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There is a class of nonlinear filtering algorithms for digital colour enhancement, characterised by data-driven local effects and high computational cost. A new method called LLL (local linear look-up table (LUT)) is presented, which speeds up these filters without losing their local effect. Usually, classic LUT-based methods are global whereas the approach presented here uses the principles of LUT transformation in a local way. The main idea of this method is to apply the colour-enhancement algorithm to a small sub-sampled version of the input image and to use a modified look-up table technique to maintain the local filtering effect of the colour-enhancement algorithm. The method increases the speed of colour-filtering algorithms, reducing the number of pixels involved in the computation by sub-sampling the input image. To overcome possible loss of detail due to sub-sampling, an optional, additional stage to maintain high-frequency content is shown. LLL with two of these filters, the Brownian Retinex implementation and the automatic colour equalisation algorithm, are tested. Results, comparison and conclusions are presented.