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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

- CORINE2000 classification of whole Finland
- Forested and natural areas are interpreted using Landsat ETM-image mosaics

- 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

- Landsat ETM 743, Kevo and digital elevation model

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)

- 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

- 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”

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

- Landsat ETM (RGB: 743) and Illumination image

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

- 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

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

- Constant ksimulates 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

- Original and corrected ETM-image
- Still some overcorrection

- Minnaert constant k varies according to illumination
LC = LO [ COS(sz) / COS(i) ]k COS(i)

- Original and corrected ETM-image

- 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

- 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

- NDVI classes and their number of samples

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

- Determined constants k and corresponding correlation coefficients r for different channels

- 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.

- Original and corrected ETM-image

- 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

- Original and corrected image

- 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

- Slopes m and correlation coefficients r for different channels

- Ground truth: Lapland biotopemap

- 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%

- 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.

- 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

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

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

- 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

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

- 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

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

- 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

- 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