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
        }
}
  • S. Joshi, M. Miller
  • Published 1 August 2000
  • Mathematics
  • IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
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… 
View on PubMed
bioen.utah.edu
550 Citations
Highly Influential Citations
34
Background Citations
206
Methods Citations
184
Results Citations
4

Figures from this paper

550 Citations

Citation Type

Citation Type

Large Deformation Registration via n-dimensional Quasi-conformal Maps
TLDR
The proposed model is efficient to obtain a diffeomorphic registration between n-dimensional data with large deformations and the time complexity and robustness of the algorithm is independent of the number of landmark constraints.
Diffeomorphic Metric Landmark Mapping Using Stationary Velocity Field Parameterization
TLDR
Compared to non-stationary parameterization, this method can achieve comparable registration accuracy in significantly reduced time, and second order metric approximation by this method improves significantly over first order, which can not be achieved by non- stationary parameterized.
Geometry of diffeomorphism groups and shape matching
The large deformation matching (LDM) framework is a method for registration of images and other data structures, used in computational anatomy. We show how to reformulate the large deformation…
Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps
TLDR
Results show the efficacy of the proposed model to obtain a folding-free landmark-matching transformation between n-dimensional spaces with large deformations.
Large deformation registration · nD quasiconformal · Conformality · Alternating direction method of multipliers · Landmarks 1
We propose a new method to obtain landmark-matching transformations between n-dimensional Euclidean spaces with large deformations. Given a set of feature correspondences, our algorithm searches for…
Teichmüller extremal mapping and its applications to landmark matching registration
TLDR
This paper proposes an efficient iterative algorithm, called the Quasi-conformal (QC) iterations, to compute the Teichm\"uller mapping, which can be accurately and efficiently computed within 10 seconds and is guaranteed to be bijective.
Non-rigid Shape Comparison of Implicitly-Defined Curves
TLDR
A novel variational model to find shape-based correspondences between two sets of level curves that can be used as a basis to compare curves of different topology and was tested on synthetic and MRI cardiac data, with good results.
Landmark Matching via Large Deformation Diffeomorphisms on the Sphere
TLDR
A methodology and algorithm for generating diffeomorphisms of the sphere onto itself, given the displacements of a finite set of template landmarks, has application in brain mapping, where surface data is typically mapped to the sphere as a common coordinate system.
Landmark Matching via Large Deformation Diffeomorphisms on the Sphere
This paper presents a methodology and algorithm for generating diffeomorphisms of the sphere onto itself, given the displacements of a finite set of template landmarks. Deformation maps are…
Invariant surface alignment in the presence of affine and some nonlinear transformations
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 44 REFERENCES
Large Deformation Fluid Diffeomorphisms for Landmark and Image Matching
Deformable templates using large deformation kinematics
TLDR
Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.
Computable Elastic Distances Between Shapes
  • L. Younes
  • Computer Science
    SIAM J. Appl. Math.
  • 1998
TLDR
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
TLDR
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
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
TLDR
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.
An introduction to differentiable manifolds and Riemannian geometry
Statistical methods in computational anatomy
TLDR
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
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.
TLDR
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.
...
1
2
3
4
5
...