Stepwise inverse consistent Euler’s scheme for diffeomorphic image registration

TY - GEN

T1 - Stepwise inverse consistent Euler’s scheme for diffeomorphic image registration

AU - Pai, Akshay Sadananda Uppinakudru

AU - Sommer, Stefan Horst

AU - Darkner, Sune

AU - Sørensen, Lauge

AU - Sporring, Jon

AU - Nielsen, Mads

N1 - Conference code: 6

PY - 2014

Y1 - 2014

N2 - Theoretically, inverse consistency in an image registration problem can be achieved by employing a diffeomorphic scheme that uses transformations parametrized by stationary velocity fields (SVF). The displacement from a given SVF, formulated as a series of self compositions of a transformation function, can be obtained by Euler integration in the time domain. However in practice, the discrete time integration produces results that are inverse inconsistent, and inverse consistency in the final solution needs to be explicitly ensured. One way of achieving this is to penalize the endpoint displacement offset obtained by evaluating a composition of the transformation with its inverse at an arbitrary point. In this paper, we propose a variation in which the displacement penalization is required only in the first composition step of the transformation thereby bringing down the computational complexity. We compare these two ways of enforcing inverse consistency by applying the registration framework on four pairs of brain magnetic resonance images. We observe that the proposed stepwise scheme maintains both precision and level of inverse consistency similar to the endpoint scheme.

AB - Theoretically, inverse consistency in an image registration problem can be achieved by employing a diffeomorphic scheme that uses transformations parametrized by stationary velocity fields (SVF). The displacement from a given SVF, formulated as a series of self compositions of a transformation function, can be obtained by Euler integration in the time domain. However in practice, the discrete time integration produces results that are inverse inconsistent, and inverse consistency in the final solution needs to be explicitly ensured. One way of achieving this is to penalize the endpoint displacement offset obtained by evaluating a composition of the transformation with its inverse at an arbitrary point. In this paper, we propose a variation in which the displacement penalization is required only in the first composition step of the transformation thereby bringing down the computational complexity. We compare these two ways of enforcing inverse consistency by applying the registration framework on four pairs of brain magnetic resonance images. We observe that the proposed stepwise scheme maintains both precision and level of inverse consistency similar to the endpoint scheme.

U2 - 10.1007/978-3-319-08554-8_23

DO - 10.1007/978-3-319-08554-8_23

M3 - Article in proceedings

SN - 978-3-319-08553-1

T3 - Lecture notes in computer science

SP - 223

EP - 230

BT - Biomedical Image Registration

A2 - Ourselin, Sébastien

A2 - Modat, Marc

PB - Springer

T2 - 6th International Workshop on Biomedical Image Registration

Y2 - 7 July 2014 through 8 July 2014

ER -