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A Variational Model for Deformable Registration of Uni-modal Medical Images with Intensity Biases

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Abstract

Deformable image registration aims at estimating a proper displacement field from a fixed image and a moving one. Variational deformable registration models often consist of a data term of the images and a regularization term of the estimated displacement field. In this paper, we propose a variational model for registering uni-modal medical images with intensity biases. Precisely, the proposed model employs local correlation coefficients (LCC) as the data term and regularizes all possible displacement fields as functions of bounded deformation (BD functions), which is thus termed as BDLCC model. A primal-dual algorithm is derived for solving the model. Two conclusions can be drawn from two-dimensional and three-dimensional numerical experiments: (1) the proposed primal-dual algorithm is effective and stable, (2) the BDLCC model is effective for deformable registration of uni-modal images with intensity biases, and competitive with other state-of-the-art deformable registration models.

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Acknowledgements

The authors would like to thank the multidisciplinary team of liver, billiary and pancreatic tumors in Nanjing Drum Tower Hospital, China for providing liver CT images used in the second 2D numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China

    Ziwei Nie, Chen Li & Xiaoping Yang

  2. School of Science, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Hairong Liu

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  1. Ziwei Nie
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  2. Chen Li
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  4. Xiaoping Yang
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Correspondence to Ziwei Nie or Xiaoping Yang.

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This work is financially supported by National Natural Science Foundation of China (Grant Nos. 11971229, 12090023)

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Nie, Z., Li, C., Liu, H. et al. A Variational Model for Deformable Registration of Uni-modal Medical Images with Intensity Biases. J Math Imaging Vis 63, 1057–1068 (2021). https://doi.org/10.1007/s10851-021-01042-2

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