title: Intensity-based hierarchical elastic registration using approximating splines.
abstract: OBJECTIVE
  We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces.
  
  
  METHODS
  The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model.
  
  
  RESULTS
  The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method.
  
  
  CONCLUSIONS
  The proposed hierarchical elastic image registration approach incorporates the GEBS approximation scheme extended with anisotropic landmark localization uncertainties as well as rotation information. Our experimental results show that the proposed scheme improved the registration result significantly.
authors.affiliation: Faculty of Electrical Engineering, University of Tuzla, Tuzla, Bosnia and Herzegovina, amira.serifovic@untz.ba.
authors.forename: Amira
authors.initials: A
authors.lastname: Serifovic-Trbalic
authors.forename: Damir
authors.initials: D
authors.lastname: Demirovic
authors.forename: Philippe C
authors.initials: PC
authors.lastname: Cattin
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D001943:Breast Neoplasms / Q000175:diagnosis*; D004548:Elasticity; D005260:Female; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008327:Mammography / Q000379:methods*; D015203:Reproducibility of Results