Elastic image registration using linear basis functions for non-continuously deforming objects

In the current study we propose an elastic image registration algorithm for a non-continuous motion field and spatially varying properties of the domain. The approach is based on using linear basis functions that inherently have non-continuous derivatives and allow geometric separation of an object from its background. We use the elastic regularization term commonly used in finite element analysis and combine it with the recent state-of-the-art image registration optimization method. We validated our algorithm´s concept using simulation of a non-continuous motion field obtained by hand articulations and tested the effect of the object´s background on the algorithm´s convergence. We show that for non-continuously deforming objects the proposed algorithm outperforms commonly used registration algorithms that work on a regular grid of control points.