  In this study, we devise a model that introduces two hierarchies into
information entropy. The two hierarchies are the size of the region for which
entropy is calculated and the size of the component that determines whether the
structures in the image are integrated or not. And this model uses two
indicators, hierarchical entropy and domain interaction. Both indicators
increase or decrease due to the integration or fragmentation of the structure
in the image. It aims to help people interpret and explain what the structure
in an image looks like from two indicators that change with the size of the
region and the component. First, we conduct experiments using images and
qualitatively evaluate how the two indicators change. Next, we explain the
relationship with the hidden structure of Vermeer's girl with a pearl earring
using the change of hierarchical entropy. Finally, we clarify the relationship
between the change of domain interaction and the appropriate segment result of
the image by an experiment using a questionnaire.
