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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

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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