One potential improvement to the importance filtering algorithm is to extend the one-dimensional shift gradients to 2D. Even though the pixels all shift along the same dimension, the shift-map on the 2D image has a 2D gradient field. We are developing methods to estimate such 2D shift gradients and then optimize their integration to construct the shift-map by methods such as alternative 1D filtering or Poisson blending. We believe this will further improve the 2D smoothness and consistency of the resized image.