Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint

Torsten Rohlfing, Calvin R. Maurer, David A. Bluemke, Michael A. Jacobs

Research output: Contribution to journalArticlepeer-review

344 Scopus citations


In this paper, we extend a previously reported intensity-based nonrigid registration algorithm by using a novel regularization term to constrain the deformation. Global motion is modeled by a rigid transformation while local motion is described by a free-form deformation based on B-splines. An information theoretic measure, normalized mutual information, is used as an intensity-based image similarity measure. Registration is performed by searching for the deformation that minimizes a cost function consisting of a weighted combination of the image similarity measure and a regularization term. The novel regularization term is a local volume-preservation (incompressibility) constraint, which is motivated by the assumption that soft tissue is incompressibility constraint is implemented by penalizing The incompressibility constraint is implemented by penalizing deviations of the Jacobian determinant of the deformation from unity. We apply the nonrigid registration algorithm with and without the incompressibility constraint to precontrast and post-contrast magnetic resonance (MR) breast images from 17 patients. Without using a constraint, the volume of contrast-enhancing lesions decreases by 1%-78% (mean 26%). Image improvement (motion artifact reduction) obtained using the new constraint is compared with that obtained using a smoothness constraint based on the bending energy of the coordinate grid by blinded visual assessment of maximum intensity projections of subtraction images. For both constraints, volume preservation improves, and motion artifact correction worsens, as the weight of the constraint penalty term increases. For a given volume change of the contrast-enhancing lesions (2% of the original volume), the incompressibility constraint reduces motion artifacts better than or equal to the smoothness constraint in 13 out of 17 cases (better in 9, equal in 4, worse in 4). The preliminary results suggest that incorporation of the incompressibility regularization term improves intensity-based free-form nonrigid registration of contrast-enhanced MR breast images by greatly reducing the problem of shrinkage of contrast-enhancing structures while simultaneously allowing motion artifacts to be substantially reduced.

Original languageEnglish (US)
Pages (from-to)730-741
Number of pages12
JournalIEEE transactions on medical imaging
Issue number6
StatePublished - Jun 2003


  • B-splines
  • Contrast-enhanced magnetic resonance (MR) breast images
  • Free-form deformation
  • Mutual information
  • Nonrigid registration
  • Volume preservation

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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