In this article, we introduce a novel geometrical index δ_, 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 δ_ exhibits the degree of the agglomerations of the particles. In the previous work (Matsutani, Shimosako, Wang, Appl. Math. Modeling 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 γ_ ∈ (0, 1). By applying the image processing procedure to the pictures of the agglomeration particles constructed following the algorithm, we show that δ_ statistically reproduces the agglomeration parameter γ_. MI: Global COE Program Education-and-Research Hub for Mathematics-for-Industry グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」