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Table 5 Landsat 5 thematic mapper candidate covariates

From: Estimating the size of urban populations using Landsat images: a case study of Bo, Sierra Leone, West Africa

Variables Covariate subset list Variable definition Number of variables Non-spectral mean values Spectral (pixel-level) transform
  Non-spectral transforms  
B \(b_i\); i = 1, 2, 3, 4, 5, 7 Mean value of Landsat 5 thematic mapper \(\hbox {band}_i\) measurement 6 *  
Bs \(bs_i\) ... SD of \(b_i\) 6 *  
Bv \(bv_i\) ... Variance of \(b_i\) 6 *  
Bc \(bc_i\) ... Coefficent of Variation [CV]: \(bc_i\) = sd(\(b_i\))/\(b_i\) = \(bs_i\)/\(b_i\) 6 *  
S \(s_i\); i = 1, 2, 3, 4, 5, 7 Square of \(b_i\) = \(b_i\) x \(b_i\) 6 *  
P \(p_{ij}\); i = 1, 2, 3, 4, 5 and j = i + 1, ..., 5, 7 Non-spectral cross products of the means \(b_i\) and \(b_j\) 15 *  
R.re \(r.re_{ij}\); i = 1, 2, 3, 4, 5 and j = i + 1, ... , 5, 7 Non-spectral ratios of means \(b_i\) and \(b_j\) = \(b_i\)/\(b_j\) 15 *  
D \(d_{12}\); i = 1, 2, 3, 4, 5 and j = i + 1 , ... , 5, 7 Non-spectral ratio of the difference-to-the-sum of the mean value \(b_i\), \(b_j\): \(d_{ij}\)= (\(b_i\)-\(b_j\))/(\(b_i\)+\(b_j\)). See text 15 *  
  Spectral transforms  
NB \(nb_i\); i = 1, 2, 3, 4, 5, 7 Mean value of the min-max normalized \(\hbox {band}_i\) measurements (see text) 6   *
NBs \(nbs_1\) ... SD of \(nb_i\) 6   *
NBv \(nbv_i\) ... Variance of \(nb_i\) 6   *
NBc \(nbc_i\) ... Coefficent of Variation [CV]: \(nbc_i\)= sd(\(nb_i\))/\(nb_i\) = \(nbs_i\)/\(nb_i\) 6   *
R \(r_{ij}\); i = 1, 2, 3, 4, 5 and j = i + 1, ... , 5, 7 \(r_{ij}\) = mean ratio of the paired pixel magnitudes 15   *
Rs \(rs_{ij}\) ... SD of \(r_{ij}\) 15   *
Rv \(rv_{ij}\) ... variance of \(r_{ij}\) 15   *
Rc \(rc_{ij}\) ... Coefficient of Variance [CV] of \(r_{ij}\) 15   *
DS \(ds_{ij}\); i = 1, 2, 3, 4, 5 and j = i + 1, ... , 5, 7 \(ds_{ij}\) = mean ratio of the difference-to–sum of the paired pixel magnitudes 15   *
DSs \(ds_{ij}s\) ... \(ds_{ij}s\) = SD of \(ds_{ij}\) 15   *
DSv \(ds_{ij}v\) ... \(ds_{ij}s\) = variance of \(ds_{ij}\) 15   *
DSc \(ds_{ij}c\) ... \(ds_{ij}s\) = coefficient of variation [CV] of \(ds_{ij}\) 15   *
CH \(ch_{ijk}\); i = 1, 2, 3, 4; j = i + 1, ... , 5; k = j + 1 Cylindrical transform of composite \(hue_{ijk}\) - see text 20   *
CHs \(ch_{ijk}s\) ... \(ch_{ijk}s\) = SD of \(ch_{ijk}\) 20   *
CHv \(ch_{ijk}v\) ... \(ch_{ijk}v\) = variance of \(ch_{ijk}\) 20   *
CHc \(ch_{ijk}c\) ... \(ch_{ijk}c\) = coefficient of variation [CV] of \(ch_{ij}\) 20   *
RH \(rh_{ijk}\); i = 1, 2, 3, 4; j = i + 1, ... ,5; k = j + 1 Rectangular transform transform of composite \(hue_{ijk}\) (see text) 20   *
RHs \(rh_{ijk}s\) ... \(rh_{ijk}s\) = SD of \(rh_{ijk}\) 20   *
RHv rh ijkv ... \(rh_{ijk}v\) = variance of \(rh_{ijk}\) 20   *
RHc \(rh_{ijk}c\) ... \(rh_{ijk}c\) = coefficient of variation [CV] of \(rh_{ij}\) 20   *
  Total variables: 379 75 304
  1. A summary of the 379 Landsat 5 thematic mapper variables calculated for this study. Only measurements collected in Bands 1 through 5 and Band 7 are used