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High Dynamic Range (HDR) images can represent the acquired scene with a greater dynamic range of luminance than classical Low Dynamic Range (LDR) ones. Despite the recent diffusion of some HDR camera models, HDR displays are not yet in the market. For this reason HDR images need to be adapted in order to be properly rendered through conventional devices. This operation mainly consists in a dynamic range compression realized by applying a Tone Mapping Operator (TMO). In this work, a new tone map algorithm, derived from the Contrast Limited Adaptive Histogram Equalization (CLAHE) technique, is presented. With respect to the original CLAHE, in the proposed implementation an adaptive contrast limit and a new strategy for the determination of local tone mapping functions have been introduced. The comparison between the obtained LDR images, and those produced by applying State of the Art TMOs, evidences how the main characteristic of the proposed algorithm is the ability to equally enhance visibility in both dark and bright areas. This could be, for example, a key feature in video surveillance applications and automotive safety camera systems.