Abstract
—Spatial normalization plays a key role in
voxel-based analyses of diffusion tensor images (DTI). We
propose a highly accurate algorithm for high-dimensional spatial
normalization of DTI data based on the technique of 3D optical
flow. The theory of conventional optic flow assumes consistency
of intensity and consistency of the gradient of intensity under a
constraint of discontinuity-preserving spatio-temporal
smoothness. By employing a hierarchical strategy ranging from
coarse to fine scales of resolution and a method of
Euler-Lagrange numerical analysis, our algorithm is capable of
registering DTI data. Experiments using both simulated and real
datasets demonstrated that the accuracy of our algorithm is
better not only than that of those traditional optical flow
algorithms or using affine alignment, but also better than the
results using popular tools such as the statistical parametric
mapping (SPM) software package. Moreover, our registration
algorithm is fully automated, requiring a very limited number of
parameters and no manual intervention.
I.
I
NTRODUCTION
any methods in image analysis have been developed to
tackle DTI registration based on the strategy of how to
set up the correspondence between two subjects, a
strategy that generally falls into one of two categories. The
first involves feature-based matching, i.e. transformations that
are calculated based on a number of anatomical
correspondences established manually, semi-automatically, or
fully automatically on a number of distinct anatomical
features, including distinct landmarks [1,2] or a combination
of curves and surfaces, such as sulci and gyri [3,4,5]. In
addition, finding anatomical correspondences is a key to the
success of the spatial normalization. To find anatomical
correspondences, conventional methods generally first extract
scalar features from each tensor individually; and then by
constructing scalar maps, regional integration and other
operations such as edge detection, a final set of features for
correspondence matching can be constituted. For example,
Manuscript received March 1, 2013. This work was supported by The
National Natural Science Foundation of China (No. 61273261 & 91232701),
Shanghai Pujiang Program (No. 12PJ1402800), Shanghai Knowledge
Service Platform Project (No. ZF1213) and also was partly supported by
Shanghai Commission of Science and Technology (No. 10440710200) .
Ying Wen is with the department of computer science and technology,
East China Normal University, Shanghai, 200241, China (e-mail: ywen@
cs.ecnu.edu.cn).
Bradley S. Peterson is with the Brain Imaging Laboratory/MRI Unit,
Department of Psychiatry, Columbia University, New York, NY, 10032,
USA (e-mail: petersob@nyspi.columbia.edu).
Dongrong Xu is with the Brain Imaging Laboratory/MRI Unit,
Department of Psychiatry, Columbia University, New York, NY, 10032,
USA (phone:2125435495; fax:2125430522; e-mail:dx2013@columbia.edu)
Timer [6] and F-Timer [7] were developed based on Hammer
[8], which adopts so-called driving voxels in addition to
geometric moments as the features upon which registration is
based. The boundary-based registration uses the measure of
the thickness of cortex in T1-weighted image [9]; Yang et al.
guided their registration using information on a tensor’s
structural geometry and orientation [10]; and Xue et al.
proposed a local fast marching method for DTI registration
[11]. These landmark-based methods numerically seek
optimal transformations (under respective model-specific
assumptions) to maximize similarity across brains.
The second category of registration methods is based on
volumetric transformations between one brain image and a
template image. These methods assume that the images are
acquired using the same pulse sequence [12,13,14] and these
methods therefore are generally more efficient, because they
do not require the construction of a specific anatomical model
using anatomic landmarks. Christensen et al [15] proposed a
viscous fluid flow model to implement registration. Unlike
fluid flow, optical flow is another volumetric transformation
method. The technique of optical flow developed in computer
vision for object tracking [16,17] is one such method. The two
approaches differ with the constraints in their
implementations. The former adopts viscous constraints and
body force while the latter adopts gradient and smooth
constants and Taylor expansion. Most of the prevailing
approaches for DTI normalization, for example, the
preservation of principal direction (PPD) [18], the
Procrustean normalization method [19,20], actually make use
of the registration method for conventional scalar images to
calculate the voxel correspondence across two imaging spaces,
following which an additional step is required to properly
reorient the tensors. Although these methods work well, they
do not yet fully consider the characteristics of DTI data, and
the 2-step schemas are computationally inefficient. Therefore,
a method for spatial normalization of DTI data that takes
advantage of optic flow would be highly attractive to the
neuroimaging community.
We propose in this work a novel approach for DTI
normalization using optical flow. We first extend the
traditional 2D optic flow to a 3D form, and then incorporate it
into a hierarchical framework that is applied to imaging data
in multiple resolution scales from coarse to fine, thereby
building up a registration approach with high accuracy.
II.
M
ATERIAL AND
M
ETHODS
A.
Data Acquisition
We acquired all the human Diffusion-Weighted Imaging
A Highly Accurate, Optical Flow -Based Algorithm for Nonlinear
Spatial Normalization of Diffusion Tensor Images
Ying Wen, Bradley S. Peterson, Dongrong Xu