# Landmark matching via large deformation diffeomorphisms

@article{Joshi2000LandmarkMV, title={Landmark matching via large deformation diffeomorphisms}, author={Sarang C. Joshi and Michael I. Miller}, journal={IEEE transactions on image processing : a publication of the IEEE Signal Processing Society}, year={2000}, volume={9 8}, pages={ 1357-70 } }

This paper describes the generation of large deformation diffeomorphisms phi:Omega=[0,1]3<-->Omega for landmark matching generated as solutions to the transport equation dphi(x,t)/dt=nu(phi(x,t),t),epsilon[0,1] and phi(x,0)=x, with the image map defined as phi(.,1) and therefore controlled via the velocity field nu(.,t),epsilon[0,1]. Imagery are assumed characterized via sets of landmarks {xn, yn, n=1, 2, ..., N}. The optimal diffeomorphic match is constructed to minimize a running smoothness…

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## References

SHOWING 1-10 OF 44 REFERENCES

Deformable templates using large deformation kinematics

- EngineeringIEEE Trans. Image Process.
- 1996

Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.

Computable Elastic Distances Between Shapes

- Computer ScienceSIAM J. Appl. Math.
- 1998

An elastic matching algorithm which is based on a true distance between intrinsic properties of the shapes, taking into account possible invariance to scaling or Euclidean transformations in the case they are required.

Volumetric transformation of brain anatomy

- BiologyIEEE Transactions on Medical Imaging
- 1997

It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.

Computational anatomy: an emerging discipline

- Mathematics
- 1998

This paper studies mathematical methods in the emerging new discipline of Computational Anatomy. Herein we formalize the Brown/Washington University model of anatomy following the global pattern…

Curve matching on brain surfaces using frenet distances

- MathematicsHuman brain mapping
- 1998

This paper describes methods for diffeomorphic matching of curves on brain surfaces and defines fundus curves on the brain surfaces as extremal curvature lines generated using dynamic programming.

Statistical methods in computational anatomy

- MathematicsStatistical methods in medical research
- 1997

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy and presents methods for estimating covariances of vector fields from a family of empirically generated maps.

Hierarchical brain mapping via a generalized Dirichlet solution for mapping brain manifolds

- MathematicsOptics & Photonics
- 1995

In this paper we present a coarse-to-fine approach for the transformation of digital anatomical textbooks from the ideal to the individual that unifies the work on landmark deformations and volume…

The Measurement of Biological Shape and Shape Change.

- Mathematics
- 1978

This chapter discusses the study of Shape Transformation after D'Arcy Thompson, which involves two types of transformations: functional craniology and craniometrics and multivariate morphometrics.