On the analysis of spatial binary images

This paper deals with the analysis of spatial images taken from microscopically heterogeneous but macroscopically homogeneous microstructures. A new method is presented, which is strictly based on integral-geometric formulae such as Crofton's intersection formulae and Hadwiger's recursive definition of the Euler number. By means of this approach the quermassdensities can be expressed as the inner products of two vectors where the first vector carries the 'integrated local knowledge' about the microstructure and the second vector depends on the lateral resolution of the image as well as the quadrature rules used in the discretization of the integral-geometric formulae. As an example of application we consider the analysis of spatial microtomographic images obtained from natural sandstones.