Statistical analysis with dilatation for development process of human fetuses

This paper is concerned with the development process of human fetuses. Though the development process of human fetuses still includes many unknown issues, it is known that a certain harmonious relationship between the organs can be observed. This knowledge is based on our intuition, but we have no theory which clarifies these harmonized developments. The paper aims to give a mathematical understanding of the notion of harmonized development through the use of dilatation, which is a measure of the departure from conformal mapping. The asymptotics for dilatation have been developed using certain efficient models of quasiconformal mapping. The proposed method of dilatation is effectively applied to the human fetus data.