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geodma_2:features [2017/02/15 17:49] raian [Landscape-based features] |
geodma_2:features [2021/08/27 19:14] (current) tkorting [Segmentation-based spatial features] |
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| - | ====== GeoDMA 2.0 Features ====== | + | ====== GeoDMA 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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| | Name | Description | Formula | Range | Units | | | Name | Description | Formula | Range | Units | | ||
| - | | AMPLITUDE_BAND | Defines the amplitude of the pixels inside the object. The amplitude means the maximum pixel value minus the minimum pixel value. | $amp = px_{max} - px_{min}$ | $\geq 0$ | $px$ | | + | | AMPL_BAND | Amplitude defines the amplitude of the pixels inside the object. The amplitude means the maximum pixel value minus the minimum pixel value. | $amp = px_{max} - px_{min}$ | $\geq 0$ | $px$ | |
| - | | BAND_RATIO_BAND | Describes the contribution of the given band to the region. | $bandRatio = \frac{\mu_{B_i}}{\sum_{j = 1}^{NB} \mu_{B_j}}$ | $\geq 0$ | $px$ | | + | | BRATIO_BAND | Band Ratio describes the contribution of the given band to the region. | $bandRatio = \frac{\mu_{B_i}}{\sum_{j = 1}^{NB} \mu_{B_j}}$ | $\geq 0$ | $px$ | |
| - | | COUNT_BAND | Defines the total number of pixels inside the object, including pixels with dummy values. | $N_{tot} = cout(X)$ | $\geq 0$ | $N$ | | + | | COUNT_BAND | Count defines the total number of pixels inside the object, including pixels with dummy values. | $N_{tot} = cout(X)$ | $\geq 0$ | $N$ | |
| - | | CONTRAST_SE_BAND | Returns a measure of the intensity contrast between a pixel and its southeast neighbor over the object. Contrast is 0 for a constant object. It is also known as //Sum of Squares Variance// | $Contrast = \sum_{i=0}^{D-1}\sum_{j=0}^{D-1}p_{i,j} . |i - j|^2$ | $[0, (size(GLCM, 1)-1)^2]$ | - | | + | | CONTSE_BAND | Contrast SE returns a measure of the intensity contrast between a pixel and its southeast neighbor over the object. Contrast is 0 for a constant object. It is also known as //Sum of Squares Variance// | $Contrast = \sum_{i=0}^{D-1}\sum_{j=0}^{D-1}p_{i,j} . |i - j|^2$ | $[0, (size(GLCM, 1)-1)^2]$ | - | |
| - | | DISSIMILARITY_SE_BAND | Measures how different the elements of the GLCM are from each other and it is high when the local region has a high contrast. | $dissimilarity = \sum_{i=0}^{D-1}\sum_{j=0}^{D-1}p_{i,j}|i-j|$ | $\geq 0$ | - | | + | | DISSE_BAND | Dissimilarity SE measures how different the elements of the GLCM are from each other and it is high when the local region has a high contrast. | $dissimilarity = \sum_{i=0}^{D-1}\sum_{j=0}^{D-1}p_{i,j}|i-j|$ | $\geq 0$ | - | |
| - | | ENERGY_SE_BAND | It returns the squared root of Angular Second Moment, computed by the sum of the squared elements in GLCM. Energy is 1 for a constant image. | $energy = \sum_{i=0}^{D-1} \sum{j=0}^{D-1} p_{i,j}^2}$ | $[0,1]$ | - | | + | | ENERGSE_BAND | Energy SE returns the squared root of Angular Second Moment, computed by the sum of the squared elements in GLCM. Energy is 1 for a constant image. | $energy = \sum_{i=0}^{D-1} \sum{j=0}^{D-1} p_{i,j}^2}$ | $[0,1]$ | - | |
| - | | ENTROPY_SE_BAND | Measures the disorder in an image. When the image is not uniform, many GLCM elements have small values, resulting in large entropy. | $entropy = -\sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} p_{ij} . \log{p_{ij}}$ | $\geq 0$ | - | | + | | ENTRSE_BAND | Entropy SE measures the disorder in an image. When the image is not uniform, many GLCM elements have small values, resulting in large entropy. | $entropy = -\sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} p_{ij} . \log{p_{ij}}$ | $\geq 0$ | - | |
| - | | HOMOGENEITY_SE_BAND | Assumes higher values for smaller differences in the GLCM. Also called //Inverse Difference Moment//. Homogeneity is 1 for a diagonal GLCM. | $homog = \sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} \frac{p_{ij}}{1 + (i - j)^2}$ | $\geq 0$ | - | | + | | HOMOGSE_BAND | Homogeneity SE assumes higher values for smaller differences in the GLCM. Also called //Inverse Difference Moment//. Homogeneity is 1 for a diagonal GLCM. | $homog = \sum_{i=1}^{D - 1} \sum_{j=1}^{D - 1} \frac{p_{ij}}{1 + (i - j)^2}$ | $\geq 0$ | - | |
| - | | KURTOSIS_BAND | Returns the kurtosis value for all the valid pixels (not dummy) inside the object. | $K = \frac{n(n+1)(n-1)}{(n-2)(n-3)} . \frac{\sum_{i=1}^{N}(px_i-\mu)^4}{(\sum_{i=1}^N (px_i - \mu)^2)^2$ | $\geq 1$ | - | | + | | KURT_BAND | Kurtosis returns the kurtosis value for all the valid pixels (not dummy) inside the object. | $K = \frac{n(n+1)(n-1)}{(n-2)(n-3)} . \frac{\sum_{i=1}^{N}(px_i-\mu)^4}{(\sum_{i=1}^N (px_i - \mu)^2)^2$ | $\geq 1$ | - | |
| - | | MAXIMUM_VAL_BAND | Computes the maximum gray level value (not dummy) inside the object. | $maxVal = max(X)$ | $X$ | $px$ | | + | | MAX_VAL_BAND | Maximum Value computes the maximum gray level value (not dummy) inside the object. | $maxVal = max(X)$ | $X$ | $px$ | |
| - | | MEAN_BAND | Computes the average value for all $N$ pixels inside the object. | $\mu = \frac{\sum_{i=1}^N px_i}{N}$ | $\geq 0$ | $px$ | | + | | MEAN_BAND | Mean computes the average value for all $N$ pixels inside the object. | $\mu = \frac{\sum_{i=1}^N px_i}{N}$ | $\geq 0$ | $px$ | |
| - | | MEDIAN_BAND | Computes the median for all $N$ pixels inside the object. | $median = p_{\frac{(n+1)}{2}}$ | $X$ | $px$ | | + | | MEDIAN_BAND | Median computes the median for all $N$ pixels inside the object. | $median = p_{\frac{(n+1)}{2}}$ | $X$ | $px$ | |
| - | | MINIMUM_VAL_BAND | Computes the minimum gray level value (not dummy) inside the object. | $minVal = min(X)$ | $X$ | $px$ | | + | | MIN_VAL_BAND | Minimum Value computes the minimum gray level value (not dummy) inside the object. | $minVal = min(X)$ | $X$ | $px$ | |
| - | | MODE_BAND | Returns the most occurring gray level value (mode) for all $N$ (not dummy) pixels inside the object. When the object is multimodal, the first value is assumed. | | $X$ | $px$ | | + | | MODE_BAND | Mode returns the most occurring gray level value (mode) for all $N$ (not dummy) pixels inside the object. When the object is multimodal, the first value is assumed. | | $X$ | $px$ | |
| - | | NUM_MODES_BAND | Returns the number of modes for the object. | | $\geq 1$ | $px$ | | + | | N_MOD_BAND | Num Modes returns the number of modes for the object. | | $\geq 1$ | $px$ | |
| - | | SKEWNESS_BAND | Returns the skewness value for all the valid pixels (not dummy) inside the object. | $S = \frac{n\sqrt{n-1}}{n-2} . \frac{\sum_{i=1}^{N}(px_i-\mu)^3}{(\sum_{i=1}^N (px_i - \mu)^2)^\frac{3}{2}$ | - | - | | + | | SKEW_BAND | Returns the Skewness value for all the valid pixels (not dummy) inside the object. | $S = \frac{n\sqrt{n-1}}{n-2} . \frac{\sum_{i=1}^{N}(px_i-\mu)^3}{(\sum_{i=1}^N (px_i - \mu)^2)^\frac{3}{2}$ | - | - | |
| - | | STD_DEVIATION_BAND | Returns the standard deviation of all $N$ (not dummy) pixels ($\mu$ is the mean value) inside the object. | $\sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^N \left(px_i - \mu \right)^2}$ | $\geq 0$ | $px$ | | + | | STDDEV_BAND | Returns the Standard Deviation of all $N$ (not dummy) pixels ($\mu$ is the mean value) inside the object. | $\sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^N \left(px_i - \mu \right)^2}$ | $\geq 0$ | $px$ | |
| - | | SUM_BAND | Returns the sum of all $N$ (not dummy) pixels inside the object. | $sum = \sum_{i = 1}^{N}px_i$ | $\geq 0$ | $px$ | | + | | SUM_BAND | Returns the Sum of all $N$ (not dummy) pixels inside the object. | $sum = \sum_{i = 1}^{N}px_i$ | $\geq 0$ | $px$ | |
| - | | VALID_COUNT_BAND | Defines the total number of pixels inside the object with not dummy values. | $N = count(X)$ | $\geq 0$ | $N$ | | + | | VLDCNT_BAND | Valid Count defines the total number of pixels inside the object with not dummy values. | $N = count(X)$ | $\geq 0$ | $N$ | |
| - | | VAR_COEFF_BAND | Returns the coefficient of variation of the values for all the valid pixels (not dummy) inside the object | $c_v = \frac{100\sigma}{\mu}$ | $[0,100]$ | % | | + | | VARCOEF_BAND | Returns the Coefficient of Variation of the values for all the valid pixels (not dummy) inside the object | $c_v = \frac{100\sigma}{\mu}$ | $[0,100]$ | % | |
| - | | VARIANCE_BAND | Returns the variance of all $N$ (not dummy) pixels ($\mu$ is the mean value) inside the object. | $s^2 = \frac{\sum_{i=1}^N \left(px_i - \mu \right)^2}{N-1}$ | $\geq 0$ | $px$ | | + | | VAR_BAND | Returns the Variance of all $N$ (not dummy) pixels ($\mu$ is the mean value) inside the object. | $s^2 = \frac{\sum_{i=1}^N \left(px_i - \mu \right)^2}{N-1}$ | $\geq 0$ | $px$ | |
| ===== Segmentation-based spatial features ===== | ===== Segmentation-based spatial features ===== | ||
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| | POL_ANGLE | Represents the main angle of an object. It is obtained by computing the minimum circumscribing ellipse, and the angle of the biggest radius of the ellipse suits to the object's angle. | | $\left[-\pi, \pi]$ | $rad$ | | | POL_ANGLE | Represents the main angle of an object. It is obtained by computing the minimum circumscribing ellipse, and the angle of the biggest radius of the ellipse suits to the object's angle. | | $\left[-\pi, \pi]$ | $rad$ | | ||
| | POL_AREA | Returns the area of the object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]^2$ | | | POL_AREA | Returns the area of the object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]^2$ | | ||
| - | | POL_BBOX_AREA | Returns the bounding box area of an object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]^2$ | | + | | PBOX_AREA | Returns the bounding box area of an object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]^2$ | |
| - | | POL_BBOX_PERIM | Returns the perimeter of the bounding box of an object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]$ | | + | | PBOX_PERIM | Returns the perimeter of the bounding box of an object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]$ | |
| - | | POL_CIRCLE| Relates the areas of the object and the smallest circumscribing circle around the object. In the equation, $R$ is the maximum distance between the centroid and all vertices. | $1 - \frac{\textit{area}}{\pi R^2}$ | $[0, 1)$ | $[m,degrees,...]^2$ | | + | | PCIRCLE| Relates the areas of the object and the smallest circumscribing circle around the object. In the equation, $R$ is the maximum distance between the centroid and all vertices. | $1 - \frac{\textit{area}}{\pi R^2}$ | $[0, 1)$ | $[m,degrees,...]^2$ | |
| - | | POL_ELLIPTIC_FIT| Finds the minimum circumscribing ellipse to the object and returns the ratio between the object's area and the ellipse area. | | $\left[0, 1\right]$ | - | | + | | PELLIP_FIT| Finds the minimum circumscribing ellipse to the object and returns the ratio between the object's area and the ellipse area. | | $\left[0, 1\right]$ | - | |
| - | | POL_FRACTALDIM | Returns the fractal dimension of an object. | $2 \frac{\log {\frac{\textit{perimeter}}{4}} }{\log area}$ | $[1, 2]$ | - | | + | | P_FRACDIM | Returns the fractal dimension of an object. | $2 \frac{\log {\frac{\textit{perimeter}}{4}} }{\log area}$ | $[1, 2]$ | - | |
| - | | POL_GYRATION_RATIUS | This feature is equals the average distance between each vertex of the polygon and it's centroid. The more similar to a circle is the object, the more likely the centroid will be inside it, and therefore this feature will be closer to 0. | $\frac{\sum{\sqrt{(x_i - x_C)^2 + (x_i - x_C)^2}}}{N}$ | $\geq 0$ | $[m, degrees, ...]$ | | + | | PGYRATIUS | This feature is equals the average distance between each vertex of the polygon and it's centroid. The more similar to a circle is the object, the more likely the centroid will be inside it, and therefore this feature will be closer to 0. | $\frac{\sum{\sqrt{(x_i - x_C)^2 + (x_i - x_C)^2}}}{N}$ | $\geq 0$ | $[m, degrees, ...]$ | |
| - | | POL_BBOX_LENGTH | It is the height of the object's bounding box, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m, degrees, ...]$ | | + | | POLRADIUS | Returns the polygon radius. It corresponds to the maximum distance between the polygon centroid its vertexes. | $R$ | $>0$ | - | |
| - | | POL_PERIMETER | Returns the perimeter of the object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]$ | | + | | PBOX_LEN | It is the height of the object's bounding box, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m, degrees, ...]$ | |
| - | | POL_PERIM_AREA_RATIO | Calculates the ratio between the perimeter and the area of an object. | $\frac{\textit{perimeter}}{\textit{area}}$ | $\geq 0$ | $px^{-1}$ | | + | | P_PERIM | Returns the perimeter of the object, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m,degrees,...]$ | |
| - | | POL_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. | $\frac{\textit{area}}{\textit{minBoxArea}}$ | $\left[0, 1\right]$ | - | | + | | P_PERARAT | Calculates the ratio between the perimeter and the area of an object. | $\frac{\textit{perimeter}}{\textit{area}}$ | $\geq 0$ | $px^{-1}$ | |
| - | | POL_BBOX_WIDTH | Returns the width of the object's bounding box, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m, degrees, ...]$ | | + | | PRECTFIT | 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. | $\frac{\textit{area}}{\textit{minBoxArea}}$ | $\left[0, 1\right]$ | - | |
| - | | POL_COMPACITY | Returns the compacity of the object. | $\frac{\textit{perimAreaRatio}}{\sqrt{\textit{area}}}}$ | $\geq 0$ | - | | + | | PBOX_WIDTH | Returns the width of the object's bounding box, measured in the unit of measure of the current Spatial Reference System. | | $\geq 0$ | $[m, degrees, ...]$ | |
| - | | POL_DENSITY | This feature corresponds to the ratio between the polygon area and the polygon radius. | $\frac{\textit{area}}{\textit{radius}}$ | $\geq 0$ | - | | + | | P_COMPAC | Returns the compacity of the object. | $\frac{\textit{perimAreaRatio}}{\sqrt{\textit{area}}}}$ | $\geq 0$ | - | |
| - | | POL_SHAPE_INDEX | This feature corresponds to the ratio between the polygon perimeter and the squared root of the polygon area. | $\frac{\textit{perimeter}}{4 * \sqrt{\textit{area}}}$ | $\geq 0$ | - | | + | | PDENSITY | This feature corresponds to the ratio between the polygon area and the polygon radius. | $\frac{\textit{area}}{\textit{radius}}$ | $\geq 0$ | - | |
| + | | PSHAPEIDX | This feature corresponds to the ratio between the polygon perimeter and the squared root of the polygon area. | $\frac{\textit{perimeter}}{4 * \sqrt{\textit{area}}}$ | $\geq 0$ | - | | ||
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| | c_MSI | MSI stands for Mean Shape Index, which is equals the sum of the patch perimeter ($m$) by divided two times the square root of patch area ($m^2$) multiplied by pi ($\pi$) for each patch of the corresponding patch type, divided by the the number of patches of the same patch type (class). | $MSI = \frac{\sum_{j=1}^n \frac{p_j}{2 \times \sqrt{\pi \times a_j}}}{n}$| $\geq 1$| - | | | c_MSI | MSI stands for Mean Shape Index, which is equals the sum of the patch perimeter ($m$) by divided two times the square root of patch area ($m^2$) multiplied by pi ($\pi$) for each patch of the corresponding patch type, divided by the the number of patches of the same patch type (class). | $MSI = \frac{\sum_{j=1}^n \frac{p_j}{2 \times \sqrt{\pi \times a_j}}}{n}$| $\geq 1$| - | | ||
| | c_AWMSI | AWMSI stands for Area-Weighted MSI, which is 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 two times the square root of the total landscape area ($m^2$) multiplied by pi ($\pi$). This first term is multiplied by the area of the corresponding patch, divided by the sum of the areas of all patches of the same patch type (class).| $AWMSI = \sum_{j=1}^n \left[ \frac{p_j}{2 \sqrt{\pi \times a_j}} \times \frac{a_j}{\sum_{j=1}^n a_j} \right]$| $\geq 1$| - | | | c_AWMSI | AWMSI stands for Area-Weighted MSI, which is 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 two times the square root of the total landscape area ($m^2$) multiplied by pi ($\pi$). This first term is multiplied by the area of the corresponding patch, divided by the sum of the areas of all patches of the same patch type (class).| $AWMSI = \sum_{j=1}^n \left[ \frac{p_j}{2 \sqrt{\pi \times a_j}} \times \frac{a_j}{\sum_{j=1}^n a_j} \right]$| $\geq 1$| - | | ||
| - | | c_MPFD | MPFD stands for the Mean Patch Fractal Dimension. | $MPFD = \frac{\sum_{j=1}^{n} \frac{2 \times \ln{p_j}}{\ln{a_j}}}{N}$ | | | | + | | c_MPFD | MPFD stands for the Mean Patch Fractal Dimension. | $MPFD = \frac{\sum_{j=1}^{n} \frac{2 \times \ln{p_j}}{\ln{a_j}}}{n}$ | | | |
| - | | c_AWMPFD| AWMPFD stands for Area-weighted Mean Patch Fractal Dimension. | $AWMPFD = \sum_{j = 1}^{n} [\frac{2 \times \ln{p_j}}{\ln{a_j}} \times \frac{a_j}{\sum_{j = 1}^{n} a_{ij}}}]$ | | | | + | | c_AWMPFD| AWMPFD stands for Area-weighted Mean Patch Fractal Dimension. | $AWMPFD = \sum_{j = 1}^{n} [\frac{2 \times \ln{p_j}}{\ln{a_j}} \times \frac{a_j}{\sum_{j = 1}^{n} a_{ij}}]$ | | | |
| | c_ED | ED stands for Edge Density, which is equals the sum of the lengths ($m$) of all edge segments involving the corresponding patch type, divided by the total landscape area ($m^2$). | $ED = \frac{\sum_{j=1}^m e_j}{A} 10^{4}$| $\geq 0$| $m/ha$ | | | c_ED | ED stands for Edge Density, which is equals the sum of the lengths ($m$) of all edge segments involving the corresponding patch type, divided by the total landscape area ($m^2$). | $ED = \frac{\sum_{j=1}^m e_j}{A} 10^{4}$| $\geq 0$| $m/ha$ | | ||
| | c_MPAR | MPAR stands for Mean Perimeter Area Ratio, which is equals the sum of ratios between perimeters and areas, divided by the number of patches of the same type. | $MPAR = \frac{ \sum_{j=1}^n \frac{p_j}{a_j}}{n}$| $\geq 0$| $m^{-1}$ | | | c_MPAR | MPAR stands for Mean Perimeter Area Ratio, which is equals the sum of ratios between perimeters and areas, divided by the number of patches of the same type. | $MPAR = \frac{ \sum_{j=1}^n \frac{p_j}{a_j}}{n}$| $\geq 0$| $m^{-1}$ | | ||
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| | c_NP | NP stands for Number of Patches, which is equals to the number of patches of a corresponding patch type (class) inside a particular landsacape. | $NP = n$ | $\geq 0$ | - | | | c_NP | NP stands for Number of Patches, which is equals to the number of patches of a corresponding patch type (class) inside a particular landsacape. | $NP = n$ | $\geq 0$ | - | | ||
| | c_TE | TE stands for Total Edges, which is equals the total size of the edges of the all patches of the given patch type (class). | $TE = \sum_{j=0}^n e_j$ | $\geq 0$ | $m$ | | | c_TE | TE stands for Total Edges, which is equals the total size of the edges of the all patches of the given patch type (class). | $TE = \sum_{j=0}^n e_j$ | $\geq 0$ | $m$ | | ||
| - | | c_IJI | IJI stands for Interspersion and Juxtaposition Index. The observed interspersion over the maximum possible interspersion for the given number of patch types. It only exists for $n > 3$. | $IJI = \frac{-\sum_{j=1}^n (\frac{e_j}{\sum_{k=1}^n e_k}) \times \ln{(\frac{e_j}{\sum_{k=1}^n e_k})}}{\ln(n - 1)} \times 100$ | $[0, 100]$ | $\%$ | | + | | c_IJI | IJI stands for Interspersion and Juxtaposition Index. The observed interspersion over the maximum possible interspersion for the given number of patch types. It only exists for $n > 3$. | $IJI = \frac{-\sum_{j=1}^n (\frac{e_j}{\sum_{k=1}^n e_k}) \times \ln{(\frac{e_j}{\sum_{k=1}^n e_k})}}{\ln(m - 1)} \times 100$ | $[0, 100]$ | $\%$ | |
| | c_TABO | TABO stands for the Total Area of the Biggest Object that intersects the landscape. | | | $ha$ | | | c_TABO | TABO stands for the Total Area of the Biggest Object that intersects the landscape. | | | $ha$ | | ||
| - | | PR | PR stands for Patch Richness, which is equals the number of different patch types present within the landscape boundary. | $PR = m$ | $\geq0$ | | | + | | c_BIA | BIA stands for the Biggest Intersection Area. | | | $ha$ | |
| + | | c_TAOBIA | TAOBIA stands for the Total Area of the Object with Biggest Intersection Area. | | | $ha$ | | ||
| + | | PR | PR stands for Patch Richness, which is equals the number of different patch types (classes) present within the landscape boundary. | $PR = m$ | $\geq0$ | | | ||
| | PRD | PRD stands for Patch Richness Density, which is equals the number of different patch types present within the landscape boundary divided by total landscape area ($m^2$), multiplied by $10,000$ and $100$ (to convert to $100$ hectares). Note, total landscape area ($A$) includes any internal background present. | $PRD = \frac{m}{A} \times 10000 \times 100$ | $\geq0$ | $Number/100 ha$ | | | PRD | PRD stands for Patch Richness Density, which is equals the number of different patch types present within the landscape boundary divided by total landscape area ($m^2$), multiplied by $10,000$ and $100$ (to convert to $100$ hectares). Note, total landscape area ($A$) includes any internal background present. | $PRD = \frac{m}{A} \times 10000 \times 100$ | $\geq0$ | $Number/100 ha$ | | ||
| | SHDI | SHDI stands for Shannon's Diversity Index, which is equals to minus the sum, across all patch types, of the proportional abundance of each patch type multiplied by that proportion. Note, $P_i$, which is the proportion of the landscape occupied by patch type (class) $i$, is based on total landscape area ($A$) excluding any internal background present. | $SHDI = -\sum_{i = 0}^{m} P_i \times \ln{P_i}$ | $\geq0$ | | | | SHDI | SHDI stands for Shannon's Diversity Index, which is equals to minus the sum, across all patch types, of the proportional abundance of each patch type multiplied by that proportion. Note, $P_i$, which is the proportion of the landscape occupied by patch type (class) $i$, is based on total landscape area ($A$) excluding any internal background present. | $SHDI = -\sum_{i = 0}^{m} P_i \times \ln{P_i}$ | $\geq0$ | | | ||
