Rigid motion invariant statistical shape modeling based on discrete fundamental forms: Data from the osteoarthritis initiative and the Alzheimer's disease neuroimaging initiative

@article{Ambellan2021RigidMI,
  title={Rigid motion invariant statistical shape modeling based on discrete fundamental forms: Data from the osteoarthritis initiative and the Alzheimer's disease neuroimaging initiative},
  author={Felix Ambellan and Stefan Zachow and Christoph von Tycowicz},
  journal={Medical image analysis},
  year={2021},
  volume={73},
  pages={
          102178
        }
}
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9 Citations
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9 Citations

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References

SHOWING 1-10 OF 60 REFERENCES

A Surface-Theoretic Approach for Statistical Shape Modeling

A novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free is presented, facilitating Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power.

An efficient Riemannian statistical shape model using differential coordinates: With application to the classification of data from the Osteoarthritis Initiative

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

  • X. Pennec
  • Mathematics
    Journal of Mathematical Imaging and Vision
  • 2006
This paper provides a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them and develops the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and χ2 law.

Principal geodesic analysis for the study of nonlinear statistics of shape

The method of principal geodesic analysis is developed, a generalization of principal component analysis to the manifold setting and demonstrated its use in describing the variability of medially-defined anatomical objects.

An Elasticity-Based Covariance Analysis of Shapes

A standard L2-type covariance metric with a metric based on the Hessian of the nonlinear elastic energy is compared and the dependence of the principal component analysis on the type of the underlying non linear elasticity is explored.

A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry

Principal Geodesic Analysis in the Space of Discrete Shells

A novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements.

Morphometry of anatomical shape complexes with dense deformations and sparse parameters

Statistics of shape via principal geodesic analysis on Lie groups

  • P. FletcherConglin LuS. Joshi
  • Mathematics
    2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings.
  • 2003
This paper shows that medial descriptions are in fact elements of a Lie group, and develops methodology based on Lie groups for the statistical analysis of medially-defined anatomical objects.

An As-Invariant-As-Possible GL+(3) -Based Statistical Shape Model

This work describes a novel nonlinear statistical shape model based on differential coordinates viewed as elements of \(\text {GL}^+(3){}\); it employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences.
...