Log-Euclidean free-form deformation

Marc Modat; Gerard R. Ridgway; Pankaj Daga; M. Jorge Cardoso; David J. Hawkes; John Ashburner; Sébastien Ourselin

doi:10.1117/12.878189

11 March 2011 Log-Euclidean free-form deformation

Marc Modat, Gerard R. Ridgway, Pankaj Daga, M. Jorge Cardoso, David J. Hawkes, John Ashburner, Sébastien Ourselin

Proceedings Volume 7962, Medical Imaging 2011: Image Processing; 79621Q (2011) https://doi.org/10.1117/12.878189
Event: SPIE Medical Imaging, 2011, Lake Buena Vista (Orlando), Florida, United States

Abstract

The Free-Form Deformation (FFD) algorithm is a widely used method for non-rigid registration. Modifications have previously been proposed to ensure topology preservation and invertibility within this framework. However, in practice, none of these yield the inverse transformation itself, and one loses the parsimonious B-spline parametrisation. We present a novel log-Euclidean FFD approach in which a spline model of a stationary velocity field is exponentiated to yield a diffeomorphism, using an efficient scaling-and-squaring algorithm. The log-Euclidean framework allows easy computation of a consistent inverse transformation, and offers advantages in group-wise atlas building and statistical analysis. We optimise the Normalised Mutual Information plus a regularisation term based on the Jacobian determinant of the transformation, and we present a novel analytical gradient of the latter. The proposed method has been assessed against a fast FFD implementation (F3D) using simulated T1- and T2-weighted magnetic resonance brain images. The overlap measures between propagated grey matter tissue probability maps used in the simulations show similar results for both approaches; however, our new method obtains more reasonable Jacobian values, and yields inverse transformations.

Citation Download Citation

Marc Modat, Gerard R. Ridgway, Pankaj Daga, M. Jorge Cardoso, David J. Hawkes, John Ashburner, and Sébastien Ourselin "Log-Euclidean free-form deformation", Proc. SPIE 7962, Medical Imaging 2011: Image Processing, 79621Q (11 March 2011); https://doi.org/10.1117/12.878189

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