Mesh free estimation of the structure model index

english

2009

volume 28, issue 3

Image Processing, Computer-Assisted   Materials Testing 

Društvo za stereologijo in kvantitativno analizo slike
(Obvezni izvod spletne publikacije)

The structure model index (SMI) is a means of subsuming the topology of a homogeneous random closed set under just one number, similar to the isoperimetric shape factors used for compact sets. Originally, the SMI is defined as a function of volume fraction, specific surface area and first derivarive of the specific surface area, where the derivative is defined and computed using a surface meshing. The generalised Steiner formula yields however a derivarive of the specific surface area that is - up to a constant- the density of the integral of mean curvature. Consequently, an SMI can be defined without referring to a discretisation and it can be estimated from 3D image data without need to mesh the surface but using the number of occurrences of 2 x 2 x 2 pixel configurations, only. Obviously, it is impossible to completely describe a random closed sei by one number. In this paper, Boolean models of balls and infinite straight cylinders serve as cautionary examples poinring out the limitations of the SMI. Nevertheless, shape factors like the SMI can be valuable tools for comparing similar structures. This is illustrated on real microstructures of ice, foams, and paper.

16.04.2011