Journal of the Operations Research Society of China >

2019 , Vol. 7 >Issue 4: 599 - 614

DOI: https://doi.org/10.1007/s40305-019-00251-2

Longitudinal Image Analysis via Path Regression on the Image Manifold

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  • 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 Department of Radiology and BRIC, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA

Received date: 2018-08-28

  Revised date: 2019-01-23

  Online published: 2019-11-28

Supported by

The research was supported by the National Natural Science Foundation of China (Nos. 11771276, 11471208), and the Capacity Construction Project of Local Universities in Shanghai (No. 18010500600).

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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.

Key words： Longitudinal image analysis; Path regression; Diffeomorphism group; Image registration; Infant brain development

Cite this article

Shi-Hui Ying, Xiao-Fang Zhang, Ya-Xin Peng, Ding-Gang Shen . Longitudinal Image Analysis via Path Regression on the Image Manifold[J]. Journal of the Operations Research Society of China, 2019 , 7(4) : 599 -614 . DOI: 10.1007/s40305-019-00251-2

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