3D structural analysis: Sensitivity of Minkowski functionals

The Minkowski functionals, a family of statistical measures based on the Euler-Poincaré characteristic of n-dimensional space, are the complete set of additive morphological measures and can be simply calculated from local contributions. As such, they have found a wide range of applications. We consider the effects of distortions (drift, noise and blurring) on the morphological properties of complex random models, representative of a wide range of structure. Such distortions arise experimentally in imaging techniques due to diffraction, absorption and sample drift. The question is asked, how critically these distortions effect image quality as measured by the Minkowski functionals. Defining a length scale based on the two-point correlation function, we consider how distortion at different scales can lead to quantitative errors in morphological measures.