Signed line intercept count
Abstract
Elements of surfaces that bound a phase (β) in a two phase mixture (α+β) may be classified as:
a. convex (++) if both principle curvatures are positive;
b. concave (--) if both are negative; and
c. saddle (+-) if one is positive and the other negative.
The traces of these surfaces that form the boundaries of the areas on a representative two dimensional section may also be:
a. convex (+) if the local curvature is positive; or
b. concave (-) if it is negative.
Line intercept counts may be tabulated separately for sections with convex (PL+) and concave (PL-) segments of boundary. This paper presents a derivation of fundamental stereological formulae that relate these counting measurements to three dimensional geometric properties of the structure they sample.