Patch Metrics

Patch metrics are computed for every patch in the landscape; the resulting patch output file contains a row (observation vector) for every patch, where the columns (fields) represent the individual metrics. The first three columns include header information about the patch:

(P1) Landscape ID.--The first field in the patch output file is landscape ID (LID). Landscape ID is set to the name of the input image obtained from the input file (see Run Parameters).

(P2) Patch ID.--The second field in the patch output file is patch ID (PID). If a Patch ID image is specified that contains unique ID's for each patch, FRAGSTATS reads the patch ID from the designated image. If an image is not specified, FRAGSTATS creates unique ID's for each patch and optionally produces an image that contains patch ID's that correspond to the FRAGSTATS output.

(P3) Patch Type.--The third field in the patch output file is patch type (TYPE). FRAGSTATS contains an option to name an ASCII file (class properties file) that contains character descriptors for each patch type. If the class properties option is not used, FRAGSTATS will write the numeric patch type codes to TYPE.

There are two basic types of metrics at the patch level: (1) indices of the spatial character and context of individual patches, and (2) measures of the deviation from class and landscape norms; that is, how much the computed value of each metric for a patch deviates from the class and landscape means. The deviation statistics are useful in identifying patches with extreme values on each metric. Because the deviation statistics are computed similarly for all patch metrics, they are described in common below:

Patch Deviation Statistics.--In addition to the standard patch metrics, FRAGSTATS computes several deviation statistics for each patch that measures how much it deviates from the class or landscape norm (i.e., how extreme an observation it is) for each metric. Specifically, for each patch and each patch metric, FRAGSTATS computes the following four measures of deviation:

Standard Deviations from the Class Mean
		x_ij = value of a patch metric for patch ij. _i = mean value of the corresponding patch metric for patch type (class) i. s_i = standard deviation of the corresponding patch metric for patch type (class) i.
Description	CSD equals the value of the metric (x) for the focal patch (ij) minus the mean of the metric across all patches in the focal class, divided by the class standard deviation (population formula).
Units	Same as the metric
Range	-∞ < metric < +∞ Although standard deviation has no theoretical limit, 66.5% of the observations (assuming a normal distribution) will be within +1 standard deviations of the mean, 95% within +2 standard deviations, and 99.7% within +3 standard deviations.
Comments	The number of standard deviations from the class mean is obtained from a z-score transformation of the observed value using the mean and standard deviation derived from all patches in the focal class. This transformation results in a standardized metric that has zero mean and unit variance for the class. Any observation that is, say, more than 2.5 standard deviations from the class mean can be considered an extreme observation. This is a quick and easy way to identify patches with extreme values of a metric. However, it is necessary to assume an underlying normal distribution in order for standard deviations to have a direct interpretation regarding the percent of the distribution greater or smaller than the observed value. CSD can be computed for each patch metric and is reported in the patch output file as the metric name followed by _CSD. For example, the class standard deviation metric for the shape index (SHAPE) would be given the variable name: SHAPE_CSD.

Percentile of the Class Distribution
		x_ij = value of a patch metric for patch ij. n_i = number of patches of the corresponding patch type (class) i.
Description	CPS equals the percentile of the rank-ordered distribution of all patches in the focal class for the corresponding metric (x); that is, the percent of observations in rank order that are smaller than the observed value for the focal patch (ij).
Units	Percent
Range	0 ≤ metric ≤ 100 CPS = 0 if the observed patch metric is the lowest value for any patch in the class. Conversely, CPS = 100 if the observed patch metric is the highest value for any patch in the class.
Comments	The percentile of the class distribution is obtained by rank ordering observations from lowest to highest and computing the percentage of observations smaller than the observed value for the focal patch. In contrast to standard deviation, this deviation statistic makes no assumption about the underlying distribution; it simply quantifies the percent of the observed distribution that is smaller than the observed value for the focal patch under consideration.

Standard Deviations from the Landscape Mean
		x_ij = value of a patch metric for patch ij.  = mean value of the corresponding patch metric across all patches in the landscape. s = standard deviation of the corresponding patch metric for all patches in the landscape.
Description	LSD equals the value of the metric (x) for the focal patch (ij) minus the mean of the metric across all patches in the landscape divided by the landscape standard deviation (population formula).
Units	Same as the metric
Range	-∞ < metric < +∞ Although standard deviation has no theoretical limit, 66.5% of the observations (assuming a normal distribution) will be within +1 standard deviations of the mean, 95% within +2 standard deviations, and 99.7% within +3 standard deviations.
Comments	The number of standard deviations from the landscape mean is obtained from a z-score transformation of the observed value using the mean and standard deviation derived from all patches in the landscape. This transformation results in a standardized metric that has zero mean and unit variance for the entire landscape. Any observation that is, say, more than 2.5 standard deviations from the landscape mean can be considered an extreme observation. This is a quick and easy way to identify patches with extreme values of a metric. However, it is necessary to assume an underlying normal distribution in order for standard deviations to have a direct interpretation regarding the percent of the distribution greater or smaller than the observed value. LSD can be computed for each patch metric and is reported in the patch output file as the metric name followed by a _LSD. For example, the landscape standard deviation metric for the shape index (SHAPE) would be given the variable name: SHAPE_LSD.

Percentile of the Landscape Distribution
		x_ij = value of a patch metric for patch ij. N = number of patches in the landscape.
Description	LPS equals the percentile of the rank ordered distribution of all patches in the landscape for the corresponding metric (x); that is, the percent of observations in rank order that are smaller than the observed value for the focal patch (ij).
Units	Percent
Range	0 ≤ metric ≤ 100 LPS = 0 if the observed patch metric is the lowest value for any patch in the landscape. Conversely, LPS = 100 if the observed patch metric is the highest value for any patch in the landscape.
Comments	The percentile of the landscape distribution is obtained by rank ordering observations from lowest to highest and computing the percentage of observations smaller than the observed value for the focal patch. In contrast to standard deviation, this deviation statistic makes no assumption about the underlying distribution; it simply quantifies the percent of the observed distribution that is smaller than the observed value for the focal patch under consideration.