Free-Form Deformation Using Lower-Order B-spline for Nonrigid Image Registration

  • Wei Sun
  • Wiro J. Niessen
  • Stefan Klein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8673)


In traditional free-form deformation (FFD) based registration, a B-spline basis function is commonly utilized to build the transformation model. As the B-spline order increases, the corresponding B-spline function becomes smoother. However, the higher-order B-spline has a larger support region, which means higher computational cost. For a given D-dimensional nth-order B-spline, an mth-order B-spline where (m ≤ n) has \((\frac{m+1}{n+1})^{D}\) times lower computational complexity. Generally, the third-order B-spline is regarded as keeping a good balance between smoothness and computation time. A lower-order function is seldom used to construct the deformation field for registration since it is less smooth. In this research, we investigated whether lower-order B-spline functions can be utilized for efficient registration, by using a novel stochastic perturbation technique in combination with a postponed smoothing technique to higher B-spline order. Experiments were performed with 3D lung and brain scans, demonstrating that the lower-order B-spline FFD in combination with the proposed perturbation and postponed smoothing techniques even results in better accuracy and smoothness than the traditional third-order B-spline registration, while substantially reducing computational costs.


Registration Method Nonrigid Registration Registration Accuracy Stochastic Gradient Descent Target Registration Error 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Wei Sun
    • 1
  • Wiro J. Niessen
    • 1
    • 2
  • Stefan Klein
    • 1
  1. 1.Biomedical Imaging Group RotterdamErasmus MCRotterdamThe Netherlands
  2. 2.Department of Image Science and Technology, Faculty of Applied SciencesDelft University of TechnologyDelftThe Netherlands

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