Symmetric Data Attachment Terms for Large Deformation Image Registration

Nonrigid medical image registration between images that are linked by an invertible transformation is an inherently symmetric problem. The transformation that registers the image pair should ideally be the inverse of the transformation that registers the pair with the order of images interchanged. This property is referred to as symmetry in registration or inverse consistent registration. However, in practical estimation, the available registration algorithms have tended to produce inverse inconsistent transformations when the template and target images are interchanged. In this paper, we propose two novel cost functions in the large deformation diffeomorphic framework that are inverse consistent. These cost functions have symmetric data-attachment terms; in the first, the matching error is measured at all points along the flow between template and target, and in the second, matching is enforced only at the midpoint of the flow between the template and target. We have implemented these cost functions and present experimental results to validate their inverse consistent property and registration accuracy.

[1]  Paul M. Thompson,et al.  Inverse Consistent Mapping in 3D Deformable Image Registration: Its Construction and Statistical Properties , 2005, IPMI.

[2]  Pengcheng Shi,et al.  Stochastic Inverse Consistency in Medical Image Registration , 2005, MICCAI.

[3]  Karl J. Friston,et al.  Image registration using a symmetric prior—in three dimensions , 1999, Human brain mapping.

[4]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Brian B. Avants,et al.  Symmetric Diffeomorphic Image Registration: Evaluating Automated Labeling of Elderly and Neurodegenerative Cortex and Frontal Lobe , 2006, WBIR.

[6]  Gary E. Christensen,et al.  Consistent image registration , 2001, IEEE Transactions on Medical Imaging.

[7]  R. Bajcsy,et al.  A computerized system for the elastic matching of deformed radiographic images to idealized atlas images. , 1983, Journal of computer assisted tomography.

[8]  Fabrice Heitz,et al.  A Topology Preserving Non-rigid Registration Method Using a Symmetric Similarity Function-Application to 3-D Brain Images , 2004, ECCV.

[9]  Alain Trouvé,et al.  Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms , 2005, International Journal of Computer Vision.

[10]  Gary E. Christensen,et al.  Consistent Linear-Elastic Transformations for Image Matching , 1999, IPMI.

[11]  Anand Rangarajan,et al.  Simultaneous Nonrigid Registration of Multiple Point Sets and Atlas Construction , 2006, ECCV.

[12]  Alain Trouvé,et al.  The Euler-Lagrange Equation for Interpolating Sequence of Landmark Datasets , 2003, MICCAI.

[13]  Karl J. Friston,et al.  High-Dimensional Image Registration Using Symmetric Priors , 1999, NeuroImage.

[14]  L. Younes,et al.  On the metrics and euler-lagrange equations of computational anatomy. , 2002, Annual review of biomedical engineering.

[15]  Benoit M. Dawant,et al.  Morphometric analysis of white matter lesions in MR images: method and validation , 1994, IEEE Trans. Medical Imaging.

[16]  Laurent Younes,et al.  Geodesic Interpolating Splines , 2001, EMMCVPR.

[17]  R. Rabbitt,et al.  3D brain mapping using a deformable neuroanatomy. , 1994, Physics in medicine and biology.

[18]  L. R. Dice.  Measures of the Amount of Ecologic Association Between Species , 1945 .

[19]  L. Younes.  Jacobi fields in groups of diffeomorphisms and applications , 2007 .

[20]  Paul Dupuis,et al.  Variational problems on ows of di eomorphisms for image matching , 1998 .

[21]  David Rey,et al.  Symmetrization of the Non-rigid Registration Problem Using Inversion-Invariant Energies: Application to Multiple Sclerosis , 2000, MICCAI.

[22]  Hemant D. Tagare,et al.  Symmetric, transitive, geometric deformation and intensity variation invariant nonrigid image registration , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).

[23]  Stanislav Kovacic,et al.  Symmetric image registration , 2003, SPIE Medical Imaging.

[24]  Gary E. Christensen,et al.  Consistent landmark and intensity-based image registration , 2002, IEEE Transactions on Medical Imaging.

[25]  Gary E. Christensen,et al.  Large Deformation Inverse Consistent Elastic Image Registration , 2003, IPMI.