1. A method for color grading input video data for display on a target display, the method comprising: obtaining target display metadata indicative of a capability of the target display; obtaining input video data metadata indicative of image characteristics of the input video data; automatically determining initial values for parameters of a parameterized transfer function, at least one of the initial values based at least in part on at least one of the target display metadata and the input video data metadata; and, mapping the input video data to color-graded video data according to the parameterized transfer function specified using the initial values, wherein the parameterized transfer function comprises a mid-range region, the mid-range region being linear in log-log space or approaching linearity in log-log space.