(P10) Linearity Index

a_ij^* =   area of patch ij in terms of number of cells.

b =      average cell value of the medial axis transformation (MAT) of a patch.

r =                   0 if the MAT skeleton contains side-by-side rows; 1 if not.

Description

LINEAR equals the area of the patch (in number of pixels) divided by 2 times the average value of the MAT skeleton minus 0 if the MAT skeleton contains side-by-side rows, 1 if not, quantity squared, minus 1, over the area of the patch (in number of cells).

Units 

None

Range

0 ≤ LINEAR < 1

LINEAR = 0 for square patches and approaches 1 for large patches which are all edge. Dividing by patch area normalizes the index since the maximum possible value of the numerator for a patch equals its area (when b = 1).

Comments

Linearity index (Gustafson and Parker 1992) is based on the medial axis transformation (MAT) of the patch. Note, this index is not influenced by patch size.