Attribute vector guided groupwise registration

Abstract

Groupwise registration has been recently introduced to simultaneously register a group of images by avoiding the selection of a particular template. To achieve this, several methods have been proposed to take advantage of information-theoretic entropy measures based on image intensity. However, simplistic utilization of voxelwise image intensity is not sufficient to establish reliable correspondences, since it lacks important contextual information. Therefore, we explore the notion of attribute vector as the voxel signature, instead of image intensity, to guide the correspondence detection in groupwise registration. In particular, for each voxel, the attribute vector is computed from its multi-scale neighborhoods, in order to capture the geometric information at different scales. The probability density function (PDF) of each element in the attribute vector is then estimated from the local neighborhood, providing a statistical summary of the underlying anatomical structure in that local pattern. Eventually, with the help of Jensen-Shannon (JS) divergence, a group of subjects can be aligned simultaneously by minimizing the sum of JS divergences across the image domain and all attributes. We have employed our groupwise registration algorithm on both real (NIREP NA0 data set) and simulated data (12 pairs of normal control and simulated atrophic data set). The experimental results demonstrate that our method yields better registration accuracy, compared with a popular groupwise registration method.

Fig. 1

An attribute vector is the signature of a given voxel (as ^①). The local pattern of an attribute is estimated from the neighborhood centered at location x, and described in the probabilistic fashion (as ^②).

Fig. 2

Non-uniform sampling is applied, and a subset of voxel locations is drawn and overlaid on the original slice in (a). Initially, only the red voxels in (a) will be sampled to drive the registration. As registration progresses, more and more voxels indicated in green and blue, will gradually take part in the registration. It is worth noting that most sampled voxels are located at the boundaries of prominent anatomical structures, as indicated by the importance map for the non-uniform sampling, as shown in (b).

Fig. 3

A typical slice (a) from the NA0 dataset, and its manual anatomical labels (b): Different colors indicate different manually delineated anatomical structures.

Fig. 4

Comparison of histograms of standard deviation volumes in (a) and the produced mean images in (b). The 3D rendering views of standard deviation volumes in (a) confirm that the attribute vector guided groupwise registration leads to lower intensity residual errors than the registration guided by intensity alone. In (b), a typical cortical/sub-cortical slice as well as the 3D rending of the mean image yielded by our method (in blue box) show more abundant details than that of the intensity guided method (in red box).

Fig. 5

L/R-PCG overlap probability maps of the intensity guided method (left) and the attribute vector guided method (right). It can be observed that the latter yields higher label consistency.

Fig. 6

The overlap ratios of 32 manually labeled ROIs by both the intensity guided and the attribute vector guided groupwise registration methods are shown in red and blue, respectively. Besides the mean ratio, the standard deviation is also plotted as error-bar for each label. Our method produces better label overlaps for all 32 labels and achieves more consistent registration results.

Fig. 7

For each label, the specificity and the sensitivity are plotted in left panel and right panel, respectively. For each label, values for both the left (top) and right (bottom) hemispheres are plotted. The cross symbol indicates mean specificity/sensitivity, and the length of the bar shows the standard deviation.

Fig. 8

Seven selected subjects are shown at the same slice after registration via (a) the intensity guided method and (b) the attribute vector guided method, respectively. Ventricles in row (b) are more similar to each other than those in row (a), especially for the locations indicated by arrows.

Fig. 9

Control images, and simulated images with atrophy introduced to the pre-central gyrus (PCG) in (a) and the superior temporal gyrus (STG) in (b). The difference between the control image and the atrophic image is provided in the bottom. Note that the contrast of the two differences has been adjusted, for better visual inspection.

Fig. 10

Random perturbations (left-right) are applied to the image in (a), to generate a set of simulated images. Normalized stack entropies of both intensity and gradient magnitude at the sampling voxel are shown in (b). The corresponding normalized JS divergence curves are displayed in (c). The arithmetic average curves (green) are the means of the red and the blue curves. This result shows the importance of using the JS divergence in improving the performance of the groupwise registration.