Signal, Image and Video Processing

, Volume 12, Issue 6, pp 1217–1225 | Cite as

A non-rigid image registration method based on multi-level B-spline and L2-regularization

  • Huizhong Ji
  • Yusen Li
  • Enqing DongEmail author
  • Peng Xue
  • Wenshuo Xiong
  • Wenyan Sun
  • Zhenchao Tang
  • Dejing ZhangEmail author
  • Wei Fang
Original Paper


To solve the problem that the cost function of the classic free-form deformation (FFD) cannot simulate transformation field of images with large elastic deformation or local distortion in image registration better, and to increase the registration accuracy and robustness, a new non-rigid image registration method based on the classic hierarchical FFD is proposed. Since the smooth term has a significant influence on registration accuracy, and its coefficient is not easy to be controlled in the classic hierarchical B-spline based FFD, a L2-regularization term with faster and more stable optimization is introduced in the cost function of the proposed model. By coordinating the coefficients of this regularization term and the smooth term, this novel L2-regularized FFD model is able to solve the problem of low registration accuracy caused by strong smooth constraint while maintaining the images topologies. The introduced L2-regularization term can impose a spatial constraint on the control lattices transformation field, and the over-registration problem can be suppressed to a certain extent, so it can register the images with local large distortion. A series of registration experiments of natural images and medical images show that the new method has an obvious advantage over the classic model in registration accuracy measured by mean square error.


Non-rigid image registration B-spline Free-form deformation L2-norm 



This work was supported by National Natural Science Foundation of China (Nos. 81371635 and 81671848), Key Research and Development Project of Shandong Province (No. 2016GGX101017), and Research Fund for the Doctoral Program of Higher Education of China (20120131110062).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Huizhong Ji
    • 1
  • Yusen Li
    • 1
  • Enqing Dong
    • 1
    Email author
  • Peng Xue
    • 1
  • Wenshuo Xiong
    • 1
  • Wenyan Sun
    • 1
  • Zhenchao Tang
    • 1
  • Dejing Zhang
    • 1
    Email author
  • Wei Fang
    • 2
  1. 1.School of Mechanical, Electrical and Information EngineeringShandong UniversityWeihaiChina
  2. 2.Department of CT-MRIYidu Central Hosptial of Weifang Medical CollegeShandongChina

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