The individual bars were segmented automatically by differentiation to find the transition regions, and then robust statistics used to determine an estimate of for each of the 11 steps, as well as the black regions of the test pattern. Using the known reflectivity of each of these 12 regions, a set of 12 ordered pairs was determined for each of the 19 exposures, as shown in Fig 7(b). Shifting these results appropriately (by the values, to line them up, gives the ground-truth, known response function, , shown in Fig 7(c).