A Liver Atlas Using the Special Euclidean Group

  • Mohamed S. HefnyEmail author
  • Toshiyuki Okada
  • Masatoshi Hori
  • Yoshinobu Sato
  • Randy E. Ellis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9350)


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.


Statistical Shape Model Special Euclidean Group Lie Groups Lie Algebras Anatomical Atlas 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mohamed S. Hefny
    • 1
    Email author
  • Toshiyuki Okada
    • 2
  • Masatoshi Hori
    • 3
  • Yoshinobu Sato
    • 4
  • Randy E. Ellis
    • 1
  1. 1.Queen’s UniversityKingstonCanada
  2. 2.Tsukuba UniversityTsukubaJapan
  3. 3.Osaka UniversityOsakaJapan
  4. 4.Nara Institute of Science and TechnologyNaraJapan

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