Geometrical attributes

The attributes representing geometrical characteristics of an object (polygon segment) make object-based image analysis (OBIA) advantageous over pixel-based measures. The geometrical attributes are calculated by analyzing the polygon boundary created during segmentation, so raster information is not required. Many of the shape descriptors used commonly are calculated. Each is described in the following table.

Note: Geometrical attributes are independent from the channel aliases, because they are calculated from the shape of objects.

Table 1. Geometrical attributes
Attribute	Short name	Description
Compactness	Compact	A measure of closely packed a shape is. A circle is the most compact. `Compactness = √(4 × As ÷ pi) ÷ O` Where `As` is the area of the object, and `O` is the perimeter of the object (outer contour).
Elongation	Elongation	The ratio of the height and width of a rotated, minimal-bounding box; that is, rotate a rectangle so it is the smallest rectangle in which the object fits, and then compare its height with its width. `Elongation = major axis length ÷ minor axis length`
Circularity	Circular	A ratio representing how like is the shape of the object to a circle. Circularity is the ratio of the area of a shape to the perimeter of the square of the shape. `Circularity = A_s ÷ O²` Where `A_s` is the area of the shape, and `O²` is square of the perimeter of the shape.
Rectangularity	Rectangular	How rectangular a shape is; that is, how much it fills its minimum bounding rectangle: `Rectangularity = A_s ÷ A_R` Where `A_s` is the area of a shape, and `A_R` is the area of the minimum bounding rectangle.
Convexity	Convexity	The relative amount that an object differs from a convex object. Convexity is calculated by forming the ratio of the perimeter of the convex hull of an object to the perimeter of the object itself. `Convexity = convex-hull perimeter ÷ object perimeter`
Solidity	Solidity	The density of an object. Solidity is calculated as the ratio of the area of an object to the area of a convex hull of the object. A value of `1` indicates a solid object, and a value less than `1` indicates an object having an irregular boundary or containing holes. `Solidity = area ÷ convex-hull area`
Form factor	FormFactor	The measure that compares the area of a polygon to the square of the perimeter. The form-factor value of a circle is `1`, and the value of a square is `pi` ÷ `4`. `Form factor = 4 × pi × area ÷ sqrt (perimeter)`
Major-axis length	MajorAxis	The length of the major axis of an oriented bounding box enclosing the polygon. Values are map units of the pixel size. If the image is not georeferenced, the values are pixels.
Minor-axis length	MinorAxis	The length of the minor axis of an oriented bounding box enclosing the polygon. Values are map units of the pixel size. If the image is not georeferenced, the values are pixels.