Image encoding and decoding are described. An input HDR image is coded using a coded tone-mapped image, a coded invertible function of a ratio image, and a look-up table representing the inverse of the invertible function, wherein the ratio image represents the pixel by pixel ratio of the luminance pixel values of the input image and the corresponding luminance values in the tone-mapped image. A method to generate the invertible function based on a cumulative histogram of the ratio image is presented.