalempirical 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 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 Ccorrection and Ekstrand correction
• The stratification according to the NDVIclass improves results in some cases,
depending on the used experiment