Microscope Image Processing

mean of the two principal curvatures, H ¼ 1=2 p

1

þ p

2

½. Several techniques are

available for curvature estimation [104]. Two approaches, surface triangulation

and the cross-patch method, are described next [104].

14.15.6.1 Surface Triangulation Method

In this method, a surface patch is approximated by a series of adjacent triangles.

Since each triangle is flat, the Gaussian curvature is estimated at the common

vertex of the triangles (the center of the patch). The Gaussian curvature,

K ¼ Du=A, where Du ¼ 2p 

P

i

u

i

, is a quantity called the angle deficit, u

i

is

the vertex angle of the individual triangles in the series, and A is the sum of the

areas of the triangles [104].

14.15.6.2 Cross-Patch Method

In this method, a discreet surface patch consisting