Fractals everywhere
Fractal image compression
Linear network optimization: algorithms and codes
Linear network optimization: algorithms and codes
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
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Computing the Kantorovich distance for images is equivalent to solving a very large transportation problem. The cost-function of this transportation problem depends on which distance-function one uses to measure distances between pixels.In this paper we present an algorithm, with a computational complexity of roughly order {\cal O}(N2), where N is equal to the number of pixels in the two images, in case the underlying distance-function isthe L1-metric, an approximation of the L2-metric or the square of the L2-metric; a standard algorithm would have a computational complexity of order {\cal O}(N3). The algorithm is based on the classical primal-dual algorithm.The algorithm also gives rise to a transportation plan from one image to the other and we also show how this transportation plan can be used for interpolation and possibly also for compression and discrimination.