Grey Level Co-occurrence Matrix (GLCM)

Grey Level Co-occurrence Matrix developed by (Haralick et al. 1973) was designed to estimate how often variation of grey level intensity of a pixel occurs within a given moving window size (defining local window within which the GLCM is computed) in a given direction (angle and distance defining neighbourhood relationship for the pixels whose GLCM is being computed) (Haralick 1979). The generation of GLCM texture involves generation of spatial relationships of the reference and neighbor pixels, the decision on the window size or separation between the pixels (d), generating symmetrical matrices and normalizing to obtain the probability of occurrence (Pradhan et al. 2014). Interpixel distance selected for the GLCM computations included 5, 7 and 9. The orientations selected, based on the position of the reference pixel, included 0° (considers pixels to the east and west of reference pixel), 45° (considers pixels to the northeast and south-west of reference pixel), 90° (considers pixels to the north and south of reference pixel), 135° (considers pixels to the north-west and south-east of reference pixel) and a selection considering all the pixels surrounding the reference pixel (direction invariant).

Taking 𝐼(𝐵_𝑥∗ 𝐵_𝑦) to be the satellite image with spatial extents in x- (𝐵_𝑥) and y-direction (𝐵_𝑦), (𝑥₁, 𝑦₁)(𝑥₂, 𝑦₂) are reference and neighborhood pixels whose texture is being computed and separation between the pixels is d, then GLCM is given by (Haralick et al. 1973):

𝐺𝐿𝐶𝑀 (𝑖, 𝑗) = {((𝑥1, 𝑦1), (𝑥2, 𝑦2)) ∈ (𝐵𝑥∗ 𝐵𝑦) × (𝐵𝑥∗ 𝐵𝑦) 𝑥₁− 𝑥₂= 0, |𝑦₁− 𝑦₂| = 𝑑, 𝑓𝑜𝑟 0° 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑥₁− 𝑥₂= 𝑑, 𝑦₁− 𝑦₂= −𝑑, 𝑓𝑜𝑟 45° 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 |𝑥1− 𝑥2| = 𝑑, 𝑦1− 𝑦2= 0, 𝑓𝑜𝑟 90° 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑥₁− 𝑥₂= 𝑑, 𝑦₁− 𝑦₂= 𝑑, 𝑓𝑜𝑟 135° 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐼(𝑥₁, 𝑦₁) = 𝑖, 𝐼(𝑥2, 𝑦2) = 𝑗} 𝑑(𝑥₁, 𝑦₁), (𝑥2, 𝑦2) = {|𝑥1− 𝑥2|, |𝑦1− 𝑦2|}

GLCM is the probability of occurrence of a pixel with value j for all values from 1 to B occurring at a distance d with respect to a pixel i for all values from 1 to B on an image (the number of times gray tones i and j have been neighbors). Different weights are then assigned to the GLCM probability values depending on the output information required (Haralick 1979, Hall-Beyer 2007) (Table 4.1). GLCM texture features can be arranged in three main groups: The contrast and orderliness groups as well as the descriptive statistics group. The contrast group is designed to enhance variations of the pixel intensities. Weights of dissimilarity increase linearly whereas those of contrast increase exponentially highlighting variation present in the image. For homogeneity, the weights decrease exponentially with increased variation of the neighboring pixels indicating large values in areas with small differences in grey levels. The orderliness group is designed to enhance regularity or commonness within a window. It comprises of Angular Second Moment which uses the square of the probability as a weight for itself whereas the square root of this is the energy/uniformity. ASM measures uniformity or repetitions of

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pixel pairs such that large values indicate less local texture variation. Entropy is obtained by multiplying the GLCM logarithm with itself, measuring image disorder. Small entropy values indicate textural uniformity of the image. Lastly, the general statistics are defined in the descriptive group based on the GLCM matrix values. The GLCM mean, variance and correlation are computed based on the frequency of occurrence in relation to the neighboring pixels. Mean incorporates the grey level of each line in the texture calculation. Variance is a measure of heterogeneity which increases when the grey level values differ from the mean. Correlation is a measure of grey tone linear dependencies in the image. High correlation values indicate linear relationships between grey levels of pixel pairs (Arzandeh and Wang 2002). Table 4.1 lists the GLCM texture feature formulation.

Table 4.1: The GLCM texture features extracted from each VV SAR image Texture feature Formulas

Contrast group Contrast _{∑ ∑ 𝐺𝐿𝐶𝑀}

𝑖,𝑗(𝑖 − 𝑗)2 𝑗 𝑖 Dissimilarity _{∑ ∑ 𝐺𝐿𝐶𝑀} 𝑖,𝑗|𝑖 − 𝑗| 𝑗 𝑖 Homogeneity

(Inverse Difference Moment) ∑ ∑

𝐺𝐿𝐶𝑀𝑖,𝑗 1 + (𝑖 − 𝑗)2 𝑗

𝑖

Orderliness group Angular Second Moment (ASM) _{∑ ∑ 𝐺𝐿𝐶𝑀} 𝑖,𝑗2 𝑗 𝑖 Energy (Uniformity) √∑ ∑ 𝐺𝐿𝐶𝑀𝑖,𝑗2 𝑗 𝑖

Maximum Probability (MAX) Gives the largest probability within the selected window

Entropy _{− ∑ ∑ 𝐺𝐿𝐶𝑀}

𝑖,𝑗(log 𝐺𝐿𝐶𝑀𝑖,𝑗) 𝑗

𝑖

Descriptive statistics GLCM Mean _{𝜇 = ∑ ∑ 𝑖(𝐺𝐿𝐶𝑀}

𝑖,𝑗) 𝑗 𝑖 GLCM Variance _𝜎2_{= ∑ ∑ 𝐺𝐿𝐶𝑀} 𝑖,𝑗(𝑖 − 𝜇)2 𝑗 𝑖 GLCM Correlation ∑ ∑ 𝐺𝐿𝐶𝑀𝑖,𝑗 [ (𝑖 − 𝜇𝑖)(𝑗 − 𝜇𝑗) √(𝜎𝑖2)(𝜎𝑗2) ] 𝑗 𝑖

63 The experiments conducted on the set of images included:

Experiment 1: Classification of multi-temporal GLCM features: The aim of this experiment is to make use of the temporal stability of GLCM texture features in generating multi-temporal time series with the aim of understanding the land cover patterns over the study site for a period of two years. Moreover, three classification schemes are applied. The aim is to identify the best classification scheme from the texture features over a floodplain overlooked by mountainous ranges. Comparative analysis of classification performance of the GLCM images and PCA images. The first three PCA features were selected following (Chamundeeswari et al. 2009) as these components capture the maximum variance in the texture features. The aim is to assess the impact of utilizing PCA features as opposed to all the GLCM texture features in the classification endeavors.

Experiment 2: Water extent assessment: Based on the classification obtained from experiment 1, temporal changes in water extents were assessed. The aim was to identify areas prone to submergence and subsequent loss of crop yield.