A Sharp Sufficient Condition for B-Spline Vector Field Invertibility. Application to Diffeomorphic Registration and Interslice Interpolation
Michaël Sdika · SIAM Journal on Imaging Sciences · 2013
In this paper, a new sufficient condition for the invertibility of a B-spline vector field as well as its extension to spatio-temporal vector fields are presented. The new condition, while guaranteeing that the vector field is diffeomorphic, is sharp enough to allow large deformations. The complexity of the constraint is also discussed. A new diffeomorphic registration algorithm using this condition and its application to interslice interpolation are presented and evaluated on synthetic images and in vivo magnetic resonance $T_2$ images of the brain. The registration method has also been compared to some state-of-the-art registration methods.