Docteur de l'université Automatic Segmentation and Shape Analysis ...

56 Chapter 3 Hippocampal segmentation using multiple atlases
search for a solution path to an efficient combination of the registration results in
addition to the similarity criteria.
3.3.1 MMR re-ranking
MMR criterion was introduced in the field of information retrieval to reduce the
redundancy in document summarization by taking diversity into consideration,
while still maintaining the relevance to the query (Carbonell and Goldstein, 1998).
Since MMR uses only the similarity measurement in re-ranking, it can be easily
translated into the context of atlas ranking and selection in multi-atlas based
segmentation. In MMR re-ranking, not only the image similarity between the
query and the transformed atlas is measured, the similarity between the atlas set
is also taken into account. We first define the atlas similarity, which is a symmetric
modification of the basic image similarity introduced in 3.1.2, and then describe
the MMR algorithm as it is applied to the atlas selection problem.
3.3.1.1 Atlas similarity and image similarity
The similarity between an atlas and the target image can be defined with trans-
formed atlas image after the registration, using NMI (3.10) as the similarity metric
Sim A
NMI(Ak, I) = NMI(Ik ◦ Tk, I). (3.20)
Respectively, when correlation coefficients (3.11) are used as the similarity metric,
we can define the measurement as
Sim A
C(Ak, I) = C(Ik ◦ Tk, I). (3.21)
This definition of Sim A
(·) is asymmetric (hence the superscript), since only the atlas
image is registered to the target. By performing mutual registration between the
atlases in the cross-validation of the atlas set, we obtain the transformation Tij and
Tji between every pair of two atlases, Ai and Aj. This enables us to symmetrize