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| - | ====== GeoDMA Features ====== | + | ====== GeoDMA 0.2 Features ====== |
| GeoDMA has metrics integrating Polygons, Cells, and Images. Through image segmentation, GeoDMA creates Polygons. | GeoDMA has metrics integrating Polygons, Cells, and Images. Through image segmentation, GeoDMA creates Polygons. | ||
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| * Segmentation-based **spatial** features | * Segmentation-based **spatial** features | ||
| * Landscape-based features | * Landscape-based features | ||
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| ===== Segmentation-based spectral features ===== | ===== Segmentation-based spectral features ===== | ||
| - | All spectral metrics are calculated inside a polygon, when _X = p_, or inside a cell, when _X = C_ The spectral channel is defined by _B_. | + | All spectral metrics are calculated inside a polygon, when $X = p$, or inside a cell, when $X = C$ The spectral channel is defined by $B$. |
| Some of the following equations describe features based on the Gray-Level Cooccurrence Matrix - GLCM. The term $p_{ij}$ is the normalized frequency in which two neighboring cells separated by a fixed shift occur on the image, one with gray tone $i$ and the other with gray tone $j$. The constant $D$ is the dimension of the GLCM, which has the same gray value range of the original image. | Some of the following equations describe features based on the Gray-Level Cooccurrence Matrix - GLCM. The term $p_{ij}$ is the normalized frequency in which two neighboring cells separated by a fixed shift occur on the image, one with gray tone $i$ and the other with gray tone $j$. The constant $D$ is the dimension of the GLCM, which has the same gray value range of the original image. | ||
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| | rX_entropy_B | Measures the disorder in an image. When the image is not uniform, many GLCM elements have small values, resulting in large entropy. | $-\sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} p_{ij} . \log{p_{ij}}$ | $\geq 0$ | - | | | rX_entropy_B | Measures the disorder in an image. When the image is not uniform, many GLCM elements have small values, resulting in large entropy. | $-\sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} p_{ij} . \log{p_{ij}}$ | $\geq 0$ | - | | ||
| | rX_homogeneity_B | Assumes higher values for smaller differences in the GLCM. | $\sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} \frac{p_{ij}}{1 + (i - j)^2}$ | $\geq 0$ | - | | | rX_homogeneity_B | Assumes higher values for smaller differences in the GLCM. | $\sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} \frac{p_{ij}}{1 + (i - j)^2}$ | $\geq 0$ | - | | ||
| - | | rX_mean_B | Returns the average value for all $N$ pixels inside the object. | $ \frac{\sum_{i=1}^N px_i} | {N}$ | $\geq 0$ | $px$ | | + | | rX_mean_B | Returns the average value for all $N$ pixels inside the object. | $ \frac{\sum_{i=1}^N px_i}{N}$ | $\geq 0$ | $px$ | |
| | rX_mode_B | Returns the most occurring value (mode) for all $N$ pixels inside the object. When the object is multimodal, the first value is assumed. | | $\geq 0$ | $px$ | | | rX_mode_B | Returns the most occurring value (mode) for all $N$ pixels inside the object. When the object is multimodal, the first value is assumed. | | $\geq 0$ | $px$ | | ||
| | rX_std_B | Returns the standard deviation of all $N$ pixels ($\mu$ is the mean value). | $\sqrt{\frac{1}{N-1}\sum_{i=1}^N \left(px_i - \mu \right)^2}$ | $\geq 0$ | $px$ | | | rX_std_B | Returns the standard deviation of all $N$ pixels ($\mu$ is the mean value). | $\sqrt{\frac{1}{N-1}\sum_{i=1}^N \left(px_i - \mu \right)^2}$ | $\geq 0$ | $px$ | | ||
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| | p_rectangular_fit | This feature fits a minimum rectangle outside the object and calculates the ratio between its area and the area of this rectangle. The closer to $1$ is this feature, the most similar to a rectangle. | | $\left[0, 1\right]$ | - | | | p_rectangular_fit | This feature fits a minimum rectangle outside the object and calculates the ratio between its area and the area of this rectangle. The closer to $1$ is this feature, the most similar to a rectangle. | | $\left[0, 1\right]$ | - | | ||
| | p_width | It is the width of the object's bounding box. | | $\geq 0$ | $px$ | | | p_width | It is the width of the object's bounding box. | | $\geq 0$ | $px$ | | ||
| + | |||
| ===== Landscape-based features ===== | ===== Landscape-based features ===== | ||
| - | When the unit is hectares, the value is divided by <math>10^4</math>. | + | When the unit is hectares, the value is divided by $10^4$. Please note that most of the following features are based on [[http://www.umass.edu/landeco/research/fragstats|Fragstats software]]. |
| - | + | ||
| - | Name Description Formula Range Units | + | |
| - | + | ||
| - | c_ca | + | |
| - | Class Area means the sum of areas of a cell. | + | |
| - | <math>\sum_{j=1}^n a_j</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | <math>ha</math> | + | |
| - | + | ||
| - | c_percentland | + | |
| - | <math>\%Land</math> equals the sum of the areas (<math>m^2</math>) of all patches of the corresponding patch type, divided by total landscape area (<math>m^2</math>). <math>\%Land</math> equals the percentage the landscape comprised of the corresponding patch type. | + | |
| - | <math>\frac{\sum_{j=1}^n a_j}{A} \times 100</math> | + | |
| - | <math>\left[0, 100\right]</math> | + | |
| - | <math>\%</math> | + | |
| - | + | ||
| - | c_pd | + | |
| - | Patch Density equals the number of patches of the corresponding patch type divided by total landscape area. | + | |
| - | <math>\frac{n}{A}</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | Patches | + | |
| - | + | ||
| - | c_mps | + | |
| - | Mean Patch Size equals the sum of the areas (<math>m^2</math>) of all patches of the corresponding patch type, divided by the number of patches of the same type. | + | |
| - | <math>\frac{\sum_{j=1}^n a_j}{n} 10^{-4}</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | <math>ha</math> | + | |
| - | + | ||
| - | c_pssd | + | |
| - | Patch Size Std is the root mean squared error (deviation from the mean) in patch size. This is the population standard deviation, not the sample standard deviation. | + | |
| - | <math>\sqrt{\frac{\sum_{j=1}^n \left(a_j - MPS \right)^2}{n}} 10^{-4}</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | <math>ha</math> | + | |
| - | + | ||
| - | c_lsi | + | |
| - | Landscape Shape Index equals the sum of the landscape boundary and all edge segments (<math>m</math>) within the boundary. This sum involves the corresponding patch type (including borders), divided by the square root of the total landscape area (<math>m^2</math>). | + | |
| - | <math>\frac{\sum_{j=1}^n e_j}{2\sqrt{\pi \times A}}</math> | + | |
| - | <math>\geq 1</math> | + | |
| - | \- | + | |
| - | + | ||
| - | c_msi | + | |
| - | Mean Shape Index equals the sum of the patch perimeter (<math>m</math>) divided by the square root of patch area (<math>m^2</math>) for each patch of the corresponding patch type. | + | |
| - | <math>\frac{\sum_{j=1}^n \frac{j}{2\sqrt{\pi \times a_j}}}{n}</math> | + | |
| - | <math>\geq 1</math> | + | |
| - | \- | + | |
| - | + | ||
| - | c_awmsi | + | |
| - | Area-Weighted MSI equals the sum, across all patches of the corresponding patch type, of each patch perimeter (<math>m</math>) divided by the square root of patch area (<math>m^2</math>). | + | |
| - | <math>\sum_{j=1}^n \left[ \frac{j}{2 \sqrt{\pi \times a_j}} \times \frac{a_j}{\sum_{j=1}^n a_j} \right]</math> | + | |
| - | <math>\geq 1</math> | + | |
| - | \- | + | |
| - | + | ||
| - | c_mpfd | + | |
| - | \- | + | |
| - | + | ||
| - | c_awmpfd | + | |
| - | \- | + | |
| - | + | ||
| - | c_ed | + | |
| - | Edge Density equals the sum of the lengths (<math>m</math>) of all edge segments involving the corresponding patch type, divided by the total landscape area (<math>m^2</math>). | + | |
| - | <math>\frac{\sum_{j=1}^m e_j}{A} 10^{-4}</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | <math>m/ha</math> | + | |
| - | + | ||
| - | c_mpar | + | |
| - | Mean Perimeter Area Ratio equals the sum of ratios between perimeters and areas, divided by the number of patches of the same type. | + | |
| - | <math>\frac{ \sum_{j=1}^n \frac{j}{a_j}}{n}</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | <math>m^{-1}</math> | + | |
| - | + | ||
| - | c_pscov | + | |
| - | Patch Size Coefficient of Variation calculates the ratio between the features _c_pssd_ and _c_mps_. | + | |
| - | <math>\frac{PSSD}{MPS} \times 100</math> | + | |
| - | <math>\geq 0</math> | + | |
| - | \- | + | |
| - | + | ||
| - | c_np | + | |
| - | \- | + | |
| - | + | ||
| - | c_te | + | |
| - | \- | + | |
| - | + | ||
| - | c_iji | + | |
| - | \- | + | |
| + | | Name | Description | Formula | Range | Units | | ||
| + | | c_ca | Class Area means the sum of areas of a cell. | $\sum_{j=1}^n a_j$ | $\geq 0$ | $ha$ | | ||
| + | | c_percentland | $\%Land$ equals the sum of the areas ($m^2$) of all patches of the corresponding patch type, divided by total landscape area ($m^2$). $\%Land$ equals the percentage the landscape comprised of the corresponding patch type. | $\frac{\sum_{j=1}^n a_j}{A} \times 100$ | $\left[0, 100\right]$ | $\%$ | | ||
| + | | c_pd | Patch Density equals the number of patches of the corresponding patch type divided by total landscape area. | $\frac{n}{A}$ | $\geq 0$ | Patches | | ||
| + | | c_mps | Mean Patch Size equals the sum of the areas ($m^2$) of all patches of the corresponding patch type, divided by the number of patches of the same type. | $\frac{\sum_{j=1}^n a_j}{n} 10^{-4}$ | $\geq 0$| $ha$ | | ||
| + | | c_pssd | Patch Size Std is the root mean squared error (deviation from the mean) in patch size. This is the population standard deviation, not the sample standard deviation. | $\sqrt{\frac{\sum_{j=1}^n \left(a_j - MPS \right)^2}{n}} 10^{-4}$ | $\geq 0$| $ha$ | | ||
| + | | c_lsi | Landscape Shape Index equals the sum of the landscape boundary and all edge segments ($m$) within the boundary. This sum involves the corresponding patch type (including borders), divided by the square root of the total landscape area ($m^2$). | $\frac{\sum_{j=1}^n e_j}{2\sqrt{\pi \times A}}$| $\geq 1$| - | | ||
| + | | c_msi | Mean Shape Index equals the sum of the patch perimeter ($m$) divided by the square root of patch area ($m^2$) for each patch of the corresponding patch type. | $\frac{\sum_{j=1}^n \frac{j}{2\sqrt{\pi \times a_j}}}{n}$| $\geq 1$| - | | ||
| + | | c_awmsi | Area-Weighted MSI equals the sum, across all patches of the corresponding patch type, of each patch perimeter ($m$) divided by the square root of patch area ($m^2$). | $\sum_{j=1}^n \left[ \frac{j}{2 \sqrt{\pi \times a_j}} \times \frac{a_j}{\sum_{j=1}^n a_j} \right]$| $\geq 1$| - | | ||
| + | | c_mpfd | MPFD stands for the Mean Patch Fractal Dimension. | | | | | ||
| + | | c_awmpfd| AWMPFD stands for Area-weighted Mean Patch Fractal Dimension. | | | | | ||
| + | | c_ed | Edge Density equals the sum of the lengths ($m$) of all edge segments involving the corresponding patch type, divided by the total landscape area ($m^2$). | $\frac{\sum_{j=1}^m e_j}{A} 10^{-4}$| $\geq 0$| $m/ha$ | | ||
| + | | c_mpar | Mean Perimeter Area Ratio equals the sum of ratios between perimeters and areas, divided by the number of patches of the same type. | $\frac{ \sum_{j=1}^n \frac{j}{a_j}}{n}$| $\geq 0$| $m^{-1}$ | | ||
| + | | c_pscov | Patch Size Coefficient of Variation calculates the ratio between the features _c_pssd_ and _c_mps_. | $\frac{PSSD}{MPS} \times 100$| $\geq 0$| - | | ||
| + | | c_np | NP equals the number of patches inside a particular landsacape. | $n$ | $\geq 0$ | - | | ||
| + | | c_te | TE equals the total size of the edge. | $\sum_{j=0}^n e_j$| $\geq 0$ | $ha$ | | ||
| + | | c_iji | IJI stands for Interspersion and Juxtaposition Index. The observed interspersion over the maximum possible interspersion for the given number of patch types. | $\frac{-\sum_{j=1}^n e_j \ln(e_j)}{\ln(n - 1)}$ | $[0, 100]$ | $\%$ | | ||
