Iterative solution methods
Mass Preserving Mappings and Image Registration
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
Journal of Computational Physics
Adaptive image retrieval based on the spatial organization of colors
Computer Vision and Image Understanding
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
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We present three novel forms of the Monge-Ampere equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The central role in this paper is played by our Fourier integral form, for which we establish positivity and sharp bound properties of the kernels. This is the basis for the development of a new method for solving numerically the space-periodic Monge-Ampere problem in an odd-dimensional space. Convergence is illustrated for a test problem of cosmological type, in which a Gaussian distribution of matter is assumed in each localised object, and the right-hand side of the Monge-Ampere equation is a sum of such distributions.