A reports the area of each class in the image

AI reports the aggregation indices upon an image. It is reported for the image as a whole as well as for each class present in the image.

An AI analysis reports values between zero and one. AI equals 1.0 when a class is completely aggregated into a single square patch. It reports numbers closer to 0.0 when each patch is narrow in one direction and long in another.

Definition: AI = total adjacent edges of class i with itself divided by the maximum possible adjacent edges of class i with itself.

Reference: He H. S., B. E. DeZonia and D. J. Mladenoff. 2000. An aggregation index (AI) to quantify spatial patterns on landscapes. Landscape Ecology 15: 591-601

AM reports the adjacency matrix probabilities between classes. Output values range between 0.00% and 100.00% and represent the proportional breakdown of neighbor cells. An AM value of 40% for class I to class J implies that it is 40% probable that a given cell on an image will be of class I and have class J adjacent to it.

Reference: Li H., and J.F. Reynolds. 1993. A new contagion index to quantify spatial patterns of landscape. Landscape Ecology 3:155-162.

ASM reports the angular second moment of the image. It is a measure of image texture. ASM ranges from 0.0 for an image with many classes and little clumping to 1.0 for an image with a single class (maximum clumping).

Note: This measure is derived from an adjacency matrix. In a paper in 1996 Riitters discusses how the method used to create the adjacency matrix can have a large impact upon resulting metrics. This can explain where IAN may differ from another package on this measure.

Definition: given an adjacency matrix between the classes present ASM = the sum of the squared adjacencies for all combinations of the classes present.

CA reports the core area measures of the image. It is reported for each class present in the image. For a single pixel core area is defined as 1 cell if all of its neighbors are of the same class as the pixel. An 8 neighbor rule is used. The total cell count for each class is then scaled to the correct units.

CO reports the contagion of the image. Contagion is a measure of the degree to which classes are clumped into polygons. It is estimated by determining the image’s departure from maximal diversity. Contagion returns a value greater than or equal to zero. Large values of contagion arise from images that are predominantly made up of a few classes. Small values of contagion arise from images that are made up of many different classes in approximately equal proportions.

Note: This measure is derived from an adjacency matrix. Different methods of computing adjacency exist. If IAN's measure departs from that of another package it may be due to differing methods of calculating adjacency.

Definition: given an adjacency matrix T between classes present contagion = maximum possible diversity - measured diversity. Maximum diversity is 2 * ln(classes present) and measured diversity is the sum of T(i,j) * ln(T(i,j)) for all combinations of classes i and j.

Reference: For more information see Li H., and J.F. Reynolds. 1993. A new contagion index to quantify spatial patterns of landscape. Landscape Ecology 3:155-162."

DO reports the dominance measure of an image. Dominance is a measure of the degree to which an image departs from maximal diversity as defined by Shannon.

DO returns a value greater than or equal to zero. Large values of DO arise from images that are predominantly made up of a few classes. Small values of DO arise from images that are made up of many different classes in approximately equal proportions.

Definition: given a probability distribution p of the classes present, dominance = maximum possible diversity - measured diversity. Maximum diversity is defined as ln(classes present) and measured diversity is defined as -1 times the sum of p(i)*ln(p(i)) for all classes present.

Reference: For more information see Turner M.G. 1990. Spatial and temporal analysis of landscape patterns. Landscape Ecology 1:21-30

ED measures the edge density (edge length per unit area) of the image. It is reported for the image as a whole as well as for each class present in the image. ED is calculated as the total edge length divided by total image area for a given image or class.

EDE reports the edge distribution evenness of the image. It is a measure of how equally distributed are the edge types of an image.

EDE can range from zero for an image with no edge other than border to 1.0 for an image whose edge types (connections between differing classes) are all equally present within the image.

Note: This measure uses an adjacency matrix. [Riitters 96] discusses how the method used to create the adjacency matrix can have a large impact upon resulting metrics.

Definition: (given t, an adjacency matrix between classes present)

First the main diagonal of the adjacency matrix is set to zero and the matrix is rescaled to sum to 1.0. Then:

EDE = measured diversity / maximum diversity

Measured diversity = -1 * the sum of all combinations of classes in the equation t(i,j) * ln(t(i,j). Maximum diversity is defined as 2 * ln (classes present).

Reference: For more information see [Riitters 96] and [Wickham 96]

[Riitters 96] - Riitters, O’Neill, et al. 1996. A note on contagion indices for landscape analysis. Landscape Ecology 11:197-202.

[Wickham 96] - Wickham J.D., K.H. Riitters, R.V. O’Neill, K.B. Jones, and T.G. Wade. 1996. Landscape ‘Contagion’ in Raster and Vector Environments. International Journal of Geographical Information Systems 7:891-89

EL reports the electivity between classes present in the image. The electivity index calculated is equivalent to log Q as specified in the [Jacobs 74] paper (detailed below).

Electivity measures the strength of association between the classes. For the purposes of EL association is measured from the number of times two classes border on each other relative to the maximum coupling possible. EL results range from minus infinity for two classes that never neighbor each other to positive infinity for two classes that always neighbor each other.

Definition: EL = (Rij * (1-Pij)) / (Pij * (1-Rij)) where
Rij = x11 / (x11 + x21) and Pij = x12 / (x12 + x22) and:
x11 = couplings in which I and J participate
x12 = couplings in which I participates and J does not
x21 = couplings in which J participates and I does not
x22 = couplings in which neither I nor J participates

Note: only 4 neighbors are considered for couplings

Reference: For more information regarding this specific electivity index see [Mladenoff 93], [Pastor 90], and [Jacobs 74]. For more information regarding electivity indices in general see [Lechowicz 82]

[Jacobs 74] - Jacobs J. 1974. Quantitative Measurement of Food Selection. Oecologia 14:413-417

[Lechowicz 82] - Lechowicz M.J. 1982. The Sampling Characteristics of Electivity Indices. Oecologia 52:22-30

[Mladenoff 93] - Mladenoff D.J., M.A. White, J. Pastor, and T.R. Crow. 1993. Comparing spatial pattern in unaltered old-growth and disturbed forest landscapes. Ecological Applications 2:294-306

[Pastor 90] - Pastor J., and M. Broschart. 1990. The spatial pattern of a northern conifer-hardwood landscape. Landscape Ecology 1:55-68.

FDB estimates the fractal dimension of the image using the box counting method. It is reported for each class present and for the image as a whole. FDB ranges from 1.0 for images made up of polygons whose outlines are very regular (or straight) to 2.0 for images made of polygons whose outlines are very irregular.

Limitations: For those images whose sample set is too small to accurately estimate fractal dimension IAN reports 0.

Definition: The calculation of FDB is the log-log regression of box size versus number of boxes required to cover the image.

Reference: For more information regarding the implementation of this fractal dimension method and regarding the use of fractal dimension estimates in landscape ecology see [Loehle 90], [Milne 91], and [Sugihara 90]. There are many techniques and much debate as to how to accurately measure fractal dimension. For more information regarding this topic refer to [Russ 94].

[Loehle 90] - Loehle C. 1990. Home range: A fractal approach. Landscape Ecology 1:39-52

[Milne 91] - Milne B.T. 1991. The utility of fractal geometry in landscape design. Landscape and Urban Planning 21:81-90

[Russ 94] - Russ, John C. 1994. Fractal Surfaces. Plenum Press. New York, New York, USA

[Sugihara 90] - Sugihara G., and R.M. May. 1990. Applications of Fractals in Ecology. TREE 3:79-86.

FDP estimates the fractal dimension of the image using the perimeter/area method as described in [Sugihari 90]. It is reported for the image as a whole as well as for each class present in the image. FDP ranges from 1.0 for images made up of polygons whose outlines are very regular (or straight) to 2.0 for images made of patches whose outlines are very irregular.

Definition: The calculation of FDP is twice the log-log regression of polygon perimeters versus polygon areas. Note that FRAGSTATS calculates this measure by regressing polygon areas versus polygon perimeters. Either method is defensible and neither is correct. This is because the linear regression model assumptions are typically violated when measuring fractal objects.

Reference: For more information regarding the implementation of this fractal dimension method and regarding the use of fractal dimension estimates in landscape ecology refer to [Sugihari 90]. There is much debate as to how to accurately measure fractal dimension. For more information regarding this topic refer to [Russ 94].

[Russ 94] - Russ, John C. 1994. Fractal Surfaces. Plenum Press. New York, New York, USA

[Sugihara 90] - Sugihara G., and R.M. May. 1990. Applications of Fractals in Ecology. TREE 3:79-86.

IDM reports the inverse difference moment of an image. It is a measure of image texture. IDM ranges from 0.0 for an image that is highly textured to 1.0 for an image that is untextured (such as an image with a single class).

Note: This measure uses an adjacency matrix. [Riitters 96] discusses how the method used to create the adjacency matrix can have a large impact upon resulting metrics.

Definition: given t, an adjacency matrix between the classes present:

IDM = sum of all combinations of classes of: (t(i,j)*t(i,j)) / (1 + (i-j)(i-j))

Limitations: Since IDM relies on the magnitude of differences between cell values it is only appropriate to compute it from interval data (as opposed to categorical data).

Reference: For more information see [Musick 91]

[Musick 91] - Musick, and Grover 1991. Image Textural Measures as Indices of Landscape Pattern, chapter in Quantitative Methods in Landscape Ecology, Turner and Gardner (1991). Springer-Verlag. New York, New York, USA.

[Riitters 96] - Riitters, O’Neill, et al. 1996. A note on contagion indices for landscape analysis. Landscape Ecology 11:197-202.

LPI measures the percentage of area taken up by the largest polygon. It is reported for the image as a whole as well as for each class present in the image. LPI is calculated as the largest polygon size divided by the total area of the image. It is multiplied by 100 to represent a percentage.

P reports the perimeter of each class and of the image as a whole.

PA reports the average perimeter to area ratio for all polygons present in the image. It is reported for the image as a whole as well as for each class present in the image.

PA is calculated by averaging the perimeter to area ratio for all polygons present. This provides a result that generally differs from dividing the total perimeter of the polygons by their total area.

Reference: For more information see Baker W.L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7:291-302

PAC reports the average corrected perimeter to area ratio for all polygons present in the image. It is reported for the image as a whole as well as for each class present in the image.

A corrected perimeter to area ratio is calculated by dividing the perimeter of a polygon by the square root of the product of 4 pi and the area of the polygon.

The average corrected perimeter to area ratio is calculated by averaging the corrected perimeter to area ratio for all polygons present. This provides a result that generally differs from dividing the total perimeter by the square root of 4 pi times the total area.

PAC results are always greater than or equal to 1. PAC equals 1.0 for polygons that are perfect circles, 1.1 for polygons that are perfect squares, and can be arbitrarily large for polygons that are extremely long and skinny.

Reference: For more information see Baker W.L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7:291-302

This analysis reports the following measures upon an image and its classes:

• Total polygons
• Mean polygon area
• Standard Deviation of polygon area
• Median polygon area
• Interquartile range of polygon area
• Area of smallest polygon
• Area of largest polygon

This analysis reports the following measures upon an image and its classes:

• Total polygons
• Mean polygon perimeter
• Standard Deviation of polygon perimeter
• Median polygon perimeter
• Interquartile range of polygon perimeter
• Perimeter of smallest polygon
• Perimeter of largest polygon

RA reports the relative proportion of each class within the image.

RCO reports the relative contagion of the image. It is based upon Riitter's version of contagion (corrections made to Li's version). Contagion is a measure of the degree to which classes are clumped into polygons.

RCO reports relative contagion values. Therefore the possible values range from 0.0 for images with minimal contagion to 1.0 for images with maximum contagion.

Note: This measure uses an adjacency matrix. [Riitters 96] discusses how the method used to create the adjacency matrix can have a large impact upon resulting metrics.

Definition: (given t, an adjacency matrix between classes present)

RCO = 1.0 - (measured diversity / maximum diversity)

Measured diversity = -1 * the sum of all combinations of classes in the equation t(i,j) * ln(t(i,j). Maximum diversity is defined as 2 * ln (classes present).

Reference: For more information see [Riitters 96]

[Riitters 96] - Riitters, O’Neill, et al. 1996. A note on contagion indices for landscape analysis. Landscape Ecology 11:197-202.

RDO reports the relative dominance measure of an image. Dominance is a measure of the degree to which an image departs from maximal diversity as defined by [Shannon 62].

RDO returns a value between 0.0 and 1.0 inclusive. Large values of RDO arise from images that are predominantly made up of a few classes. Small values of RDO arise from images that are made up of many different classes in approximately equal proportions.

Definition: (given p, a probability distribution of the classes present)

RDO = 1.0 - (measured diversity / maximum diversity)

where measured diversity = -1 * sum over all classes of p(i)*ln(p(i)) and maximum diveristy = ln(classes present).

Reference: For more information about dominance see [Turner 90]

[Shannon 62] - Shannon and Weaver. 1962. The mathematical theory of communication. University of Illinois Press. Urbana, Illinois, USA.

[Turner 90] - Turner M.G. 1990. Spatial and temporal analysis of landscape patterns. Landscape Ecology 1:21-30.

This metric calulates a statistical summary of the Shape Index upon the image. The summary includes mean, standard deviation, median, first quartile, third quartile, min, and max of the shape index of the polygons within the image.",

The Shape Index for a polygon is defined as (perimeter / minimum perimeter) where minimum possible perimeter is calculated in the following manner:

Find the edge length of the largest square smaller than the area of the polygon (n = floor(sqrt(area))). Let m be the difference between the area of the polygon and the area of sqr(n). Then the minimum perimeter equals
4n if m == 0
4n+2 if sqr(n) < area <= n(n+1)
4n+4 if area > n(n+1)

The Shape Index is always >= 1 and is unitless. Values close to 1 imply that the shape of the polygon is compact. Large values imply an irregular shape.

The Shape Index is scale independent. Polygons of the same shape but differing sizes will have the same shape index.

SP reports the shared perimeter between classes. It reports perimeter for every 2 color combination of the classes present in the image.

SWD reports the diversity of the image as described by [Shannon 62]. SWD results are always greater than or equal to zero. A low diversity measure implies an image is dominated by a single class. A high diversity measure implies an image that contains many classes in approximately equal proportions.

Definition: (given p, a probability distribution of the classes present)
SWD = -1 * sum over all classes of p(i)*ln(p(i))

Reference: For more information see [Turner 90]

[Shannon 62] - Shannon and Weaver. 1962. The mathematical theory of communication. University of Illinois Press. Urbana, Illinois, USA.

[Turner 90] - Turner M.G. 1990. Spatial and temporal analysis of landscape patterns. Landscape Ecology 1:21-30.

SWE reports the relative diversity of the image where diversity is defined as described by [Shannon 62]. Relative diversity is computed as the measured diversity of the image divided by the maximum possible diversity for the image. SWE values range between 0 and 1 inclusive.

Definition: (given p, a probability distribution of the classes present), SWE = measured diversity / maximum diversity where measured diversity = -1 * sum over all classes of p(i)*ln(p(i)) and maximum diversity = ln(classes present).

[Shannon 62] - Shannon and Weaver. 1962. The mathematical theory of communication. University of Illinois Press. Urbana, Illinois, USA.