2.2. Forest Imagery and Pre-Processing
The analysis of deforestation patterns in Central Carpathians followed three main steps as shown in the flowchart (
Figure 2). The first is related to the Landsat-7 Enhanced Thematic Mapper Plus (Landsat-7 ETM+) image data pre-processing and Geographic Information System Analysis (GIS analysis) for mapping the changes in deforestation patterns (
Table 1), while the second part is the statistical validation (classification accuracy assessment) of them. The last part was based on the
GLCM and fractal analysis of forest area dynamics.
The process starts with the collection of satellite images from 2000–2017 (a spatial resolution of 30 m) from Global Forest Change (GFC) dataset from the Department of Geographical Sciences, University of Maryland (UMD) [
41]. These images were used to extract the deforested areas (annually 2001 to 2017) and, tree cover areas.
The primary data source for our study is the GFC, and the process for obtaining the numerical information followed an entire algorithm.
The first step consisted of downloading the Raster data. Having a different projection (World Geodetic System (WGS) 84-European Petroleum Standards Group (EPSG): 4326) than the other spatial data (Dealul Piscului 1970 (Stereo 70)–European Petroleum Standards Group (EPSG): 31700), used in the study, a projection transformation step followed.
Next, a mask was applied to delineate the study area. To extract the numerical information, the raster image was converted from raster to vector, each pixel being transformed into a point by classes, but keeping all their properties. So, 18 classes were obtained for the deforestation image (class 0—was ignored because it corresponded to the entire surface of the study area—no interesting information, class 1 for deforestation of the year 2001, class 2 for deforestation of the year 2002, till class 17 for deforestation of 2017). From the tree cover image, of the same data source, 100 classes were obtained, each class corresponding to the degree of forest cover in each pixel (class 0 for pixels with 0% tree cover, class 100 to 100% tree cover). In all cases, the spatial dimension (resolution) of each pixel was taken by each point. For the numerical data extracted from the deforestation image, the number of the points for each class was multiplied with the surface of the point/spatial resolution of pixel (24.514 × 24.514 = 600.97 m²), but for the tree cover, the entire surface (600.97 m²) was giving only for pixels/points in class 100 (with 100% of tree cover). For the other classes, the surface decreasing proportionally, until class 0.
In order to have accurate information, and to compare with other economic indicators at a territorial administrative unit level, a spatial join was done. Then, all this information was compiled into Excel tables, which were used to continue the analysis.
2.4. Preprocessing of GFC for GLCM and Fractal Analysis
To perform the GLCM and fractal analysis, it was necessary to go through several processes for making the maps for analysis. The first step was to estimate the tree cover and loss areas for Central Carpathians in grayscale. The second requirement was to export images to the same proportional scale in TIFF format to preserve their properties.
Subsequently, images were transformed into binary images using ImageJ 1.52 [
43] and analysed using a macro for calculating the area and the percentage of forest pixels. The binarization was made by converting foreground pixels (which in turn corresponds to tree cover and loss) of grey and white tones, with intensities between 1 and 255, only in white pixels with the intensity of 255. The black background pixels (non-tree cover and non-loss) with 0 intensity remained the same.
The resolution of the analyzed images was 2716 × 2716 pixels. Pixels representing the tree cover and loss areas are automatically extracted from the GFC dataset on a grey scale. These images were used for Entropy GLCM analysis, but for the and FFI, the same images were binarized, all pixels indicating tree cover and loss becoming white.
GFC dataset provides information about the 2000 tree cover and loss areas for 2001–2017. Using the function Image Calculator operator (from ImageJ) the cumulative loss and tree cover data were obtained. Cumulative loss (the summed values for each year) was obtained using the Add function in Image Calculator. i.e., Cumulative loss for 2017 was obtained by adding the loss of each year from 2001 to 2017. The tree cover for the years 2001–2017 was obtained by using the Difference function in the Image Calculator. i.e., Tree cover 2017 was obtained by using difference between Tree cover 2000 and Cumulative loss 2017.
2.5. GLCM and Fractal Analysis
GLCM analysis, also known as the grey-level spatial dependence matrix, is a statistical method of examining texture that considers the spatial relationship of pixels. The GLCM functions characterise the composition of an image by calculating how often pairs of the pixel of specific values and in a specified spatial relationship occur in an image, creating a GLCM, and then extracting statistical measures from this matrix. They provide information about shape, i.e., the spatial relationships of pixels in an image. The GLCM measures how often a pixel of grey-level 8-bits images (grayscale intensity or tone) value i occurs either horizontally, vertically, or diagonally to adjacent pixels with the value j.
To determine the Entropy, a significant method for non-texturally uniform images and for small values of elements, a GLCM analysis was used.
Complex textures tend to have high entropy values. The entropy is measured according to Equation (1) [
44].
where
p(
i,
j) are co-occurrence probabilities and
i and
j are coordinates of the co-occurrence matrix.
Entropy measures the degree of disorder inside patches of tree cover and loss based on the relationship between pixels with different degrees of forest coverage. Complex texture tends to have high entropy values. The entropy expresses the degree of disturbance of the tree cover canopy of the forest, and it is in strong relation with the degree of fragmentation expressed by FFI. GLCM Entropy is complemented by FFI and , two binary analyzes, where all foreground pixels become white, measure the degree of fragmentation of the patches, some relative to each other.
For the analysis of fractal indices as
FFI and
, were used FFI plugin [
45] and Frac2D plugin [
46] in the IQM 3.5 software [
47].
These indices are relevant because they quantify the spatial pattern of tree cover and loss areas by analysing the degree of fragmentation (FFI), and heterogeneity (). It is expected that as the loss increases, fragmentation and heterogeneity of forests will increase and at the same time a process of homogenization and compacting of cumulative losses will occur.
Fractal fragmentation is very useful in estimating fragmentation or compaction of fractal and natural objects that do not follow the classical geometry.
FFI is calculated according to the Equation (2) and can be interpreted as a compaction index [
40]:
where
is the box-counting fractal dimension of the summed-up areas;
is the box-counting fractal dimension of the summed-up perimeters;
ε is the side length of the box;
N(
ε) is the number of contiguous and non-overlapping boxes required to cover the area of the object; and
N’(
ε) is the number of contiguous and non-overlapping boxes required to cover just the perimeter of the object [
48,
49].
The tree cover patches and loss are very small and highly fragmented and appear as point-like objects in the image; the degree of fragmentation is maximum,
FFI = 0, according to Equation (2), in the situation where
=
. As the analyzed areas are more compact, the
FFI value will increase to 1, and as they are more fragmented, irregular, the
FFI will be closer to 0. The maximum compaction, when the areas are perfectly geometric, have an
FFI = 1. However, self-similar objects, such as forests, with an identical fractal dimension may differ significantly in their textural appearance [
50,
51]. Therefore, the use of fractal fragmentation only is not useful for discriminating against objects, while the fractal fragmentation dimension quantifies the way space is occupied, and the lacunarity completes the fractal dimension with its ability to quantify how space is filled. Moreover, lacunarity discriminates the spatial distribution of gaps in texture at multiple scales, and is not sensitive to the edges of the images. In this paper, the Tug-of-War algorithm lacunarity [
46] was calculated based on the equation:
with
is the number of boxes,
is the second moment for each width as the median of
values, each is the mean of
squares of the counter values.
and
are two random variables for each width that indicate the accuracy and confidence.
Finally, , where p(r,i) is the number of occupied sites in the i-th box. The values are directly influenced by the heterogeneity of the spatial distribution of tree cover and loss areas. So, the indicates the size of deforestation when gaps are more unevenly distributed.