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Comunicació presentada a: 6th Pacific-Rim Symposium on Image and Video Technology, celebrat del 28 d'octubre a 1 de novembre de 2013 a Guanajuato, Mèxic. Given any metric that compares images of di erent dynamic range, we propose a method to reduce their distance with respect to this metric. The key idea is to consider the metric as a non local operator. Then, we transform the problem of distance reduction into a non local variational problem. In this context, the low dynamic range image having the smallest distance with a given high dynamic range is the minimum of a suitable energy, and can be reached through a gradient descent algorithm. Dealing with an appropriate metric, we present an application to Tone Mapping Operator (TMO) optimization. We apply our gradient descent algorithm, where the initial conditions are Tone Mapped (TM) images. Experiments show that our algorithm does reduce the distance of the TM images with the high dynamic range source images, meaning that our method improves the corresponding TMOs. This work was supported by the European Research Council, Starting Grant ref. 306337, and by Spanish grants ref. TIN2011-15954-E and ref. TIN2012-38112.