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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Splines for diffeomorphisms.

Nikhil Singh1, François-Xavier Vialard2, Marc Niethammer1

  • 1The University of North Carolina, Chapel Hill, NC 27514, USA.

Medical Image Analysis
|May 19, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces higher-order parametric regression for diffeomorphisms, enabling more complex image deformation analysis than traditional geodesic methods. The new approach captures intricate spatio-temporal changes using splines on the diffeomorphism manifold.

Keywords:
DiffeomorphismsImage regressionLDDMMPolynomialsSplinesTime series

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Area of Science:

  • Computational anatomy
  • Medical image analysis
  • Differential geometry

Background:

  • Computational anatomy utilizes the large deformation diffeomorphic image analysis framework.
  • Geodesic-based methods have been standard for analyzing image changes over time.
  • Existing methods struggle to capture complex spatio-temporal deformations.

Purpose of the Study:

  • To develop a higher-order parametric regression method for diffeomorphisms.
  • To enable the modeling of image changes with non-zero acceleration and jerk.
  • To extend existing geodesic regression techniques for enhanced image analysis.

Main Methods:

  • A variational approach is employed, governed by an energy formulation on the manifold of diffeomorphisms.
  • The method defines quadratic, cubic, and piecewise cubic splines on the diffeomorphism manifold.
  • A shooting formulation is developed to manage temporal control points and spline behavior.

Main Results:

  • The proposed method effectively models complex spatio-temporal deformations in images.
  • Experimental results demonstrate the synthesis of polynomial paths and regression of imaging data.
  • The performance is quantitatively compared against standard geodesic regression.

Conclusions:

  • Higher-order parametric regression on diffeomorphisms offers a more powerful tool for analyzing complex image dynamics.
  • The variational spline formulation provides a physically analogous approach to particle motion.
  • This work advances the field of computational anatomy by enabling richer modeling of image transformations.