Conversion of Cancer Features to Number Using Topology

－Hole Analysis－

Abstract

We attempt to classify cancer tumors into several feature groups by counting holes based on topology. In our opinion, image features of cancer tumors depend on several factors such as tumor cells, necrosis, and angiogenesis. When analyzing tumors topologically, we assume that the image features of cancer can be decomposed into three structural components (three-dimensional space): connected components, holes, and cavities. In this paper, we would like to describe a topology-based “hole analysis” including why cancer features are converted into numbers with topology, the theory of the hole analysis, why cancer features are related to topology, and several applications of the hole analysis.