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

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Topographic correction of Landsat ETM-images

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Topographic correction of landsat etm images

Topographic correction of Landsat ETM-images

Markus Törmä

Finnish Environment Institute

Helsinki University of Technology


Background

Background

  • CORINE2000 classification of whole Finland

  • Forested and natural areas are interpreted using Landsat ETM-image mosaics


Background1

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


Background2

Background

  • Landsat ETM 743, Kevo and digital elevation model


Background3

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

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 correction1

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

Example

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


Example1

Example

  • Landsat ETM (RGB: 743) and Illumination image


Example2

Example

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


Lambert cosine correction

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 correction1

Lambert cosine correction

  • Original and corrected ETM-image

  • Note overcorrection on the shadow side of hills


Minnaert correction

Minnaert correction

  • 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


Minnaert correction1

Minnaert correction

  • Original and corrected ETM-image

  • Still some overcorrection


Ekstrand correction

Ekstrand correction

  • Minnaert constant k varies according to illumination

    LC = LO [ COS(sz) / COS(i) ]k COS(i)


Ekstrand correction1

Ekstrand correction

  • Original and corrected ETM-image


Determination of minnaert constant k

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

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 k1

Minnaert constant k

  • NDVI classes and their number of samples


Minnaert constant k2

Minnaert constant k

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


Determination of minnaert constant k1

Determination of Minnaert constant k

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


Statistical empirical correction

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 correction1

Statistical-Empirical correction

  • Original and corrected ETM-image


C correction

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 correction1

C-correction

  • Original and corrected image


Determination of slope m and intercept b

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 b1

Determination of slope m and intercept b

  • Slopes m and correlation coefficients r for different channels


Maximum likelihood classification

Maximum Likelihood-classification

  • Ground truth: Lapland biotopemap


Maximum likelihood classification1

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 classification2

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

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 statistics1

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 statistics2

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

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 regression1

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

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 height1

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

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


Conclusion1

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


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