The measurement of the local curvature of arbitrary discrete 3-D medical images is complicated by the difficulties of defining a local neighborhood and then mapping the surface of the neighborhood onto the unit square as a way to unambiguously define a parameterization. Five practical methods are presented for deriving one or more measures of curvature about a point on an arbitrary discretized surface. The first 3 methods approximate the surface patch using continuous biquadratics while the next 2 methods obtain the curvature directly from the discrete data points on the surface which define the neighborhood. The 5 methods are compared in computational complexity accuracy and robustness in the presence of a noisy surface. 1.
Shang You Wu,
Ernest M. Stokely,
"Curvature sampling of 3-D objects in medical images", Proc. SPIE 1233, Medical Imaging IV: Image Processing, (1 July 1990); doi: 10.1117/12.18892; https://doi.org/10.1117/12.18892