Shape Index

Shape index Si, a quantitative measure of the shape of a surface at a point p, is defined by (1),

$$S_{i\,} (p)\,\, = \,\,{1 \over 2}\,\, - \,\,{1 \over \pi }\,\tan ^{ - 1} {{k_1 (p)\, + \,k_2 (p)} \over {k_1 (p)\, - \,k_2(p)}}$$

((1))

where k1 and k2 are maximum and minimum principal curvatures, respectively. With this definition, all shapes can be mapped into the interval S _i ∈[0,1]. The larger shape index values represent convex surfaces and smaller shape index values represent concave surfaces.

Ear Biometrics, 3D