We present a new mathematical model to construct mean- like and median-like average STN (subthalamic nucleus) atlases based on  image registration and reconstruction. The average STN atlases (ASAs) have average intensities and shapes of the STN regions. In particular, the construction of the ASAs does not depend on selecting a particular image as the template and is optimal to the datasets with respect to  minimizing a cost functional.  For the application in deep brain stimulation, the ASAs can be used  to accurately localize the target points of the STNs. For the validation of the outperformace of the ASAs, we compare them with anatomical  atlases by executing the atlas to patient data registrations using clinical  datasets.