Symmetry detection for astronomical object study

In the study of astronomical objects such as planetary nebulas, it appears that symmetry detection is an important task to achieve. Actually, symmetry detection is an appropriate way for determining how the nebula was born. In this paper we suggest two different methods for estimating the symmetry according to a point. The first method gives a global estimation of the symmetry degree whereas the second one determines this symmetry degree in a given neighborhood. Finally a full study is led on a particular astronomical image: the planetary nebula Messier 1. Both the RGB color image and the corresponding gray-level image are taken under consideration and results are analyzed.