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We address the problem of re-rendering images to high dynamic range (HDR) displays, which were originally tone-mapped to standard displays. As these new HDR displays have a much larger dynamic range than standard displays, an image rendered to standard monitors is likely to look too bright when displayed on a HDR monitor. Moreover, because of the operations performed during capture and rendering to standard displays, the specular highlights are likely to have been clipped or compressed, which causes a loss of realism. We propose a tone scale function to re-render images first tone-mapped to standard displays, that focuses on the representation of specular highlights. The shape of the tone scale function depends on the segmentation of the input image into its diffuse and specular components. In this article, we describe a method to perform this segmentation automatically. Our method detects specular highlights by using two low-pass filters of different sizes combined with morphological operators. The results show that our method successfully detects small and middle sized specular highlights. The locations of specular highlights define a mask used for the construction of the tone scale function. We then propose two ways of applying the tone scale, the global version that applies the same curve to each pixel in the image and the local version that uses spatial information given by the mask to apply the tone scale differently to diffuse and to specular pixels.