A Combination of the Total Variation Filter and a Fourth-Order Filter for Image Registration

Algorithm 1

The proposed algorithm.

(1) Set up pyramids , , and their derivatives at each layer.

(2) (a) If at the coarsest layer, initialize: .

   (a′) If not (a), upsample and from the previous layer to the current layer.

   Warp using bilinear interpolation.

   For

      (see (17))

     (see (22))

      (see (25))

   end, go to the finer layer.

   end of the finest layer.