1. A method of image processing comprising correcting, by processing circuitry, an image on an area-by-area basis to generate an output image intensity (Oij) of an area which is different to an input image intensity (Iij) of the area, the output image intensity (Oij) of an area being related to the input image intensity (Iij) of the area by: 
 Oij =amplification coefficient× Iij , wherein the method comprises: generating, by the processing circuitry and using a non-linear image transform, an amplification coefficient of a given area using the input image intensity (Iij); varying, by the processing circuitry, the amplification coefficient of the given area based on a substantially minimum amplification coefficient of a set of neighbouring areas, the set comprising the given area; and generating, by the processing circuitry, an output image intensity (Oij) of the given area using the varied amplification coefficient, in order that, in at least part of the image, the local contrast of the input image is at least partially preserved in the output image.