Diffusion Tensor Image Registration Using Tensor Geometry and Orientation Features* Jinzhong Yang1, Dinggang Shen1,2, Christos Davatzikos1, and Ragini Verma1
1 Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA 19104
{Jinzhong.Yang, Dinggang.Shen, Christos.Davatzikos,
Ragini.Verma}@uphs.upenn.edu
2 Department of Radiology and Biomedical Rearch Imaging Center,
University of North Carolina, Chapel Hill, NC 27510
dgshen@med.unc.edu
Abstract. This paper prents a method for deformable registration of diffusion
tensor (DT) images that integrates geometry and orientation features into a hier-
worry的过去式archical matching framework. The geometric feature is derived from the struc-
tural geometry of diffusion and characterizes the shape of the tensor in terms of
prolateness, oblateness, and sphericity of the tensor. Local spatial distributions
of the prolate, oblate, and spherical geometry are ud to create an attribute vec-
tor of geometric feature for matching. The orientation feature improves the
matching of the WM fiber tracts by taking into account the statistical informa-
tion of underlying fiber orientations. The features are incorporated into a北京朝阳外国语学校
hierarchical deformable registration framework to develop a diffusion tensor
image registration algorithm. Extensive experiments on simulated and real brain
DT data establish the superiority of this algorithm for deformable matching of
diffusion tensors, thereby aiding in atlas creation. The robustness of the method
makes it potentially uful for group-bad analysis of DT images acquired in
large studies to identify dia-induced and developmental changes.
Keywords: Diffusion tensor imaging, structural geometry, tensor orientation,
attribute vector, deformable registration.
1 Introduction
Diffusion tensor imaging (DTI) has emerged as a powerful and effective technique for analyzing the underlying white matter structure of brains [1]. DTI provides unique micro-structural and physiological insight into white matter tissue of brains, which in turn facilitates the study of development, aging, and dia on specific white matter regions of interest. In order to carry out group-bad analysis and statistics, it is im-perative to make different subjects comparable, thus requiring the spatial normaliza-tion of diffusion tensor (DT) images. However, spatial normalization of DT images is *This work was supported by the National Institute of Health via grants R01-MH-070365 and R01-MH-079938.
D. Metaxas et al. (Eds.): MICCAI 2008, Part II, LNCS 5242, pp. 905–913, 2008.
© Springer-Verlag Berlin Heidelberg 2008
906 J. Yang et al.
rendered challenging by the fact that the data reprentation is high dimensional and it requires not only the spatial warping, but also the tensor reorientation at each voxel
[2, 3]. Recent advances in DT image registration either employed a combination of different scalar maps derived from full tensor image for a multi-channel registration
[4], or developed registration algorithms bad on the full tensor similarity measure-ments [5, 6]. However, spatial normalization bad on features extracted from full tensors has not been extensively rearched yet. An earlier study applied oriented 3-D Gabor features extracted from tensors for matching [7], while a recent method em-ployed major fiber bundles to align tensors[8]. Both methods demonstrate that regis-tration can be improved in the white matter if features that characterize both tensor shape and orientation are ud for matching with carefully chon metrics.
In this paper, we apply tensor geometry and orientation features to DTI registra-tion. We capitalize on the structural geometry of diffusion tensor [9] and develop a novel attribute vector consisting of geometric moments computed from the local spa-tial histograms of tensor geometric measures. This attribute vector is rotationally in-variant, and integrates spatial information from local histograms computed at different scales. In order to improve the registration accuracy of white matter (WM) fiber
tracts, we also incorporate the local statistical information of underlying fiber orienta-tions for feature matching. The features provide richer anatomical information than merely using voxel’s tensor by integrating anisotropy, shape, and orientation from an entire neighborhood of a voxel. We include the features into a hierarchical deform-able registration technique on the lines of [10], to develop a deformable registration method for diffusion tensor images. Extensive experiments demonstrate the robust-ness and accuracy of DT image registration using the features.
2 Methods
Let 0321≥≥≥λλλ be the three eigenvalues of a symmetric tensor D , and i e
ˆ be the normalized eigenvector corresponding to i λ, then the tensor D can be denoted by
T T T 333222111ˆˆˆˆˆˆe e e e e e D λλλ++=. (1)
Geometrically, tensor D can be reprented by an ellipsoid with three axes oriented along its three eigenvectors, and three mi-axis lengths proportional to the square root of its three eigenvalues. Different shapes of the ellipsoid give ri to three geo-metric structures of diffusion tensors: prolate (linear) structure, in which diffusion is
mainly in the direction corresponding to 1ˆe
; oblate (planar) structure, in which diffu-sion is restricted to a plane spanned by 1ˆe
and 2ˆe ; and spherical structure with iso-tropic diffusion. Three geometric measures were propod in [9] to describe how clo the diffusion tensor is to the generic structures of prolateness, oblateness, and sphericity. They are respectively defined as
捉弄上司13132121,,λλλλλλλλ=−=−=s p l c c c . (2)
DT Image Registration Using Tensor Geometry and Orientation Features 907
2.1 Tensor Geometric Feature for Matching
A discriminative attribute vector is defined at each voxel from the geometric meas-ures in (2). This attribute vector characterizes the local diffusion property by combin-ing the local distributions of prolate, oblate, and spherical structures. For a specified voxel v , local histograms )(v l h of l c , )(v p h of p c , and )(v s h of s c are computed from a spherical neighborhood region of voxel v with a given appropriate radius r . The histograms roughly characterize the distribution of the tensor geometry in the neighborhood region. For each histogram, we compute its regular geometric momen
ts as the statistical geometric features, i.e.
;,,,),(),(s p l k i v i n v m i k n k ==∑h (3)
where )
,(i v k h is the frequency of index i in histogram )(v k h , and ),(n v m k is the n th order moment of this histogram. Low-order geometric moments are ud to repre-nt the geometric features for a histogram and form a vector as
.,,},
2,1,0|),({)(s p l k n n v m v k hist
k ===a (4) In order to improve the accuracy of matching, we include the edge strength )(v b edge
FA of fractional anisotropy (FA) and the edge strength )(v b edge ADC of apparent dif-fusion coefficient (ADC) into the attribute vector. The edge attributes are computed by a Canny edge detector [11] from FA and ADC scalar maps of DT image respec-tively. Therefore, the complete attribute vector at voxel v can be reprented as
ap培训)](),(),(),(),([)(v b v b v v v v edge ADC edge FA hist s hist
p hist l a a a a =. (5)
The attribute vector defined in (5) is rotationally invariant, which makes it attrac-tive for registration. To make the feature vector more discriminative, the above attrib-ute vector is computed at three different scales so that both global and local geometric features are accounted for. In each scale, the similarity of two attribute vectors, )(u a
and )学习电脑
(v a , of two points, u and v , is defined as ()∏−−=i i i v u v u m |)()(|1))(),((a a a a ,
(6)
where )
(⋅i a is the i th element in the attribute vector. Due to the redundancy between l c , p c , and s c , we normally discard the 0th and 1st order geometric moments derived from p c when computing the similarity in (6).
id是什么意思
We demonstrate the discrimination of the propod attribute vector of geometric feature in Figs. 1 and 2 by comparing it with the FA feature [10] for diffusion tensor matching. Both points in major fiber tracts and small tracts have been examined. From the color-coded maps of similarities illustrated in Figs. 1 and 2, we can con-clude that the geometric feature is much more discriminative than just using FA fea-ture on both major and small fiber tracts (even on a single scale), with geometric fea-ture being far superior on the smaller tracts.
908 J. Yang et al.
familiar用法2.2 Fiber Orientation Feature for Matching
Properly aligning WM fiber tracts is a major concern in DTI registration. In order to further improve the registration accuracy of WM fiber tracts, we incorporate the local statistical information of underlying fiber orientations into the attribute vector defined in (5). The fiber orientation at voxel v is approximated by the principal direction (PD) of tensor D weighted by the FA value at this voxel. Local spatial distribution of PD in the 3D space at voxel v , denoted by )(v PD H , can be estimated from the samples in a spherical neighborhood region with a radius r . The similarity of two points, u and v , in terms of local PD distribution is characterized by entropy cross correlation (ECC) [12], a normalized form of mutual information, as
[][][])()()(),(22),(v E u E v u E v u ECC PD PD PD PD PD H H H H +−=, (7)
where E denotes the joint or marginal differential entropy of the random variables of local PD distribution. The similarity with the orientation features at points u and v is then determined by the combination of Eqs. (6) and (7) as
),())(),((),(v u ECC v u m v u M PD ⋅=a a . (8)
西安少儿英语
呼吁英文
(a) (b) (c) (d) (e) Fig. 1. Similarity of the points on major fiber tracts. The attribute vector of the crosd point in (a) is compared with the attribute vectors of other points in the image. (b) and (c) show the re-sulting map of similarities using the geometric feature computed at a coar scale and a fine scale, respectively. (d) and (e) show the resulting map of similarities using the FA feature com-puted at a coar scale and a fine scale, respectively. Red indicates high similarity.
(a) (b) (c) (d) (e)
Fig. 2. Similarity of the points on small fiber tracts. Legends are the same as tho in Fig. 1.
DT Image Registration Using Tensor Geometry and Orientation Features 909 ),(v u M ranges from 0 to 1 where 1 indicates the most similar features. Since the PD of a tensor is meaningful only in high anisotropic anatomies such as WM fiber tracts, we consider the matching of orientation feature only for voxels with a high FA value.
2.3 Deformable Registration with Geometry and Orientation Features
The attribute vector of tensor geometry and orientation features described above is ud in conjunction with the deformable techniques on the lines of the intensity histogram bad HAMMER algorithm [10] to develop a DTI registration algorithm. In this algo-rithm, the input DT images are pre-registered linearly. In a first step, only the geometric feature is ud for registration. Features are extracted once and not recalculated during registration, which requires features being rotationally invariant. Next, both tensor ge-ometry and orientation features are included in registration. It rves to further refine the matching of WM fiber tracts. Due to the orientation feature applied, feature extraction is performed in each iteration and the tensors are warped and reoriented accordingly. The
deformation field obtained as part of the spatial warping is ud to determine the tensor reorientation, bad on a spatially adaptive procedure that estimates the underlying fiber orientation [2], to produce properly reoriented tensors.
This algorithm employs a hierarchical structure to lect distinct features, thus re-ducing ambiguity in finding correspondences. The edge strengths of FA and ADC maps are the criteria for choosing active points to drive the registration. In the initial stages of matching, only a few points with high edge strength are lected for match-ing in order to avoid local minima. As the matching progress, more and more points with lower edge strengths become reliable and thus are lected to drive the registra-tion. This hierarchical structure assists in achieving a robust and accurate registration. 3 Results
We have demonstrated the high matching accuracy of the geometric feature in differ-ent parts of the white matter fiber tracts in Figs. 1 and 2. In this ction, we applied our method to register both human brains and mou brains to demonstrate the effi-ciency of our method by comparing with two alternative deformable registration algo-rithms, intensity histogram bad HAMMER [10] and Demons algorithm [13], when applied to FA maps. For the sake of simplicity and fairness, we compare FA feature-bad registration with the geometric feature, establishing the superiority of the l
atter. In the next stage we also demonstrate that the orientation feature together with the geometric feature improves the matching of the WM fiber tracts.
日语歌词3.1 Matching Accuracy Comparison: Geometric Feature and FA Feature
Ten simulated human brain DT images are generated by applying ten simulated de-formation fields [14] to warp a real DT image that is regarded as the template. The ten simulated DT images are then registered back to the template space by our method using geometric feature and the intensity histogram bad HAMMER using FA fea-ture, respectively. The deformation errors between the registration results and the
