On the analysis of spatial binary images

This paper deals with the analysis of spatial images taken from microscopic ally heterogeneous but macroscopically homogeneous microstructures. A new m ethod 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 b e expressed as the inner products of two vectors where the first vector car ries the 'integrated local knowledge' about the microstructure and the seco nd vector depends on the lateral resolution of the image as well as the qua drature rules used in the discretization of the integral-geometric formulae . As an example of application we consider the analysis of spatial microtom ographic images obtained from natural sandstones.