In this paper, we described a set of computational technologies for image analysis with applications in Brain Morphometry. The proposed technologies are based on a new Variational Principle which constructs a transformation with prescribed Jacobian determinant (which models local size changes) and prescribed curl-vector (which models local rotations). The goal of this research is to convince the image research community that Jacobian determinant as well as curl-vector should be used in all steps of image analysis. Specifically, we develop an optimal control method for non-rigid registration; a new concept and construction of average transformation; and a general robust method for construction of unbiased template from a set of images. Computational examples are presented to show the effects of curl-vector and the effectiveness of optimal control methods for non-rigid registration and our method for construction of unbiased template.
@article{arxiv.1810.04833,
title = {Computational Technologies for Brain Morphometry},
author = {Zicong Zhou and Ben Hildebrandt and Xi Chen and Guojun Liao},
journal= {arXiv preprint arXiv:1810.04833},
year = {2018}
}