To enable a good HDR image or video coding technology, being able to yield high dynamic range images as well as low dynamic range images, we invented a method of encoding a high dynamic range image (M_HDR), comprising the steps of: converting the high dynamic range image to an image of lower luminance dynamic range (LDR_o) by applying a) scaling the high dynamic range image to a predetermined scale of the luma axis such as [0,1], b) applying a sensitivity tone mapping which changes the brightnesses of pixel colors falling within at least a subrange comprising the darker colors in the high dynamic range image, c) applying a gamma function, and d) applying an arbitrary monotonically increasing function mapping the lumas resulting from performing the steps b and c to output lumas of the lower dynamic range image (LDR_o); and outputting in an image signal (S_im) a codification of the pixel colors of the lower luminance dynamic range image (LDR_o), and outputting in the image signal (S_im) values encoding the functional behavior of the above color conversions as metadata, or values for the inverse functions, which metadata allows to reconstruct a high dynamic range image (Rec_HDR) from the lower luminance dynamic range image (LDR_o).