Fig 1.
An illustration of Enhanced Hierarchical Unbiased Graph Shrinkage (eHUGS) method.
In this example, the images are clustered into 5 subgroups based on their similarity. Then a hierarchical graph is constructed with each low-level graph (indicated by solid lines) describing the image distribution in each subgroup, and each high-level graph (indicated by dashed lines) encodes the interaction between the subgroups. Groupwise registration is formulated as the dynamic shrinkage of this hierarchical graph.
Fig 2.
Illustration of images residing on a high dimensional manifold and connected via the geodesic paths.
The geodesic distances between image Ii and other images are shown by dash arrows.
Fig 3.
Registration via graph shrinkage.
At time t, all the images in the graph (denoted by blue points) are connected to each other by the geodesic path (denoted by blue dash lines). At time t+Δt, all the images are deformed according to their connected images through geodesic paths (denoted by purple dash lines). The deformed images (denoted by red points) become closer to each other and a new graph describing their relationship is generated (denoted by red dash lines).
Fig 4.
Image samples of elderly subjects obtained from the ADNI database.
In this figure, large variations across subjects can be observed.
Fig 5.
Clustering and graph construction.
(a) Images are clustered into 20 subgroups, represented with different markers and colors, by using affinity propagation. (b) Intra-subgroup (black color) and inter-subgroup (orange color) connections in the graph.
Table 1.
Computation times of the standard group-mean method, ABSORB, HUGS, and eHUGS on the elderly brain image dataset, obtained from ADNI.
Fig 6.
The box plots of Dice ratios of WM, GM and CSF for the elderly brain dataset (ADNI).
(a) Dice ratio produced by the standard group-mean method. (b) Dice ratio produced by ABSORB. (c) Dice ratio produced by HUGS. And (d) Dice ratio produced by eHUGS.
Table 2.
Dice ratios of WM, GM, CSF and all tissues, obtained by the standard group-mean method, ABSORB, HUGS, and eHUGS, respectively, for the elderly brain dataset (ADNI).
Fig 7.
Changes of Dice ratios with progress of groupwise registration for the elderly brain dataset (ADNI).
Fig 8.
Sample images of two subjects from the infant database.
We can observe large structural variation across subjects, and also large appearance variation across different images of same subject.
Fig 9.
Clustering and graph construction.
(a) Images are clustered into 2 subgroups, represented with different markers and colors, by using affinity propagation. (b) Intra-subgroup (black color) and inter-subgroup (orange color) connections in the graph.
Table 3.
Computation times of the standard group-mean method, ABSORB, HUGS, and eHUGS for the infant brain image dataset.
Fig 10.
The box plots of the Dice ratios of WM, GM and CSF for the infant dataset.
(a) By the standard group-mean method. (b) By ABSORB. (c) By eHUGS.
Table 4.
Dice ratios of WM, GM, CSF and all tissues, obtained by the standard group-mean method, ABSORB, and eHUGS, respectively, for the infant dataset.
Fig 11.
Changes of Dice ratios with progress of groupwise registration for the infant brain dataset.
Fig 12.
Illustration of the atlases of infant brains.
A-C are obtained by the standard group-mean method, ABSORB, and eHUGS, respectively. In each panel, from left to right are the mean image, and tissue probability maps for CSF, GM and WM, respectively.