Adaptive FEM-based nonrigid image registration using truncated hierarchical B-splines

Aishwarya Pawar, Yongjie Zhang, Yue Jia, Xiaodong Wei, Timon Rabczuk, Chiu Ling Chan, Cosmin Anitescu

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework minimizes an energy functional using an FEM-based method and thus involves solving a large system of linear equations. This framework is carried out on a set of successively refined grids. However, due to the increased number of control points during subdivision, large linear systems are generated which are generally demanding to solve. Instead of using uniform subdivision, an adaptive local refinement scheme is carried out, only refining the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency. The performance of the proposed method is demonstrated on 2D synthetic and medical images.

Original languageEnglish
Pages (from-to)2028-2040
Number of pages13
JournalComputers and Mathematics with Applications
Volume72
Issue number8
DOIs
Publication statusPublished - 2016 Oct 1

Bibliographical note

Funding Information:
The medical images were provided from ( http://overcode.yak.net/15 ). The research at Carnegie Mellon University was supported in part by NSF CAREER Award OCI-1149591 . The research at Bauhaus University Weimar was supported in part by the ITN-INSIST and ERC-COMBAT funded by the EU-FP7 ( PITN-GA-2011-289361 ).

Publisher Copyright:
© 2016 Elsevier Ltd

Keywords

  • Adaptive local refinement
  • Finite Element Method
  • Nonrigid image registration
  • Truncated hierarchical B-splines

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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