Large Deformation Diffeomorphic Metric Mapping of Orientation Distribution Functions

We propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by Orientation Distribution Functions (ODF). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. We first extend ODFs traditionally defined in a unit sphere to a generalized ODF defined in R3. This makes it easy for an affine transformation as well as a diffeomorphic group action to be applied on the ODF. We then construct a Riemannian space of the generalized ODFs and incorporate its Riemannian metric for the similarity of ODFs into a variational problem defined under the large deformation diffeomorphic metric mapping (LDDMM) framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the generalized ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.

[1]  Dinggang Shen,et al.  SPHERE: SPherical Harmonic Elastic REgistration of HARDI data , 2011, NeuroImage.

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

[3]  Anuj Srivastava,et al.  Riemannian Analysis of Probability Density Functions with Applications in Vision , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[4]  R. Deriche,et al.  Regularized, fast, and robust analytical Q‐ball imaging , 2007, Magnetic resonance in medicine.

[5]  Michael I. Miller,et al.  Large Deformation Diffeomorphic Metric Curve Mapping , 2008, International Journal of Computer Vision.

[6]  A. Dale,et al.  Quantitative Histological Validation of Diffusion MRI Fiber Orientation Distributions in the Rat Brain , 2010, PloS one.

[7]  Shun-ichi Amari,et al.  Differential-geometrical methods in statistics , 1985 .

[8]  Rachid Deriche,et al.  Riemannian Framework for Estimating Symmetric Positive Definite 4th Order Diffusion Tensors , 2008, MICCAI.

[9]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[10]  Christopher J. Taylor,et al.  Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009 , 2009, Lecture Notes in Computer Science.

[11]  G. Sapiro,et al.  Reconstruction of the orientation distribution function in single‐ and multiple‐shell q‐ball imaging within constant solid angle , 2010, Magnetic resonance in medicine.

[12]  Christophe Lenglet,et al.  A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry , 2011, NeuroImage.

[13]  T. Mareci,et al.  Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging , 2003, Magnetic resonance in medicine.

[14]  L. Frank.  Characterization of anisotropy in high angular resolution diffusion‐weighted MRI , 2002, Magnetic resonance in medicine.

[15]  Baba C. Vemuri,et al.  Non-rigid Registration of High Angular Resolution Diffusion Images Represented by Gaussian Mixture Fields , 2009, MICCAI.

[16]  Rachid Deriche,et al.  A Riemannian Framework for Orientation Distribution Function Computing , 2009, MICCAI.

[17]  Adam W Anderson,et al.  Spatial normalization of the fiber orientation distribution based on high angular resolution diffusion imaging data , 2009, Magnetic resonance in medicine.

[18]  Can Ceritoglu,et al.  Increasing the power of functional maps of the medial temporal lobe by using large deformation diffeomorphic metric mapping. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Baba C. Vemuri,et al.  Registration of High Angular Resolution Diffusion MRI Images Using 4 th Order Tensors , 2007, MICCAI.

[20]  Luke Bloy,et al.  Demons registration of high angular resolution diffusion images , 2010, 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[21]  P. Basser,et al.  Estimation of the effective self-diffusion tensor from the NMR spin echo. , 1994, Journal of magnetic resonance. Series B.

[22]  Gabor Fichtinger,et al.  Medical Image Computing and Computer-Assisted Intervention - MICCAI 2008, 11th International Conference, New York, NY, USA, September 6-10, 2008, Proceedings, Part I , 2008, International Conference on Medical Image Computing and Computer-Assisted Intervention.

[23]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[24]  Duan Xu,et al.  Q‐ball reconstruction of multimodal fiber orientations using the spherical harmonic basis , 2006, Magnetic resonance in medicine.

[25]  Baba C. Vemuri,et al.  Regularized positive-definite fourth order tensor field estimation from DW-MRI , 2009, NeuroImage.

[26]  Nicholas Ayache,et al.  Medical Image Computing and Computer-Assisted Intervention - MICCAI 2007, 10th International Conference, Brisbane, Australia, October 29 - November 2, 2007, Proceedings, Part I , 2007, MICCAI.

[27]  N. Čencov.  Statistical Decision Rules and Optimal Inference , 2000 .

[28]  Mark W. Woolrich,et al.  Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? , 2007, NeuroImage.

[29]  Yihong Yang,et al.  Diffeomorphic Image Registration of Diffusion MRI Using Spherical Harmonics , 2011, IEEE Transactions on Medical Imaging.