Computational Technologies for Brain Morphometry

TL;DR

This paper introduces new computational techniques for brain image analysis based on a variational principle that models local size and rotation changes, improving registration and template construction.

Contribution

It proposes a novel variational framework incorporating Jacobian and curl-vector constraints, along with optimal control methods for non-rigid registration and unbiased template creation.

Findings

Effective non-rigid registration using optimal control methods

New approach for constructing unbiased brain templates

Demonstrated benefits of curl-vector in image analysis

Abstract

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.