
112 Computing in Geographic Information Systems
FIGURE 6.1
Edge surface with Gaussian curvature K = 0, λ
1
= 0 and λ
2
< 0. The princi-
pal eigenvalues are directed in orthogonal directions.
The classification of the image surface can be done using the mean gaus-
sain curvature. For elliptic surface patches the curvature is positive in any
directions i.e. K ≥ 0.
In other words if H ≥ 0 then the surface is convex.
If H ≤ 0 then the surface is concave and curvature in any direction is
negative.
For hyperbolic patches: K ≤ 0, the curvature is positive in some direction
and negative in some other direction.
For K = 0, i.e. one or both of the principal curvature ...