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Decomposition of Longitudinal Deformations via Beltrami Descriptors

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Abstract

We present a mathematical model to decompose a longitudinal deformation into normal and abnormal components. The goal is to detect and extract subtle abnormal deformation from periodic motions in a video sequence. It has important applications in medical image analysis. To achieve this goal, we consider a representation of the longitudinal deformation, called the Beltrami descriptor, based on quasiconformal theories. The Beltrami descriptor is a complex-valued matrix. Each longitudinal deformation is associated to a Beltrami descriptor and vice versa. To decompose the longitudinal deformation, we propose to carry out the low rank and sparse decomposition of the Beltrami descriptor. The low rank component corresponds to the periodic motions, whereas the sparse part corresponds to the abnormal motions of a longitudinal deformation. Experiments have been carried out on both synthetic and real video sequences. Results demonstrate the efficacy of our proposed model to decompose a longitudinal deformation into regular and irregular components.

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Acknowledgements

L.M. Lui is supported by HKRGC GRF (Project ID: 2130549).

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  1. The Chinese University of Hong Kong, Shatin, China

    Ho Law & Lok Ming LUI

  2. Cornell University, Ithaca, NY, USA

    Chun Yin Siu

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HKRGC GRF (Project ID:2130549, Reference ID: 14306917), CUHK Direct Grant (Project ID: 4053292).

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Law, H., Siu, C.Y. & LUI, L.M. Decomposition of Longitudinal Deformations via Beltrami Descriptors. J Sci Comput 89, 6 (2021). https://doi.org/10.1007/s10915-021-01569-x

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