Spatial Integrity:

Spatial integrity refers to undivided space and is often used to compare the spatial complexity of two or more landscapes. This perspective is relevant in studies of biodiversity or wildlife habitat, for instance.

A fragmented category, one containing several discrete patches, or containing many inclusions has less spatial integrity than a category containing fewer patches or inclusions. A quantitative measure of spatial integrity is the Euler number (see formula below). Large negative or positive numbers indicate spatially complex landscapes, whereas an Euler number of zero indicates spatially homogeneous areas.

Convexity and edge are characteristics of shape related to boundary configuration of areal features.

Convexity, the extent to which an area is enclosed by its background, in relation to the extent the area envelops parts of the background, measures the spatial complexity of the polygon form. The convexity index is the ratio of a polygon's perimeter to the square root of its area. A circle, for instance, is totally enclosed by its background and thus has the least complex configuration. By comparing a polygon's convexity index with that of a circle of the same area, a standard measure of the regularity of its boundary can be computed.