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Longitudinal Image Analysis via Path Regression on the Image Manifold

  • Shi-Hui Ying
  • Xiao-Fang Zhang
  • Ya-Xin PengEmail author
  • Ding-Gang Shen
Article
  • 98 Downloads

Abstract

Longitudinal image analysis plays an important role in depicting the development of the brain structure, where image regression and interpolation are two commonly used techniques. In this paper, we develop an efficient model and approach based on a path regression on the image manifold instead of the geodesic regression to avoid the complexity of the geodesic computation. Concretely, first we model the deformation by diffeomorphism; then, a large deformation is represented by a path on the orbit of the diffeomorphism group action. This path is obtained by compositing several small deformations, which can be well approximated by its linearization. Second, we introduce some intermediate images as constraints to the model, which guides to form the best-fitting path. Thirdly, we propose an approximated quadratic model by local linearization method, where a closed form is deduced for the solution. It actually speeds up the algorithm. Finally, we evaluate the proposed model and algorithm on a synthetic data and a real longitudinal MRI data. The results show that our proposed method outperforms several state-of-the-art methods.

Keywords

Longitudinal image analysis Path regression Diffeomorphism group Image registration Infant brain development 

Mathematics Subject Classification

68T05 97K80 

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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina
  2. 2.Department of Radiology and BRICUniversity of North Carolina at Chapel HillChapel HillUSA

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