In this paper we present a computationally efficient Optimal Mass Transport algorithm. This method is based on the
Monge-Kantorovich theory and is used for computing elastic registration and warping maps in image registration and
morphing applications. This is a parameter free method which utilizes all of the grayscale data in an image pair in a
symmetric fashion. No landmarks need to be specified for correspondence. In our work, we demonstrate significant
improvement in computation time when our algorithm is applied as compared to the originally proposed method by
Haker et al [1]. The original algorithm was based on a gradient descent method for removing the curl from an initial
mass preserving map regarded as 2D vector field. This involves inverting the Laplacian in each iteration which is now
computed using full multigrid technique resulting in an improvement in computational time by a factor of two. Greater
improvement is achieved by decimating the curl in a multi-resolutional framework. The algorithm was applied to 2D
short axis cardiac MRI images and brain MRI images for testing and comparison.
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