Current Projects

Construction of Average Image R03MH120627

Award Notice (for more detail, contact the grant office of UT Arlington at 817 272 2011)

This project received positive reviews, with the impact score: 20, percentile 5+.

Summary: 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 demonstrate 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 invertibility 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. Graduate and undergraduate students will participate in the project.

Summary: R03MH120627: Novel Construction of Unbiased Templates for Brain Morphometry

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 demonstrate that the Jacobian determinant and the 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 invertibility 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. The resample of he 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 the method for averaging deformations and our method for construction of unbiased template.

Research Papers and Codes

References Cited

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[3] [Ashburner 2010] Ashburner, J.: VBM Tutorial. http://www.fil.ion.ucl.ac.uk/∼john/misc/VBMclass10.pdf, Mar 15, 2010.

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[6] [Chen and Liao 2016] Chen, X. and Liao, G. Preprint: New method of averaging diffeomorphisms based on Jacobian determinant and curl vector. https://arxiv.org/abs/1611.03946, 2016.

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[13] [Joshi et al. 2004] Joshi, S., Davis, B., Jomier, M. and Gerig, G.: Unbiased Diffeomorphic Atlas Construction for Computational Anatomy NeuroImage, Vol. 23, pp151-160, 2004. doi:10.1016/j.neuroimage.2004.07.068

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[24] [Zhou et al. 2018] Zicong Zhou, Ben Hildebrand, Xi Chen, Guojun Liao, Preprint: Computational Technologies for Brain Morphometry, arXiv.org/pdf/1810.04833.pdf