We obtained (apparently) linear responses to luminance from three special displays of apparent motion, Vernier offset and stereoscopic depth. In our motion stimulus a dark and a light bar exchanged luminances repetitively on a grey surround. Motion was attributed to the bar that differed more from the surround, that is, on a dark surround the light bar appeared to jump, and on a light surround the dark bar appeared to jump. The apparent motion disappeared when the luminance of the surround lay halfway between that of the bars--on a linear, not a logarithmic scale. Similar results were obtained for special Vernier offset and stereo stimuli. These results cannot be explained if all luminances are processed within the same luminance pathway and that pathway transforms input luminance using non-linear compression. However, the apparent linearity of our results could arise from opposite and equal non-linearities cancelling out within separate ON- and OFF-spatial luminance pathways. A second set of experiments presented one bar separately into each eye on different surrounds (dichoptic presentation of competing apparent motion signals) or manipulated the display spatially so that different surrounds were associated with different bars (binocular presentation of competing Vernier targets). Results showed that apparent motion and Vernier signals of equal Weber contrast (normalisation of linear difference to surround luminance) evoked equal-motion and equal Vernier offset strengths. Given that motion and Vernier strength followed Weber's law, we infer that the ON- and OFF-pathways transform luminance non-linearly. Our third experiment presents an example of a brightness bisection task in which we were able to influence the bisection steps, to follow either a linear or non-linear series. The benefits of parsing the visual scene so that visual information is processed within two opposite luminance pathways is discussed.