(P11) Related Circumscribing Circle 


a_{ij} = area (m^{2}) of patch ij. a_{ij}^{s} = area (m^{2}) of smallest circumscribing circle around patch ij. 

Description 
CIRCLE equals 1 minus patch area (m^{2}) divided by the area (m^{2}) of the smallest circumscribing circle. Note, the smallest circumscribing circle is computed mathematically based on the geometry of a true circle, despite the raster data format. In addition, to ensure that the minimum value is always zero, the diameter of the circumscribing circle is computed as the maximum distance between periphery cells based on outer edgetoouter edge distance, as opposed to cell centertocell center distance used in all nearest neighbor calculations. 

Units 
None 

Range 
0 ≤ CIRCLE < 1 CIRCLE = 0 for circular patches and approaches 1 for elongated, linear patches one cell wide. CIRCLE = 0 for one cell patches. 

Comments 
Related circumscribing circle (CIRCLE) uses the smallest circumscribing circle instead of the smallest circumscribing square despite the raster data format because it is much simpler to implement. In contrast to the linearity index, related circumscribing circle provides a measure of overall patch elongation. A highly convoluted but narrow patch can have a high linearity index if the medial axial skeleton is close to the patch edge, but have a low related circumscribing circle index due to the relative compactness of the patch. Conversely, a narrow and elongated patch can have a high linearity index as well as a high related circumscribing circle index. This index may be particularly useful for distinguishing patches that are both linear (narrow) and elongated. 