title: A matrix lie group approach to statistical shape analysis of bones.
abstract: Statistical shape models using a principal-component analysis are inadequate for studying shapes that are in non-linear manifolds. Principal tangent components use a matrix Lie group that maps a non-linear manifold to a corresponding linear tangent space. Computations that are performed on the tangent space of the manifold use linear statistics to analyze non-linear shape spaces. The method was tested on bone surface from proximal femurs. Using only three components, the new model recovered 94% of the medical dataset, whereas a conventional method that used linear principal components needed 24 components to achieve the same reconstruction accuracy.
authors.affiliation: School of Computing, Queen's University, Kingston, Ontario, Canada.
authors.forename: Mohamed S
authors.initials: MS
authors.lastname: Hefny
authors.affiliation: Kingston General Hospital, Kingston, Ontario, Canada.
authors.forename: John F
authors.initials: JF
authors.lastname: Rudan
authors.affiliation: School of Computing, Queen's University, Kingston, Ontario, Canada.
authors.forename: Randy E
authors.initials: RE
authors.lastname: Ellis
mesh_terms: D000465:Algorithms; D001842:Bone and Bones / Q000033:anatomy & histology*; D003198:Computer Simulation; D021621:Imaging, Three-Dimensional; D008953:Models, Anatomic