  The Quermass-interaction model allows to generalise the classical germ-grain
Boolean model in adding a morphological interaction between the grains. It
enables to model random structures with specific morphologies which are
unlikely to be generated from a Boolean model. The Quermass-interaction model
depends in particular on an intensity parameter, which is impossible to
estimate from classical likelihood or pseudo-likelihood approaches because the
number of points is not observable from a germ-grain set. In this paper, we
present a procedure based on the Takacs-Fiksel method which is able to estimate
all parameters of the Quermass-interaction model, including the intensity. An
intensive simulation study is conducted to assess the efficiency of the
procedure and to provide practical recommendations. It also illustrates that
the estimation of the intensity parameter is crucial in order to identify the
model. The Quermass-interaction model is finally fitted by our method to P.
Diggle's heather dataset.
