# GIS Analysis → Patch Shape Tools

- BoundaryShapeComplexity
- CompactnessRatio
- EdgeProportion
- ElongationRatio
- FindPatchOrClassEdgeCells
- HoleProportion
- LinearityIndex
- NarrownessIndex
- PatchOrientation
- PerimeterAreaRatio
- RadiusOfGyration
- RelatedCircumscribingCircle
- ShapeComplexityIndex
- ShapeComplexityIndexRaster

# BoundaryShapeComplexity

This tools calculates a type of shape complexity index for raster objects, focused on the complexity of the
boundary of polygons. The index uses the **LineThinning** tool to estimate a skeletonized network for each
input raster polygon. The Boundary Shape Complexity (BSC) index is then calculated as the percentage of the
skeletonized network belonging to exterior links. Polygons with more complex boundaries will possess
more branching skeletonized networks, with each spur in the boundary possessing a short exterior branch. The
two longest exterior links in the network are considered to be part of the main network. Therefore,
polygons of complex shaped boundaries will have a higher percentage of their skeleton networks consisting
of exterior links. It is expected that simple convex hulls should have relatively low BSC index values.

Objects in the input raster (`--input`

) are designated by their unique identifers. Identifer values should be
positive, non-zero whole numbers.

*See Also*:
**ShapeComplexityIndexRaster**, **LineThinning**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input raster file |

-o, --output | Output raster file |

*Python function*:

```
wbt.boundary_shape_complexity(
i,
output,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=BoundaryShapeComplexity -v ^
--wd="/path/to/data/" -i=input.tif -o=output.tif --zero_back
```

*Author*: Dr. John Lindsay

*Created*: 17/02/2019

*Last Modified*: 17/02/2019

# CompactnessRatio

The compactness ratio is an indicator of polygon shape complexity. The compactness
ratio is defined as the polygon area divided by its perimeter. Unlike some other
shape parameters (e.g. **ShapeComplexityIndex**), compactness ratio does not standardize
to a simple Euclidean shape. Although widely used for landscape analysis, compactness
ratio, like its inverse, the **PerimeterAreaRatio**, exhibits the undesirable property
of polygon size dependence (Mcgarigal et al. 2002). That is, holding shape constant,
an increase in polygon size will cause a change in the compactness ratio.

The output data will be contained in the input vector's attribute table as a new field (COMPACT).

*See Also*:
**PerimeterAreaRatio**, **ShapeComplexityIndex**, **RelatedCircumscribingCircle**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.compactness_ratio(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=CompactnessRatio -v ^
--wd="/path/to/data/" --input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 27/09/2018

*Last Modified*: 13/10/2018

# EdgeProportion

This tool will measure the edge proportion, i.e. the proportion of grid cells in a patch that are located along the
patch's boundary, for an input raster image (`--input`

). Edge proportion is an indicator of polygon shape complexity
and elongation. The user must specify the name of the output raster file (`--output`

), which will be raster layer
containing the input features assigned the edge proportion. The user may also optionally choose to output text data
for easy input to a spreadsheet or database.

Objects in the input raster are designated by their unique identifers. Identifer values must be positive, non-zero whole numbers.

*See Also*:
**ShapeComplexityIndexRaster**, **LinearityIndex**, **ElongationRatio**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input raster file |

-o, --output | Output raster file |

--output_text | flag indicating whether a text report should also be output |

*Python function*:

```
wbt.edge_proportion(
i,
output,
output_text=False,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=EdgeProportion -v --wd="/path/to/data/" ^
-i=input.tif -o=output.tif --output_text
```

*Author*: Dr. John Lindsay

*Created*: 13/07/2017

*Last Modified*: 18/10/2019

# ElongationRatio

This tool can be used to calculate the elongation ratio for vector polygons. The elongation ratio values calculated for each vector polygon feature will be placed in the accompanying database file (.dbf) as an elongation field (ELONGATION).

The elongation ratio (`E`

) is:

E = 1 - S / L

Where `S`

is the short-axis length, and `L`

is the long-axis length. Axes
lengths are determined by estimating the minimum bounding box.

The elongation ratio provides similar information as the Linearity Index. The ratio is not an adequate measure of overall polygon narrowness, because a highly sinuous but narrow polygon will have a low linearity (elongation) owing to the compact nature of these polygon.

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.elongation_ratio(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=ElongationRatio -v ^
--wd="/path/to/data/" --input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 25/09/2018

*Last Modified*: 13/10/2018

# FindPatchOrClassEdgeCells

This tool will identify all grid cells situated along the edges of patches or class features within an
input raster (`--input`

). Edge cells in the output raster (`--output`

) will have the patch identifier value
assigned in the corresponding grid cell. All non-edge cells will be assigned zero in the output raster.
Patches (or classes) are designated by positive, non-zero values in the input image. Zero-valued
and NoData-valued grid cells are interpreted as background cells by the tool.

*See Also*:
**EdgeProportion**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input raster file |

-o, --output | Output raster file |

*Python function*:

```
wbt.find_patch_or_class_edge_cells(
i,
output,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=FindPatchOrClassEdgeCells -v ^
--wd="/path/to/data/" -i=input.tif -o=output.tif
```

*Author*: Dr. John Lindsay

*Created*: 14/07/2017

*Last Modified*: 13/10/2018

# HoleProportion

This calculates the proportion of the total area of a polygon's holes (i.e. islands) relative to the area of the polygon's hull. It can be a useful measure of shape complexity, or how discontinuous a patch is. The user must specify the name of the input vector file and the output data will be contained within the input vector's database file as a new field (HOLE_PROP).

*See Also*:
**ShapeComplexityIndex**, **ElongationRatio**, **PerimeterAreaRatio**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.hole_proportion(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=HoleProportion -v --wd="/path/to/data/" ^
--input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 26/09/2018

*Last Modified*: 26/09/2018

# LinearityIndex

This tool calculates the linearity index of polygon features based on a regression analysis.
The index is simply the coefficient of determination (r-squared) calculated from a regression
analysis of the x and y coordinates of the exterior hull nodes of a vector polygon. Linearity
index is a measure of how well a polygon can be described by a straight line. It is a related
index to the **ElongationRatio**, but is more efficient to calculate as it does not require
finding the minimum bounding box. The Pearson correlation coefficient between linearity index
and the elongation ratio for a large data set of lake polygons in northern Canada was found
to be 0.656, suggesting a moderate level of association between the two measures of polygon
linearity. Note that this index is not useful for identifying narrow yet sinuous polygons, such
as meandering rivers.

The only required input is the name of the file. The linearity values calculated for each vector polygon feature will be placed in the accompanying attribute table as a new field (LINEARITY).

*See Also*:
**ElongationRatio**, **PatchOrientation**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.linearity_index(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=LinearityIndex -v --wd="/path/to/data/" ^
--input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 01/10/2018

*Last Modified*: 13/10/2018

# NarrownessIndex

This tools calculates a type of shape narrowness index (*NI*) for raster objects. The index is equal to:

NI=A/ (πMD^{2})

where *A* is the patch area and *MD* is the maximum distance-to-edge of the patch. Circular-shaped patches
will have a narrowness index near 1.0, while more narrow patche shapes will have higher index values. The
index may be conceptualized as the ratio of the patch area to the area of the largest contained circle,
although in practice the circle defined by the radius of the maximum distance-to-edge will often fall
outside the patch boundaries.

Objects in the input raster (`--input`

) are designated by their unique identifers. Identifer values must
be positive, non-zero whole numbers.

*See Also*:
**LinearityIndex**, **ElongationRatio**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input raster file |

-o, --output | Output raster file |

*Python function*:

```
wbt.narrowness_index(
i,
output,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=NarrownessIndex -v ^
--wd="/path/to/data/" -i=input.tif -o=output.tif --zero_back
```

*Author*: Dr. John Lindsay

*Created*: 17/02/2019

*Last Modified*: 17/02/2019

# PatchOrientation

This tool calculates the orientation of polygon features based on the slope of a reduced major axis (RMA) regression line. The regression analysis use the vertices of the exterior hull nodes of a vector polygon. The only required input is the name of the vector polygon file. The orientation values, measured in degrees from north, will be placed in the accompanying attribute table as a new field (ORIENT). The value of the orientation measure for any polygon will depend on how elongated the feature is.

Note that the output values are polygon orientations and not true directions. While directions may take values ranging from 0-360, orientation is expressed as an angle between 0 and 180 degrees clockwise from north. Lastly, the orientation measure may become unstable when polygons are oriented nearly vertical or horizontal.

*See Also*:
**LinearityIndex**, **ElongationRatio**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.patch_orientation(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=PatchOrientation -v ^
--wd="/path/to/data/" --input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 16/10/2018

*Last Modified*: 16/10/2018

# PerimeterAreaRatio

The perimeter-area ratio is an indicator of polygon shape complexity. Unlike some other shape parameters (e.g. shape complexity index), perimeter-area ratio does not standardize to a simple Euclidean shape. Although widely used for landscape analysis, perimeter-area ratio exhibits the undesirable property of polygon size dependence (Mcgarigal et al. 2002). That is, holding shape constant, an increase in polygon size will cause a decrease in the perimeter-area ratio. The perimeter-area ratio is the inverse of the compactness ratio.

The output data will be displayed as a new field (P_A_RATIO) in the input vector's database file.

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.perimeter_area_ratio(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=PerimeterAreaRatio -v ^
--wd="/path/to/data/" --input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 26/09/2018

*Last Modified*: 03/03/2020

# RadiusOfGyration

This can be used to calculate the radius of gyration (RoG) for the polygon features within a raster image. RoG measures how far across the landscape a polygon extends its reach on average, given by the mean distance between cells in a patch (Mcgarigal et al. 2002). The radius of gyration can be considered a measure of the average distance an organism can move within a patch before encountering the patch boundary from a random starting point (Mcgarigal et al. 2002). The input raster grid should contain polygons with unique identifiers greater than zero. The user must also specify the name of the output raster file (where the radius of gyration will be assigned to each feature in the input file) and the specified option of outputting text data.

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input raster file |

-o, --output | Output raster file |

--text_output | Optional text output |

*Python function*:

```
wbt.radius_of_gyration(
i,
output,
text_output=False,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=RadiusOfGyration -v ^
--wd="/path/to/data/" -i=polygons.tif -o=output.tif ^
--text_output
```

*Author*: Dr. John Lindsay

*Created*: 31/12/2017

*Last Modified*: 18/10/2019

# RelatedCircumscribingCircle

This tool can be used to calculate the related circumscribing circle (Mcgarigal et al. 2002) for vector polygon features. The related circumscribing circle values calculated for each vector polygon feature will be placed in the accompanying attribute table as a new field (RC_CIRCLE).

Related circumscribing circle (RCC) is defined as:

RCC = 1 - A / Ac

Where `A`

is the polygon's area and `Ac`

the area of the smallest circumscribing circle.

Theoretically, **RelatedCircumscribingCircle** ranges from 0 to 1, where a value of 0 indicates
a circular polygon and a value of 1 indicates a highly elongated shape. The circumscribing
circle provides a measure of polygon elongation. Unlike the **ElongationRatio**, however, it
does not provide a measure of polygon direction in addition to overall elongation. Like the
**ElongationRatio** and **LinearityIndex**, **RelatedCircumscribingCircle** is not an adequate
measure of overall polygon narrowness, because a highly sinuous but narrow patch will have
a low related circumscribing circle index owing to the compact nature of these polygon.

Note: Holes are excluded from the area calculation of polygons.

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.related_circumscribing_circle(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=RelatedCircumscribingCircle -v ^
--wd="/path/to/data/" --input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 27/09/2018

*Last Modified*: 13/10/2018

# ShapeComplexityIndex

This tool provides a measure of overall polygon shape complexity, or irregularity, for vector polygons. Several shape indices have been created to compare a polygon's shape to simple Euclidean shapes (e.g. circles, squares, etc.). One of the problems with this approach is that it inherently convolves the characteristics of polygon complexity and elongation. The Shape Complexity Index (SCI) was developed as a parameter for assessing the complexity of a polygon that is independent of its elongation.

SCI relates a polygon's shape to that of an encompassing convex hull. It is defined as:

SCI = 1 - A / Ah

Where `A`

is the polygon's area and `Ah`

is the area of the convex hull containing
the polygon. Convex polygons, i.e. those that do not contain concavities or holes,
have a value of 0. As the shape of the polygon becomes more complex, the SCI
approaches 1. Note that polygon shape complexity also increases with the greater
number of holes (i.e. islands), since holes have the effect of reducing the lake
area.

The SCI values calculated for each vector polygon feature will be placed in the accompanying database file (.dbf) as a complexity field (COMPLEXITY).

*See Also*:
**ShapeComplexityIndexRaster**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input vector polygon file |

*Python function*:

```
wbt.shape_complexity_index(
i,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=ShapeComplexityIndex -v ^
--wd="/path/to/data/" --input=polygons.shp
```

*Author*: Dr. John Lindsay

*Created*: 25/09/2018

*Last Modified*: 13/10/2018

# ShapeComplexityIndexRaster

This tools calculates a type of shape complexity index for raster objects. The index is equal to the average
number of intersections of the group of vertical and horizontal transects passing through an object. Simple
objects will have a shape complexity index of 1.0 and more complex shapes, including those containing numberous
holes or are winding in shape, will have higher index values. Objects in the input raster (`--input`

) are
designated by their unique identifers. Identifer values should be positive, non-zero whole numbers.

*See Also*:
**ShapeComplexityIndex**, **BoundaryShapeComplexity**

*Parameters*:

Flag | Description |
---|---|

-i, --input | Input raster file |

-o, --output | Output raster file |

*Python function*:

```
wbt.shape_complexity_index_raster(
i,
output,
callback=default_callback
)
```

*Command-line Interface*:

```
>>./whitebox_tools -r=ShapeComplexityIndexRaster -v ^
--wd="/path/to/data/" -i=input.tif -o=output.tif --zero_back
```

*Author*: Dr. John Lindsay

*Created*: 16/02/2019

*Last Modified*: 16/02/2019