Optimal mass transport for deformable registration and warping of 2D images

We implement a warping method which is using the properties of elastic materials to compute the deformation between two images. The proposed elastic registration method incorporates the L2 Kantorovich-Wasserstein distance, also known as the Earth Mover’s Distance (EMD), as a similarity measure. The implemented paper presents an efficient partial differential equation approach for a first-order solution of this problem that is simpler than existing works suggested high-order solutions and is computationally simpler than existing works based on linear programming. Specifically, we implement the following paper Steven Haker, Lei Zhu, Allen Tannenbaum, and Sigurd Angenent, “Optimal mass transport for registration and warping”, International Journal of Computer Vision, 60(3), p. 225-240, 2004.