The Monge-Ampere equation: various forms and numerical methods

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.Comment: 24 pages, 2 tables, 5 figures, 32 references. Submitted to J. Computational Physics. Times of runs added, multiple improvements of the manuscript implemented

Analyse et recherche d'oeuvres d'art 2D selon le contenu pictural

État de l'art des méthodes manuelles et automatiques d'analyse des oeuvres d'art 2D -- Recherche d'images selon l'organisation spatiale des couleurs -- Seuil automatique pour la recherche d'images selon l'OSC -- Extraction des contours des traits -- Analyse de l'impact pictural dans les oeuvres au trait -- Conclusion et perspectives

Adaptive image retrieval based on the spatial organization of colors

International audienceThis work proposes to compare the spatial organization of colors between images through a global optimization procedure relying on the Earth Mover's Distance. The resulting distance is applied to image retrieval. Unlike most region-based retrieval systems, no segmentation of images is needed for the query. We then address the decision stage of the retrieval, that is the problem of automatically deciding which images from a database match a query. To this aim, we make use of an a contrario method. Two images are matched if their proximity is unlikely to be due to chance; more precisely, a matching threshold on distances is computed by controlling the average number of false matchings in an unsupervised way. This threshold is adaptive, yielding different numbers of result images depending on the query and the database