Interpolating between images using optimal mass transport

Sammanfattning: Optimal mass transport (OMT) is an optimization problem that obtains the way to move mass, or values, from one function to another, in the most efficient way, or at the lowest cost. This technique is used in various fields, e.g. computer vision, machine learning and economics. Transforming an image to a matrix containing values corresponding to the images gray scale, enables OMT so that it can be used in the transformation between two images. For images normal by today’s standard the problems becomes too large to be pratically solvable. This paper presents a method using Monge-Kantorovich theory to formulate the problem, then further studies the Sinkhorn-Knopp algorithm to make it solvable for larger scale images. Using only Monge-Kantorovich theory to solve the problem leads to n^2 variables, where n is the number of pixels in the images transformed, implementing the Sinkhorn-Knopp algorithm decreases the number of variables to 2n.