  In this article, we introduce a novel geometrical index $\delta_{agg}$, which
is associated with the Euler number and is obtained by an image processing
procedure for a given digital picture of aggregated particles such that
$\delta_{agg}$ exhibits the degree of the agglomerations of the particles. In
the previous work (Matsutani, Shimosako, Wang, Appl.Math.Modeling {\bf{37}}
(2013), 4007-4022), we proposed an algorithm to construct a picture of
agglomerated particles as a Monte-Carlo simulation whose agglomeration degree
is controlled by $\gamma_{agg} \in (0,1)$. By applying the image processing
procedure to the pictures of the agglomeration particles constructed following
the algorithm, we show that $\delta_{agg}$ statistically reproduces the
agglomeration parameter $\gamma_{agg}$.
