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Table 5 Texture metrics as measures of spatial landscape heterogeneity

From: Quantifying how urban landscape heterogeneity affects land surface temperature at multiple scales

Metric Value range Expected relationshipa Equation
First-order texture
Variance ≥ 0 HX \( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{\left(i-\upmu \right)}^2p\left(i,j\right) \)
Mean ≥ 0 HX \( \sum \limits_k^{N_g}{kp}_{x-y}(k) \)
Second-order texture
Contrast ≥ 0 HX \( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{\left(i-j\right)}^2{p}_d\left(i,j\right) \)
Dissimilarity ≥ 0 HX \( \sum \limits_i^{N_g}\sum \limits_j^{N_g}p\left(i,j\right)\left|i-j\right| \)
Entropy ≥ 0 HX \( -\sum \limits_i^{N_g}\sum \limits_j^{N_g}p\left(i,j\right)\mathit{\log}\left[p\left(i,j\right)\right] \)
Homogeneity ≥ 0; ≤ 1 HX \( \sum \limits_i^{N_g}\sum \limits_j^{N_g}\frac{1}{1+{\left(i-j\right)}^2}{p}_d\left(i,j\right) \)
Correlation ≥ 0; ≤ 0 HX \( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{p}_d\left(i,j\right)\frac{\left(i-{\mu}_x\right)\left(j-{\mu}_y\right)}{\sigma_x{\sigma}_y} \)
Energy ≥ 0; ≤ 1 HX \( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{g}_{ig^2} \)
  1. aHX, larger values indicate greater heterogeneity; H X, lower values indicate greater heterogeneity.