Author(s)： Shigeki Matsutani and Yoshiyuki Shimosako

J. Math-for-Ind. 5B (2013) 83-91.

• File： JMI2013B-1.pdf (1877KB)

Abstract
In this article, we introduce a novel geometrical index $\delta_{\mathrm{agg}}$, 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 $\delta_{\mathrm{agg}}$ 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 $\gamma_{\mathrm{agg}} \in (0,1)$. By applying the image processing procedure to the pictures of the agglomeration particles constructed following the algorithm, we show that $\delta_{\mathrm{agg}}$ statistically reproduces the agglomeration parameter $\gamma_{\mathrm{agg}}$.

Keyword(s).　 agglomeration, digital image processing procedure, Euler number