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Published in:
2015 | OriginalPaper | Chapter
A Liver Atlas Using the Special Euclidean Group
Authors : Mohamed S. Hefny, Toshiyuki Okada, Masatoshi Hori, Yoshinobu Sato, Randy E. Ellis
Published in: Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2015
Publisher: Springer International Publishing
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An atlas is a shape model derived using statistics of a population. Standard models treat local deformations as pure translations and apply linear statistics. They are often inadequate for highly variable anatomical shapes. Non-linear methods has been developed but are generally difficult to implement.
This paper proposes encoding shapes using the special Euclidean group
$\mathbb{SE}(3)$
for model construction.
$\mathbb{SE}(3)$
is a Lie group, so basic linear algebra can be used to analyze data in non-linear higher-dimensional spaces. This group represents non-linear shape variations by decomposing piecewise-local deformations into rotational and translational components.
The method was applied to 49 human liver models that were derived from CT scans. The atlas covered 99% of the population using only three components. Also, the method outperformed the standard method in reconstruction. Encoding shapes as ensembles of elements in the
$\mathbb{SE}(3)$
group is a simple way of constructing compact shape models.