Hierarchical entropy and domain interaction to understand the structure in an image

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.