Abstract
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.
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Hefny, M.S., Okada, T., Hori, M., Sato, Y., Ellis, R.E. (2015). A Liver Atlas Using the Special Euclidean Group. In: Navab, N., Hornegger, J., Wells, W., Frangi, A. (eds) Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2015. MICCAI 2015. Lecture Notes in Computer Science(), vol 9350. Springer, Cham. https://doi.org/10.1007/978-3-319-24571-3_29
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