Groupwise Elastic Registration Method

Groupwise Registration method for 2D motion estimation over MR-CINE sequences.

The local transformation is represented as a combination of B-spline Free Form Deformations (FFD). The intensities of the deformed images are obtained by linear interpolation.

A gradient-descent optimization scheme is performed; the step size is updated according to the variation of the registration metric. Implemented metric consist in the sum of squared differences of image intensities, known as variance of intensities. Spatio-temporal regularization is added as a penalty term for artifact correction from the first and second derivatives of the transformation matrix.

B-spline parameters (B-spline order and control points density), as well as the weights of the spatio-temporal regularization (if needed) are set empirically. 

Matlab implementation for segmentation propagation along cardiac cycle is provided: