To enable better color and in particular color saturation control for HDR image handling systems which need to do luminance dynamic range conversion, e.g. from a SDR image to an image optimized for rendering on a display of higher display peak brightness and dynamic range, the inventors invented an apparatus (400) for processing a color saturation (C′bL, C′rL) of an input color (Y′L, C′bL, C′rL) of an input image (Im_RLDR) to yield an output color (Y′M, Cb′M, Cr′M) of an output image (Im3000nit) corresponding to the input image, which output image is a re-grading of the input image characterized by the fact that its pixel colors have a different normalized luminance position (Y2) compared to the normalized luminance positions of the input colors (Y1), the normalized luminances being defined as the luminance of a pixel divided by the respective maximal codeable luminance of the image's luminance representation, whereby the ratio of the maximum codeable luminance of the input image and the maximum codeable luminance of the output image is at least 4 or larger, or ¼th or smaller, the apparatus comprising: a receiver (206) arranged to receive a luminance mapping function (F_L_s2h) defining a mapping between the luminance of the input color (Y′L) and a reference luminance (L′_HDR), and an initial saturation processing function (F_sat) defining saturation boost values (b) for different values of the luminance of the input color (Y′L); a display tuning unit (1009) arranged to calculate a display tuned luminance mapping function (F_L_da) based on the luminance mapping function (F_L_s2h) and at least one of a display peak brightness (PB_D) and a minimum discernable black (MB_D); a luminance processor (401) arranged to apply the display tuned luminance mapping function (F_L_da) to determine an output luminance (Y′M) from the input luminance (Y′L) of the input color; and a saturation processing unit (410, 411), arranged to map the input color saturation (C′bL, C′rL) to the color saturation (Cb′M, Cr′M) of the output color on the basis of a saturation processing strategy which specifies saturation multipliers for the normalized luminance values (Y_norm); characterized in that the apparatus further comprises a saturation factor determination unit (402) arranged to calculate a final saturation processing strategy (b; Bcorr) based on the initial saturation processing strategy (F_sat) and based on a secondary luminance value (Y′_H) which is derivable from the output luminance (Y′M) by applying a luminance mapping function (F_M2H) based on the luminance mapping function (F_L_s2h), and wherein the saturation processing unit is arranged to calculate the color saturation (Cb′M, Cr′M) of the output color by applying the final saturation processing strategy (b; Bcorr).