A spline-based non-linear diffeomorphism for multimodal prostate registration

Jhimli Mitra, Zoltan Kato, Robert Martí, Arnau Oliver, Xavier Lladó, Désiré Sidibé, Soumya Ghose, Joan C. Vilanova, Josep Comet, Fabrice Meriaudeau

Research output: Contribution to journalArticle

35 Citations (Scopus)


This paper presents a novel method for non-rigid registration of transrectal ultrasound and magnetic resonance prostate images based on a non-linear regularized framework of point correspondences obtained from a statistical measure of shape-contexts. The segmented prostate shapes are represented by shape-contexts and the Bhattacharyya distance between the shape representations is used to find the point correspondences between the 2D fixed and moving images. The registration method involves parametric estimation of the non-linear diffeomorphism between the multimodal images and has its basis in solving a set of non-linear equations of thin-plate splines. The solution is obtained as the least-squares solution of an over-determined system of non-linear equations constructed by integrating a set of non-linear functions over the fixed and moving images. However, this may not result in clinically acceptable transformations of the anatomical targets. Therefore, the regularized bending energy of the thin-plate splines along with the localization error of established correspondences should be included in the system of equations. The registration accuracies of the proposed method are evaluated in 20 pairs of prostate mid-gland ultrasound and magnetic resonance images. The results obtained in terms of Dice similarity coefficient show an average of 0.980 ± 0.004, average 95% Hausdorff distance of 1.63 ± 0.48. mm and mean target registration and target localization errors of 1.60 ± 1.17. mm and 0.15 ± 0.12. mm respectively.

Original languageEnglish
Pages (from-to)1259-1279
Number of pages21
JournalMedical Image Analysis
Issue number6
Publication statusPublished - Aug 1 2012



  • Multimodal images
  • Non-linear registration
  • Prostate biopsy
  • Regularization
  • Thin-plate splines

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging
  • Computer Vision and Pattern Recognition
  • Health Informatics
  • Computer Graphics and Computer-Aided Design

Cite this

Mitra, J., Kato, Z., Martí, R., Oliver, A., Lladó, X., Sidibé, D., Ghose, S., Vilanova, J. C., Comet, J., & Meriaudeau, F. (2012). A spline-based non-linear diffeomorphism for multimodal prostate registration. Medical Image Analysis, 16(6), 1259-1279. https://doi.org/10.1016/j.media.2012.04.006