Groupwise image registration based on a total correlation dissimilarity measure for quantitative MRI and dynamic imaging data

Abstract

The most widespread technique used to register sets of medical images consists of selecting one image as fixed reference, to which all remaining images are successively registered. This pairwise scheme requires one optimization procedure per pair of images to register. Pairwise mutual information is a common dissimilarity measure applied to a large variety of datasets. Alternative methods, called groupwise registrations, have been presented to register two or more images in a single optimization procedure, without the need of a reference image. Given the success of mutual information in pairwise registration, we adapt one of its multivariate versions, called total correlation, in a groupwise context. We justify the choice of total correlation among other multivariate versions of mutual information, and provide full implementation details. The resulting total correlation measure is remarkably close to measures previously proposed by Huizinga et al. based on principal component analysis. Our experiments, performed on five quantitative imaging datasets and on a dynamic CT imaging dataset, show that total correlation yields registration results that are comparable to Huizinga's methods. Total correlation has the advantage of being theoretically justified, while the measures of Huizinga et al. were designed empirically. Additionally, total correlation offers an alternative to pairwise mutual information on quantitative imaging datasets.

Figure 1

Registration results for a CT-LUNG dataset. The images denoted ‘2’ and ‘3’ stack the voxel information of G = 10 images at the locations defined by the dotted lines drawn in the image denoted ‘1’ (vertical line: ‘2’, horizontal line: ‘3’).

Figure 2

Tissue maps generated before image registration (top), after image registration with ${\mathcal{D}}_{\mathrm{PCA2}}$ (middle), and after image registration with ${\mathcal{D}}_{\mathrm{TC}}$ (bottom). The fitted values are shown in the myocardium for T1MOLLI-HEART, in the carotid artery wall for T1VFA-ABDOMEN, in the spleen for ADC-ABDOMEN, in the brain parenchyma for DTI-BRAIN, and in the pancreas for DCE-ABDOMEN. Slight visual changes between the tissue maps obtained with ${\mathcal{D}}_{\mathrm{PCA2}}$ and ${\mathcal{D}}_{\mathrm{TC}}$ are identified by green arrows.

Figure 3

Cumulative distribution functions for one subject of the six image datasets (aligned case). The observed CDF (blue) is compared with the theoretical CDF of a chi-square distribution with G degrees of freedom (red).

Figure 4

Average time per iteration with respect to the number of B-spline control points per image (a), the number of images G (b), and the number of spatial samples (c).

Figure 5

(a) Pairwise registration scheme (the orange frame indicates that this method requires the selection of a reference image), (b) semi-groupwise registration scheme proposed by Seghers et al., and (c) groupwise registration scheme.

Figure 6

Venn diagram representations for three images M₁, M₂ and M₃. (a) The green, red and cyan circle represent the entropy of each image. The fact that the images share information is symbolized by the fact that these circles overlap. Subfigures (b), (c) and (d) were constructed based on Equations (3), (5) and (6). In (c), the dark greay area signifies that its contribution to the dissimilarity measure is twice as high as the contribution of each light-grey area.