Surface Curvature

Measurements of the curvature of a surface are commonly used in 3D biometrics. The normal curvature on a point p on the surface is defined as the curvature of the curve that is formed by the intersection of the surface with the plane containing the normal vector and one of the tangent vectors at p. Thus the normal curvature is a function of the tangent vector direction. The minimum and maximum values of this function are the principal curvatures k1 and k2 of the surface at p. Other measures of surface curvature are the Gaussian curvature defined as the product of principal curvatures, the mean curvature defined as the average of principal curvatures and the shape index given by

$$SI\, = \,{2 \over \pi }\,{{K_2 + K_1 } \over {K_2 - K_1 }}$$

Computation of surface curvature on discrete surfaces such as those captured with 3D scanners is usually accomplished by locally fitting low order surface patches (e.g. biquadratic surfaces, splines) over each point. Then the above curvature features...