# Novel Construction of Unbiased Templates for Brain Morphometry

> **NIH NIH R03** · UNIVERSITY OF TEXAS ARLINGTON · 2020 · $152,385

## Abstract

Summary (11/16/2019)
In this project, we develop novel computational methods for image analysis with applications in brain
structure variability studies. The proposed methods are based on a new Variational Principle which
constructs a deformation with prescribed Jacobian determinant (which models local tissue size changes)
and prescribed curl vector (which models local rotations).
The goal of this research is to convince the medical image researchers and users that Jacobian
determinant as well as curl vector should both be used in all steps of image analysis. Specifically, we
develop:
(1) A method of averaging a set of deformations based on Jacobian determinants and the curl vectors;
the new method constructs the average as a deformation whose Jacobian determinant is equal to the
average of the Jacobian determinants and whose curl vector is the average of curl vectors. This new
method is biologically meaningful; it also preserves invertibilty of the deformations in the set.
(2) A general robust method for construction of unbiased templates from a set of images. The method
begins with registering a randomly chosen image in the set to all images in the set. Then the resample of
the initial template on the average of the registration deformations is a good approximation; but it may
still be biased toward the initial template. We then repeat the averaging process to remove bias and
obtain unbiased template. Computational examples are presented to show the effects of curl vector
and the effectiveness of method for averaging deformations and our method for construction of
unbiased template.
The project will significantly enhance our ability to analyze brain image data; improve diagnosis, monitor
, and treatment of brain diseases and mental disorder. The project has an important training and
educational component. Specifically, a PhD student will participate in algorithm design, computer code
development, testing, and software management.

## Key facts

- **NIH application ID:** 10058143
- **Project number:** 1R03MH120627-01A1
- **Recipient organization:** UNIVERSITY OF TEXAS ARLINGTON
- **Principal Investigator:** Guojun Gordon Liao
- **Activity code:** R03 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2020
- **Award amount:** $152,385
- **Award type:** 1
- **Project period:** 2020-05-20 → 2023-05-19

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/10058143

## Citation

> US National Institutes of Health, RePORTER application 10058143, Novel Construction of Unbiased Templates for Brain Morphometry (1R03MH120627-01A1). Retrieved via AI Analytics 2026-05-26 from https://api.ai-analytics.org/grant/nih/10058143. Licensed CC0.

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